Chapter 1.INTRODUCTION NC RFQ rms RRR SC SR SRF SW, TW UHV 1.1 HOW TO USE THIS BOOK This is an accelerator designer’s and operator’s handbook of formulae, tables, figures and references. It is meant to be a concise working tool. An effort has been made to provide an index which is as complete as possible. Each subsection (e.g. 2.3.4) is treated as a unit which is more or less self-contained. Numbering of all figures and tables are reset at each subsection, and references are found following each subsection. References are not meant to be exhaustive but represent the experts’ recommendation about a reliable place to begin. While the linear and circular accelerators for high energy physics and synchrotron radiation applications are our primary concern, we have tried to provide connections to other types of accelerators in the glossary section 1.6. Abbreviations of references APAC APL EPAC IJMP IPAC JAP JETP JINST JVST NIM NJP PA PAC PL PR PRL PRST-AB 1.2 NOMENCLATURE Boldface symbol means matrix quantity. At is ˜ means Fourier the transpose of A. A tilde, A, is a vector. a transform. A ˆ is a unit vector. √ For complex numbers, we use i = −1, and a sinusoidal time dependence is described by e−iωt unless otherwise noted. Abbreviations ac, dc BBU BPM CM c.w. EM FEL FWHM HOM IR, UV IP, IR LHe l.h.s., r.h.s. n-D rf normal conducting rf quadrupole root mean square residual resistivity ratio superconducting synchrotron radiation superconducting rf standing wave, traveling wave ultrahigh vacuum RAST RMP RSI Asian PAC Applied Physics Letters European PAC International Journal of Modern Physics International PAC Journal of Applied Physics Journal of Experimental and Theoretical Physics Journal of Instrumentation Journal of Vacuum Science and Technology Nuclear Instruments & Methods New Journal of Physics Particle Accelerators Particle Accelerator Conference Physics Letters Physical Review Physical Review Letters Physical Review Special Topics – Accelerators & Beams Reviews of Accelerator Science & Technology Reviews of Modern Physics Review of Scientific Instruments Tabulated below are symbols adopted throughout this Handbook unless otherwise noted. More symbols are defined in the table of fundamental constants in Sec.1.3. and locally in the text. alternating current, direct current beam break-up (instability) beam position monitor center of mass continuous wave electromagnetic free electron laser full-width at half-maximum higher order mode infrared, ultraviolet interaction point, region liquid helium left-hand side, right-hand side n-dimension(al) radio frequency Symbol αp αT αx,y B B (Bρ) β, β 1 Quantity momentum compaction factor thermal expansion coefficient horizontal (x), vertical (y) CourantSnyder alpha functions brightness magnetic induction = P/e, rigidity of a particle of charge e (Bρ) [T-m] = 3.335641 P0 [GeV/c] = (v, v )/c, (speed, velocity) relative to light Sec.1.2: NOMENCLATURE βx,y C c v , cp D δ Dx,y Dx,y detA E E E0 E0 E x,y,L N x,N y η f0 γ γx,y γt H H h H H(x) I0 Ib Jx,y,s J k κ L λ μ μ N NB nB νx,y,s νsp ω ω0 ωx,y,s horizontal (x), vertical (y) Courant-Snyder beta functions circumference specific heat displacement current = ΔP/P0 , relative momentum error horizontal (x), vertical (y) dispersion functions beam-beam disruption parameters determinant of matrix A Young’s modulus particle total energy design particle energy = mc2 rest mass energy electric field horizontal (x), vertical (y), longitudinal (L) emittances (unnormalized) = βγx,y , normalized emittances = αp − (1/γ 2 ), phase slip factor revolution frequency = 1/ 1 − β 2 , relativistic factor horizontal (x), vertical (y) Courant-Snyder gamma functions transition gamma Hamiltonian synchrotron integral H-function rf harmonic number magnetic field step function, = 1 if x > 0, = 0 if x < 0 = NB ef0 , average bunch current peak bunch current horizontal (x), vertical (y), synchrotron (s) partition numbers current density = 2π/λ, wave number thermal conductivity luminosity wavelength Poisson’s ratio betatron phase advance per turn or period total no. of particles in beam number of particles per bunch in a bunched beam number of bunches in beam horizontal betatron (x), vertical betatron (y), synchrotron (s) tune spin tune = 2πf , angular frequency = 2πf0 , angular revolution freq. = νx,y,s ω0 , betatron (x, y), synchrotron (s) angular freq. Ω P,P ,p, p P0 , p0 P Q q R ρ ρ ρr s σ σc σx,y,z σx ,y σE,δ sgn(x) t T T trA T0 U0 Υ v, v vg vp Vrf Wm , W⊥m ⊥ (or Wm ,Wm ) x x X0 ξx,y y y ψ ψx,y z Zm , Z⊥m ⊥ (or Zm ,Zm ) 2 solid angle particle momentum design particle momentum power quality factor of oscillator charge on a particle = C/(2π), average radius bending radius volume density resistivity longitudinal coordinate along an accelerator interaction cross-section = 1/ρr , conductivity horiz. (x), vert. (y), long. (z) rms beam size horiz. (x ), vert. (y ) rms angular spread energy (E), relative momentum (δ) rms spread sign function, = 1 if x > 0, = −1 if x < 0 time temperature kinetic energy trace of matrix A revolution period synchrotron radiation loss per revolution beamstrahlung parameter speed, velocity group velocity phase velocity rf voltage longitudinal, transverse wake function of mode m (W if m = 0, W⊥ if m = 1) horiz. displacement = dx/ds, horiz. angular deviation of a particle radiation length = (dνx,y /dδ), horizontal (x), vertical (y) chromaticity vert. displacement = dy/ds, vert. angular deviation of a particle distribution density in phase space, normalized to unity horiz. (x), vert. (y) betatron phase long. displacement of a particle relative to synchronous particle (z > 0 ahead, z < 0 behind) longitudinal, transverse impedance of mode m (Z if m = 0, Z⊥ if m = 1) Ch.1: INTRODUCTION 1.3 FUNDAMENTAL CONSTANTS [1] Quantity pi exponential constant Euler’s constant speed of light permeability of vacuum permittivity of vacuum electronic charge Planck constant reduced Planck constant Boltzmann constant Avogadro number gravitational constant std. grav. accel. electron mass proton mass rest mass energy of electron proton neutron deuteron muon Z-particle W -particle anomalous gyromagnetic ratio electron muon proton deuteron fine structure constant Symbol π e γ c μ0 0 = 1/(μ0 c2 ) e h = h/(2π) kB NA G g me mp Value 3.141592653589793238 2.718281828459045235 0.5772156649 2.99792458 E8 m s−1 (exact) 4π E-7 Henry m−1 (exact) 8.854187817 E-12 Farad m−1 1.6021765 E-19 C = 4.8032043 E-10 esu 6.626069 E-34 J s 1.054572 E-34 J s = 6.582119 E-16 eV s 1.380650 E-23 J K−1 6.022142 E23 mole−1 6.67428 E-11 Newton m2 kg−2 9.80665 m s−2 9.1093822 E-31 kg 1.6726216 E-27 kg me c2 mp c2 mn c2 md c2 mμ c2 mZ c2 mW c2 G = (g − 2)/2 0.51099891 MeV 938.27201 MeV 939.5653 MeV 1875.6128 MeV 105.65837 MeV 91.188 GeV 80.399 GeV 0.00115965219 0.001165923 1.79284739 -0.1429878 αF = e2 /(4π0 c) Z0 = μ0 /0 = μ0 c impedance of free space classical radius of electron re = e2 /(4π0 me c2 ) proton rp = e2 /(4π0 mp c2 ) electron Compton wavelength λe = h/(me c) ¯λe = λe /(2π) Alfv´en current IA = ec/re Bohr radius a∞ = 4π0 2 /(me e2 ) Thomson cross section σT = (8π/3)re2 Bohr magneton μB = e/(2me c) nuclear magneton μN = e/(2mp c) 4 /(3 c2 ) Stefan-Boltzmann constant σSB = (π 2 /60)kB gas constant R = NA kB 1/137.0359997 376.7303 Ω 2.8179403 E-15 m 1.534698 E-18 m 2.4263106 E-12 m 0.3861593 E-12 m 17.045093 kA 5.29177209 E-11 m 6.65246 E-29 m2 5.7883818 E-5 eV/Tesla 3.1524512 E-8 eV/Tesla 5.67040 E-8 W m−2 K−4 8.3145 J K−1 mole−1 References [1] K. Nakamura et al. (Particle Data Group), J. Phys. G37, 075021 (2010) 3 0. kilogram.5888E6 sq. Jackson.685E6 4π0 Φ 4π A √ μ0 4π0 V √ 4π0 E 4π D 0 4π μ B √ 0 4πμ0 H σc 4π0 /0 μ μ0 4π0 R 4π0 L C 4π0 Table below gives some numerical conversions between Gaussian and SI units. m3 . atm 1. etc. yr. kg. m. Quantity Gaussian SI speed of light charge charge density current c q ρ I J √1 μ0 0 √q 4π0 √ρ 4π0 √I 4π0 √J √4π0 current density scalar potential vector potential voltage electric field Φ A V E displacement D magnetic induction magnetic field conductivity dielectric constant permeability resistance inductance B H σc μ R L capacitance C Quantity in SI = Quantity to be converted × conversion factor. ft lb 1. F .356 horsepower hour 2. s. cu.. [ML/T2 ] dyne 1. Joule.4516E-4 sq. in. meter.4470 Force. [L] inch. [L/T] foot/sec.946E16 Area. ρ. Abbr. Length. foot. 3.4.639E-5 cu. in3 gallon. Newton. References [1] J. E2 = 100.Sec.1 dyne/cm2 6.54E-2 foot.] Quantity to be converted. ha 1E4 2. [L2 ] 6.1 1. m2 . meter/sec. mile. lb/in3 Time.59 Density.9876E11 cm 1. mmHg @ 0◦ C Energy. (liquid) 3.0E5 0.. gal. [M/T2 L] atmosphere.4: UNITS AND CONVERSIONS 1. Tigner.9876E9 s−1 =1 mho/m Resistance Capacitance Inductance 1. ft2 acre 4. dBc (reference to the carrier power). MKSA) units throughout this Handbook unless otherwise noted. or 20 log10 (V1 /V2 ) Other notations: dBm (reference point 1 milliwatt). sq. then dB = 10 log10 (P1 /P2 ). N. mi/hr 0. [T] year. Pa. dBa is used in acoustics in reference to a standard sound pressure of 2E-4 microbar. Cornell U. Pascal. conversion factor We use the SI (Syst`eme International.0E-7 foot-pound. in2 9.3048 mile/hour.448 Pressure. meter.1..1127E-12 =1 ohm =1 farad =1 henry Conversions M. Chao. ft/s 0. Classical Electrodynamics. N/m2 .156E7 Speed. Table below gives the conversion of various physical quantities from Gaussian to SI unit systems [1]. [M] slug 14. mi2 barn. [ML2 /T2 ] BTU 1055 erg 1. ft. W .3332E2 Torr. second.3048 ˚ angstr¨om.2 Units A. bn 1E-28 Volume. .4 UNITS AND CONVERSIONS 1. fm 1. M .768E4 pound/cu in.491E2 in.0E-5 pound. [dim. kg/m3 .4 2. SLAC key: Quantity.1127E-12 s/cm 8.0E-10 fermi. t. psi 2.D.W. symbol. name in SI.4.895E3 pound/in2 .2903E-2 sq. P . m/s. [L3 ] 1. V .013E5 bar 1. inch. lb 4. A. v. E1 = 10. H2 O @ 4◦ C 1.0E-15 light year. ft. 3rd ed. A 1. 2. J.785E-3 2. If P is power and V is voltage.0468E3 hectare. [M/L3 ] slug/cu ft 515. Wiley (1999) 4 . ly 0. meter. inch.832E-2 cu. ft3 Mass. Quantity Gaussian SI Conductivity 8. [M1/2 /L1/2 T] Gauss 1. D.654E-7 statcoulomb/cm2 Mag. I. cv. [M1/2 /L1/2 T] Oersted 79.0E-8 statvolt 2. eV 1. B. Jν (x) ≈ Nν (x) ≈ Iν (x) ≈ 2 πx cos(x − π2 ν − π4 ) 2 πx sin(x − π2 ν − π4 ) √1 2πx ex . L. [M1/2 L1/2 ] abcoulomb 10 statcoulomb 3.0E2 Resistivity. volt/m. abvolt-s 1. [1/T] Curie.6.6. ohm meter. [L] abhenry 1. ρr .58 Displacement. V/m.0E-5 BTU/hr 0. farad. Ampere.7 calorie/sec. watt. E.Ch.186 Thermal conductivity. [M1/2 /L3/2 ] 7. Kν (x) ≈ √1 2πx For roots of Jn and Jn . V. Ci 3.356 horsepower 745. siemens/m.[ML/T3 ] Watt/cm K 1. C. P . g/cm·s 0. [L2 /T2 ] 4. Bq.16 T[◦ F]= 9/5(T[◦ C]) + 32 1.0E2 1.0E-9 stathenry 8. Field. bequerel.186E3 cal/gm ◦ C 4. W.602E-19 liter atmosphere 101. [M1/2 L1/2 /T] abampere 10 statampere 3. Tesla. W/m K. σc . [L/T] abohm 1.73 BTU/hr/ft2 /◦ F/ft cal/cm·s 418.987E11 Capacitance. flux.5. Kelvin. H.W. K0 = −K1 For x 1. R. [M1/2 L1/2 /T2 ] abvolt/cm 1. Nν (x). Weber. A. Φ.336E-10 Current.0E-4 esu 2. q. gray.T. Kν (x): d 2 Jν 1 dJν ν2 dx2 + x dx + (1 − x2 )Jν = 0 ∞ e−ix cos θ = n=−∞ i−n Jn (x)einθ 2π 1 Jn (x) = 2π dθ e−inθ+ix sin θ 0 2π in = 2π 0 dθ einθ−ix cos θ In (x) = i−n Jn (ix) Jn (−x) = J−n (x) = (−1)n Jn (x) In (−x) = (−1)n I−n (x) = (−1)n In (x) 1 (x/2)n for |x| 1 Jn (x) ≈ In (x) ≈ n! Jν (x) cos νπ−J−ν (x) Nν (x) = sin νπ Kν (x) = 2 sinπ νπ [I−ν (x) − Iν (x)] J0 = −J1 .186E3 BTU/lb ◦ F Viscosity. J/kg K.p .958E3 abcoulomb/cm2 2. Γ(x + 1) = xΓ(x) Γ(x)Γ(1 − x) = sinππx √ Γ(1/2) = π. Γ(1/4) ≈ 3.336E-10 Potential. cal/s 4.31 Power. κ. [L2 /T2 ] rad 1.9979E2 Elec. [M1/2 L3/2 /T] 1 Tesla m2 maxwell.6E6 electron volt. henry.0E-2 Exposure. Ω-m. S/m [T/L2 ] mho/cm 1.9979E4 Mag. Gy.79E1 Charge.1: INTRODUCTION calorie. SLAC 1. f.112E-11 Inductance. Chao.0E9 statfarad 1.7E10 Dose. cal 4. hy. [L2 /T] microhm cm 1. Iν (x).9979 Flux density. V . N0 = −N1 I0 = I1 .5 FUNDAMENTAL FORMULAE A.9979E6 Conductivity.1 slug/ft·s 4.6 Specific heat.186 kilowatt hour. kWhr 3. h. Ω. [M/LT] poises. statvolt-s 2. A-turn/m.0E-8 statweber.1 Special Functions Error function erf(x). [ML2 /T3 ] erg/s 1. [T2 /L] abfarad 1. T .0E-9 statohm 8.2930 foot pound/sec. C. ft lb/s 1.0E-6 statvolt/cm 2. see Ch. [M1/2 L3/2 /T2 ] abvolt 1.9874E11 Activity.273.0E-8 Resistance. see Sec. Coul/m2 . kg/m·s. K T[◦ C]=T[K] .8 Temperature. Coulomb. volt.626 5 e−x . volt-s. erf(∞) = 1 erf(x) = √ π 0 Bessel functions Jν (x). erfc(x) = 1− erf(x): x 2 2 dt e−t . ohm. Field. Gamma function Γ(x): ∞ Γ(x > 0) = 0 dt e−t tx−1 Γ(n + 1) = n!. 1. u3 ) [1]: System u1 u2 u3 h1 h2 h3 Cartesian x y z 1 1 1 Cylindrical r θ z 1 r 1 Spherical r θ φ 1 r r sin θ Frenet-Serret x y s 1 1 r ∂r x ρ 1+ ds ≡ h1 du1 u ˆ1 + h2 du2 u ˆ2 + h3 du3 u ˆ3 ds2 = h21 du21 + h22 du22 + h23 du23 dV = h1 h2 h3 du1 du2 du3 ∂ψ ∂ψ ∂ψ ∇ψ = h11 ∂u u ˆ1 + h12 ∂u u ˆ2 + h13 ∂u u ˆ3 2 3 1 ∂ ∂ = 1 ∇·A h1 h2 h3 ∂u1 (h2 h3 A1 ) + ∂u2 (h3 h1 A2 ) + ∂u∂ 3 (h1 h2 A3 ) 2 ∂ ψ 1 + r2 sin 2 θ ∂φ2 = 1 × ∇×A h1 h2 h3 ˆ1 ∂u∂ 2 (h3 A3 ) − ∂u∂ 3 (h2 A2 ) h1 u ˆ2 ∂u∂ 3 (h1 A1 ) − ∂u∂ 1 (h3 A3 ) +h2 u ˆ3 ∂u∂ 1 (h2 A2 ) − ∂u∂ 2 (h1 A1 ) +h3 u .Sec.2 Spherical: Curvilinear Coordinate Systems ds2 = dr 2 + r 2 dθ 2 + r 2 sin2 θdφ2 dV = r 2 sin θdrdθdφ 1 ∂ψ ˆ ˆ ˆ + 1r ∂ψ ∇ψ = ∂ψ ∂r r ∂θ θ + r sin θ ∂φ φ = 12 ∂ (r 2 Ar ) + 1 ∂ (sin θAθ ) ∇·A General Orthogonal System (u1 . u2 .5.5: FUNDAMENTAL FORMULAE 1. ∂ψ ∇2 ψ = h1 h12 h3 ∂u∂ 1 hh2 h1 3 ∂u 1 . ∂ψ h1 h2 ∂ψ ∂ + + ∂u∂ 2 hh3 h2 1 ∂u ∂u3 h3 ∂u3 2 References [1] J. Murphy, Synchrotron Light Source Data Book, BNL 42333 (version 3.0) (1993) 1.5.3 ∂t + ∂B = 0 ∇×E ∂t = E, = μH D B = ∇ × A, = −∇Φ − ∂ A B E ∂t Continuity ∂ρ + ∇ · J = 0 ds2 = dx2 + dy 2 + dz 2 dV = dxdydz ˆ + ∂ψ ˆ + ∂ψ ˆ ∇ψ = ∂ψ ∂x x ∂y y ∂z z ∇2 ψ = ∂2ψ ∂x2 + ∂2ψ ∂y 2 + ∂t ∂Az ∂x q1 q2 ˆ static Coulomb force F = 4π 2r 0r + v × B) Lorentz force F = q(E ·E +H · B) energy density u = 1 (D 2 ×H momentum density g = c12 E =E ×H Poynting vector S ∂2ψ ∂z 2 Steady-state boundary conditions between two media: 1) · n 2 − D ˆ = ρsurface (D (B2 − B1 ) · n ˆ=0 Cylindrical: ds2 dr 2 r 2 dθ 2 Electromagnetism =0 ∇·B ∇·D =ρ − ∂D = J ∇×H Cartesian: = ∂Ax + ∂Ay + ∂Az ∇·A ∂x ∂y ∂z ∂Ay z x =x ∇×A ˆ ∂A − + yˆ ∂A ∂y ∂z ∂z − ∂A x +ˆ z ∂xy − ∂A ∂y r sin θ ∂θ ∂A φ 1 + r sin θ ∂φ = 1 rˆ ∂ (sin θAφ ) − ∂Aθ ∇×A r sin θ ∂θ ∂φ 1 ∂Ar 1 ∂ +θˆ r sin θ ∂φ − r ∂r (rAφ ) ∂ r (rAθ ) − ∂A + 1r φˆ ∂r ∂θ . . ∂ψ ∂ ∂ 1 r 2 ∂ψ ∇2 ψ = r12 ∂r ∂r + r 2 sin θ ∂θ sin θ ∂θ dz 2 = + + dV = rdrdθdz ˆ ∂ψ ˆ ˆ + 1r ∂ψ ∇ψ = ∂ψ ∂r r ∂θ θ + ∂z z = 1 ∂ (rAr ) + 1 ∂Aθ + ∂Az ∇·A ∂z r ∂r . r ∂θ = rˆ 1 ∂Az − ∂Aθ + θˆ ∂Ar − ∂Az ∇×A r ∂θ ∂z ∂z ∂r ∂ (rA ) − ∂Ar + 1r zˆ ∂r . 6 . Jsurface is the surface current on the boundary. θ 2 ∂θ 2 ∂ ψ ∂ 1 ∂ ψ r ∂ψ ∇2 ψ = 1r ∂r ∂r + r 2 ∂θ 2 + ∂z 2 1) × n 2 − E ˆ=0 (E ˆ = −Jsurface (H2 − H1 ) × n where ρsurface is the surface charge density. n ˆ is the unit vector normal to the boundary and points into medium 2. E. and γ [1]: β cp T E γ cp/E0 ep cp E T 0 −2 2 √ β= β 1 − (1 + E0 ) 1−(E ) = E 1 − γ −2 E = (cp/E0 )2 +1 cp = E0 / β −2 − 1 cp [T (2E0 + T )]1/2 E 2 − E02 E0 γ 2 − 1 . kinetic energy T .1: INTRODUCTION 1.4 Kinematical Relations Relations between β. rest mass energy E0 .Ch. cp.5. 1/2 = Eβ = T γ+1 = Eβ γ−1 2 −1/2 E0 = cp/βγ cp(γ − 1) T /(γ − 1) E 2 − c2 p2 E/γ = E(1 − β 2 )1/2 T = [√ γ= − 1]E0 1 1−β 2 (1 − β 2 )−1/2 E02 + c2 p2 − E0 . Variables (B. p) (B. and revolution frequency f : Of the four quantities (B. Bovet et al. DL/70/4 (1970) 7 E0 dγ β .. p. momentum p. CERN/MPS-SI/Int. mean orbit radius R.1/2 = cp γ−1 γ+1 cp E0 β = [1 − ( Ecp0 )2 ]1/2 T E − E0 E0 (γ − 1) 1 + T /E0 E/E0 γ First derivatives: dβ = dβ d(cp) dγ = dE/E0 = dT /E0 dβ [1+(cp/E0 )2 ]−3/2 d(cp)/E0 γ −2 (γ 2 − 1)−1/2 dγ = γ −3 d(cp)/E0 = β −1 γ −3 dγ E0 γdγ √ = 2 d(cp) = E0 (1−β 2 )−3/2 dβ = E0 γ 3 dβ d(cp) dγ = dE/E0 β(1 − β 2 )−3/2 dβ [1+(E0 /cp)2 ]−1/2 d(cp)/E0 = dT /E0 = = βγ 3 dβ γ −1 dγ = βd(cp)/E0 Logarithmic first derivatives: dβ/β = dβ/β dp/p dT /T dE/E = dγ/γ dβ/β γ −2 dp/p [γ(γ + 1)]−1 dT /T (γ 2 − 1)−1 dγ/γ = (βγ)−2 dγ/γ = dp/p − dγ/γ dp/p = γ 2 dβ/β dp/p [γ/(γ + 1)]dT /T β −2 dγ/γ dT /T = γ(γ + 1)dβ/β (1 + γ −1 )dp/p dT /T γ(γ − 1)−1 dγ/γ dE/E = (βγ)2 dβ/β β 2 dp/p (1 − γ −1 )dT /T dγ/γ dγ/γ = = (γ 2 − 1)dβ/β = dp/p − dβ/β Relations between bending magnetic field B. R) dp 2 df 2 dR p =γ f +γ R 2 γ −γt2 dp dB 2 df B = γt f + γ 2 p dB 2 df 2 2 dR B = γ f + (γ − γt ) R (B. f. R. only two can be independently chosen. f. R) differential relation dp dB 2 dR p = γt R + B (f. yielding the table on the right (γt is the transition gamma). p. f ). p. R) References [1] C. 5 Vector Analysis Energy-momentum : E = γ(E − cβPx ) Px = γ(Px − βc E).Sec.5.6 GLOSSARY OF ACCELERATOR TYPES 1. Pz = Pz Py = Py .1. t ) = cβ with be a frame moving with velocity V respect to F .1 ∇ · (a × b) = b · (∇ × a) − a · (∇ × b) ∇ × (a × b) = a(∇ · b) − b(∇ · a) Relativity Let F be the stationary laboratory frame with space time coordinates (x. 1. Lorentz transformations: Coordinates : x = x + γ β γ γ+1 β · x − ct t = γ(t − 1c β · x) v Velocity : = . t).6. Ey = γ(Ey − cβBz ). By = γ(By + βc Ez ) a · (b × c) = b · (c × a) = c · (a × b) a × (b × c) = (a · c)b − (a · b)c = (a · c)(b · d) − (a · d)( b · c) (a × b) · (c × d) ∇ × ∇ψ = 0 ∇ · (∇ × a) = 0 ∇(φψ) = φ∇ψ + ψ∇φ ∇ × (∇ × a) = ∇(∇ · a) − ∇2a ∇ · (ψa) = a · ∇ψ + ψ∇ · a ∇ × (ψa) = ∇ψ × a + ψ∇ × a ∇(a · b) = (a · ∇)b + (b · ∇)a +a × (∇ × b) + b × (∇ × a) Ez = γ(Ez + cβBy ). EM fields : Bx = Bx Ex = Ex . Let F with (x .6: GLOSSARY OF ACCELERATOR TYPES 1. γ v ·V 2 −1 γ+1 c γ 1− V 2·v c v +γ V Energy-momentum : . but excessive energy deposition from pair production limits their usefulness.1 shows typical proton beam parameters. and the secondary p ¯ beam is several orders of magnitude less dense than the primary proton beam. Vx ) c2 E d3 σ = [0. The production process is inefficient.4. The rf voltage is lowered so that the beam fills the bucket and then raised to its maximum value. vx −V Velocity : vx = βvx 1− vy = vy /γ 1− βvcx . Gollwitzer.5.1) and electron cooling (Sec. A primary proton beam is used to produce p ¯’s on a target.065(1 − xr )8 exp(−3p2t )] σabs dp3 × 1 + 24s−2 exp (8xr ) × a exp bp2t exp (−cxr ) c vz = Antiproton Sources K. z = z y = y. The resulting beam focal length is comparable to typical nuclear interaction lengths. J. FNAL Antiproton (¯ p) sources are complete accelerator complexes utilizing many accelerator technologies [1]–[4]. The production cross-section has been parameterized as [5] +(b · ∇)a − (a · ∇)b a × (b × c) + b × (c × a) + c × (a × b) = 0 1. The proton beam can obtain a short bunch length by a bunch rotation process (Sec.2). The bunch rotates 90◦ in phase space and achieves a momentary short length. favoring the use of high-Z targets. γ β · P − 1c E P = P + γ β γ+1 E = γ(E − cβ · P ) EM fields : + cβ × B) − γ 2 (β · E) β = γ(E E − 1 β × E) − = γ(B B c γ+1 γ2 γ+1 (β β · B) =Vx When V ˆ. Marriner.10).7. The design strategy consists of maximizing the p ¯ phase space density by (a) appropriate preparation of the proton beam and (b) beam cooling using some combination of stochastic cooling (Sec. see Fig. It is advantageous for the proton beam to have a short time spread and a small spot size at the p ¯ target since these properties are transferred to the secondary p ¯ beam.7.2.2. The proton beam is strongly focused transversely to a minimum spot size at the target.6 Bz = γ(Bz − βc Ey ) vz /γ 1− βvcx 8 .1. Tab. the above becomes Coordinates : t = γ(t − x = γ(x − V t). E = 8. s the square of the CM energy [GeV2 ]. For the FNAL Accumulator. Λ = ln (fmax /fmin ) .1: INTRODUCTION Table 2: Beam parameters of the collected p ¯ beam. xr the radial scal¯ energy in CM diing variable (= E/Emax . Parameter Momentum (GeV/c) Protons/pulse (1012 ) Cycle time (s) # Bunches RF bucket length (ns) RF bunch length (ns) Beam radius σ at target (mm) FNAL (MI) 120 8 2. see Fig. a = 1. The parameterization consists of three multiplicative factors: (i) a cross section for a hydrogen target at infinite energy. In [6].5 0. Ed ∼ 10 MeV. The secondary beam is focused by a lithium lens or horn. Both stochastic and electron cooling are used to increase the p ¯ beam density. V is exponentially decreasing with E while the particle density increases as a function of energy Ψ(E) ∝ eE/Ed . The initial large angular divergence of the p ¯ beam is largely eliminated by a collection element: a high-gradient lithium lens (Sec. the p ¯ beam is transferred from the Accumulator to the Recycler.4. Values for a.5 with σabs the absorption cross-section. (ii) deviations from scaling (including s-dependence).2 81 19 1.3. A difficult step is to accumulate p ¯’s from 104 or more pulses.2 0. At FNAL.5 0. η = slip factor.57 4.5 CERN (PS) 26 15 100 5 105 5 0.02. E is the beam energy. where high density beams can be formed and extracted.Ch.18 35π 3π 200π 5π 4-8 0. The beam is then pre-cooled with stochastic cooling. Some parameters of the stacking process are given in Tab. The stacking process is accomplished with stochastic cooling in an accumulator ring.1 6 1. p vided by its kinematically allowed value).16 1. un-normalized. c = 1.56. (1) 9 . b.2. and E1d = V1 dV dE with V (E) the voltage gain per turn.9-1.6 Figure 2: Antiproton Stacking.9 MeV).43. For copper. η = 0.4. The proton beam is given a short time spread via bunch rotation and focused to a small spot size on the production target. Individual particles are stochastically decelerated towards the stack core. The electron cooling system is notable for its high energy electron beam (4.9 GeV. The flux of p ¯’s that can be accumulated is [6] Φ0 = Ed T0 W 2 |η| β 2 EΛ FNAL (Debunch. Table 1: Proton beam parameters for the FNAL Main Injector and CERN Proton Synchrotron. b = 1.10). Δp/p is the full momentum spread of the beam.7.) 8. and (iii) the nuclear dependence. pt the transverse momentum [GeV/c]. Parameter Momentum (GeV/c) Δp/p (%) Before rotation After rotation After cooling 6π (mm-mrad) Before cooling After cooling Stochastic cooling bandwidth (GHz) Figure 1: Antiproton Targeting. The parameters of the collected beam are given in Tab. A small momentum spread is recovered from the secondary beam via a bunch rotation and the beam is injected into an accumulation ring where the longitudinal density is increased by stochastic stacking.9 CERN (AD) 3. β is the relativistic velocity factor. The large momentum spread is reduced as the beam is debunched through a second bunch rotation.12) or a pulsed horn. where W = fmax −fmin is the system bandwidth.2. a large storage ring that stacks the beam azimuthally using barrier bucket rf manipulations (Sec.50. 6π is for 95% beam. Final p ¯ beam parameters are in Tab.2. c for various nuclei are given in [5]. van der Meer. The low energy antiproton ring (LEAR) was the first accelerator dedicated to particle experiments with p ¯’s. 43 (1993) 253 [2] B. max 2-4 2-4.html [8] G. Blanford et al. ed. A section perpendicular to the equilibrium orbit plane is shown in Fig. Tab. p ¯’s will be used at the AD and FAIR in the future to study antihydrogen. NIM 206 (1983) 67 [6] S. Maury. Tevatron I Project (1984) [4] S. E. Iron core machines of energies up to 300 MeV have been constructed. Hojvat. LEAR has been decommissioned. Nature 419 (2002) 456 [11] G. The FAIR project at GSI [7] will include a p ¯ source and storage rings to support experiments with p ¯ beams.2 1.2π 1π At CERN the p ¯ source consisted originally of an antiproton accumulator (AA) to which was added the antiproton collector (AC) to increase production by increasing the p ¯ beam acceptance and by using the bunch rotation technique pioneered at FNAL. Rev.H.1 [2]. which have now significantly diverged in their primary uses. dielectric (e. with the antihydrogen existing long enough for physics measurements [12]. Tigner. Ann. glass) chamber with a thin conducting film on the inside to prevent charging. Stochastic cooling is used initially while electron cooling is used at the lower energies. Sci. Cornell U. a reconfiguration of the original CERN p ¯ source that emphasizes economical production of low energy p ¯’s [4].D. Experiments at the AD have used trapped p ¯’s to produce antihydrogen [10.01 0. Wilson et al. J. A. PRL 89 (2002) 233401 [12] G. 6π (mm-mrad) FNAL (Recyc. The accelerating electric field is produced by the changing magnetic flux within the equilibrium orbit.5x1012 0. Nature Physics 7 (2011) Table 4: Final antiproton beam properties.1. The Betatron [1] is a cyclic electron accelerator with a circular orbit of approximately constant radius which provides acceleration through Magnetic Induction. Andresen et al. CERN/PS 96-43 (1996) [5] C.04 CERN (AD) 100 s 1x107 0. Antiprotons are not accumulated but each pulse of p ¯’s is decelerated and cooled several times before extracting the entire beam for low energy/stopping beam experiments. Amoretti et al. FAIR will also provide low energy p ¯ beams (down to 30 MeV) for experiments with low energy or stopped p ¯’s.de/fair/ reports/btr. Nucl. CERN 83-10 (1983) [3] Fermilab Design Report. 11]. The guide field in the classical Betatron is weak focusing. FAIR will provide high energy p ¯ beams (up to 14 GeV) interacting with an internal gas jet target at high luminosity (2 × 1032 cm−2 s−1 ). Marriner.. 3 References FNAL (Accum.g. http://www. By combining Newton’s law and Faraday’s law of induction together with the Lorentz force law we can write e ∂Φ dp = . Autin et al.25. Parameter Cycle time Total particles Final Δp/p (%) Final emit.) 20 hr 5. evacuated.2 Betatron M. Lett.Sec. ed. 6π (mm-mrad) Bandwidths (GHz) Stacktail Core cooling Total particles (1012 ) typical. Phys. but low energy p ¯’s continue to be produced by the CERN Antiproton Decelerator (AD)..4 gives typical beam parameters for the current CERN and FNAL sources.) 28 20 24 0. B 368 (1996) 251 [9] G.B. 0. Antiproton beams have been used to produce relativistic antihydrogen atoms at CERN [8] and Fermilab [9]. The relativistic antiatoms lasted a few tens of ns. Gutbrod.6. Church. CERN/PS/AA 78-22 (1978) [7] H. van Ginneken. The beam travels in a doughnut shaped. Bauer et al. CERN/PS/AA 78-3 (1978).5π [1] M.gsi. p = Beρ (1) dt 2πρ ∂t 10 . PRL 80 (1998) 3037 [10] M. Part.4-8 with the FNAL Accumulator. FAIR Baseline Technical Report (2006).6: GLOSSARY OF ACCELERATOR TYPES Table 3: Beam properties in the accumulation ring. Gabrielese et al.J. Parameter Stack Rate (1010 hr−1 ) p ¯/pulse (107 ) Yield (¯ p/proton) (10−6 ) Final Δp/p (%) Final emit. extending the technique that was first used briefly in the CERN ISR and then later 1. In an attempt to overcome the space charge engendered limitation to beam current in the classical betatron. Flux Core Vacuum Chamber Flux Magnet 8–98 8355A64 6 Field Magnets (2) Flux Core the famous 2 to 1 condition that the flux change within the orbit must be twice that which one would obtain if the field were uniform throughout the region inside the orbit and equal to the field at the orbit.... and find that 2 ΔΦ = 2πρ B Expansion Side Package Electron Orbit yyyyy .600 R/min. yyyyy . at 1 m in Pb while the machines used for therapy produce typically about 100 R/min. and pulsing it negatively at tens to more than 100 kV for r0 = 10 in. Even so the highest energy betatrons achieve only about 5% duty factor due to the large hysteresis and eddy current losses coupled with the difficulty of cooling the massive iron cores. This effect spoils the linearity of Eq.2. a few microseconds at injection time.. Ejection or targeting is done in the same way by pulsewise distortion of the orbit enough to drive the beam into a weak field region and out of the doughnut through a thin window or into a tungsten bremsstrahlung target within the doughnut with subsequent extraction of the x-rays through a thin window. yyy .. yy .. Injection efficiency can be greatly enhanced by adding pulsed coils to draw the equilibrium orbit temporarily away from the gun just after injection and slowly restoring it as the initial betatron oscillations damp. lighter and more easily controlled..4. increase in maximum energy means increase in radius of the core and thus the volume of the iron.. While betatrons using the combined function. y . the synchrotron radiation begins to become important at ∼100 MeV and limits beam energies that can be obtained with iron and copper magnet technology to ∼300 MeV.Ch. .. While some betatrons. just outside or just inside the equilibrium orbit... more flexible. The iron of the 300 MeV Illinois Betatron weighed > 300 tons. particularly the 300 MeV machine were used for nuclear physics research.1 have been successfully operated at low energies. As the beam energy rises synchrotron radiation loss rises and competes with the energy gain due to magnetic induction.(1) and requires special means for adding the extra energy needed..yy yyy . yy .. Injection is accomplished by insertion of an electron gun into the sealed. at 1 m. The magnetic elements are punched 0. design of Fig. wound with litz wire to minimize eddy current. There is another constraint on the maximum energy which can be obtained using the betatron principle.1: INTRODUCTION yyyyyyyy yyyyyyyy yyyyyyyy Guide Field Central Flux Bo Bc Laminated Pole Piece Figure 1: Betatron schematic.355 mm laminations of silicon transformer steel. the majority were used for medical therapy or diagnostic x-raying of industrial equipment.5. doughnut vacuum chamber. yyy . the concept of the “Modified Betatron” was developed.3 [2] shows some typical power cycles of various betatrons.. one magnetic circuit. In the Modified Betatron. Since the field in an iron core magnet is limited by saturation. These machines have been largely supplanted by linacs which are more powerful. a torroidal field and strong 11 . The scale refers to an 80 MeV machine.yyy .. Injection is complicated and involves space charge effects (Sec. In practice.2 [2]. ... Fig.1) in a central way [3].. The 300 MeV machine was capable of producing 14. 12–97 8355A63 Figure 2: Separated function betatron. considerable efficiency in size and operation can be achieved by separating the functions as shown in Fig. 4. The interaction rate of a collider is measured by its luminosity (Sec. The first linear collider was the SLAC Linear Collider (SLC) and was based on an idea that was first proposed in 1965 [3]. In this case. References [1] M. [3] L. E1 Saturation (c) Field Bias O –B Pulse Interval Typically m1 = m2 and E1 = E2 (= E) and θ = 0 with Ecm = 2 E and the CM is stationary in the laboratory. The beam particles can interact many times in this configuration.1. Hartill. McGraw-Hill Book Co.6: GLOSSARY OF ACCELERATOR TYPES higher available energies. focusing both are added to the normal. Various instabilities can limit the performance of a collider but a variety of feedback systems and careful selection of operating Field B Inject Eject Flux t Flux Bias 12–97 8355A65 Figure 3: Typical power cycles. Fluids B5 (1993) 2295 [5] G.Sec. Particle Accelerators. Ecm ≈ 2 (E1 E2 )1/2 for θ = 0. J. The SLC used a single linac with two beamline arcs to collide the particles. EPAC08 (2008) 1860 1. weak focusing. APAC 2007 (2007) 628 [6] S. Gonella.6) in a betatron configuration [6]. One approach proposes very high frequency operation to achieve high beam power [5].6. beams of e− ’s and e+ ’s are collided with different energies so that the CM is moving with high velocity. Most colliders are based on storage rings where the beams are allowed to interact at one or more collision points and can be either double rings or a single ring employing electrostatic separation to keep the oppositely charged beams apart except at the collision points.S.1. Cornell U. A beam of ∼1 kA has been accelerated this way to 20 MeV [4]. Princeton-Stanford 500 MeV two ring e− e− . Particle beam colliders were developed to increase the center of mass energy available for new particle production and interaction. Colliding beam storage rings were first described in 1956 [1]. Short lived particles produced in the collisions then move a measureable distance before decay enabling important experiments in CP violation.P. The center of mass energy Ecm for the collision of two particles of mass m1 and m2 with energies E1 and E2 with a crossing angle θ is (1) Ecm = 2E1 E2 + (m21 + m22 )c4 1 1 1 2 + 2(E12 − m21 c4 ) 2 (E22 − m22 c4 ) 2 cos θ Flux B (a) Field Field Bias t O Inject Eject –B Flux (b) B –B m2. Boucher et al. Other new ideas have come forward recently. Blewett. The proposed ILC [4] and CLIC [5] colliders use two linacs each aimed at the collision point. Livingston. The ISR at CERN was the first hadron collider that collided protons using two intersecting storage rings [2]. For a stationary target this energy scales only as the square root of the beam energy while with a collider the collision energy scales linearly allowing for much 12 . Another approach uses the FFAG principle (Sec. vertical (mirror) field of the classical betatron. Kapetanakos et al.V. and the 250 MeV e+ e− AdA at Frascati were the first operating e± storage rings. With the advent of B factories. Dolbilov et al. Supplement to Nuovo Cimento 3 (1966) 303 [4] C.A.3 θ 12–97 8355A18 Colliders D.6. the two ring 140 MeV e− e− ring VEP-1 at Novosibirsk. Another configuration is the use of one or two linacs with the beam particles colliding only once. inspired by new materials and new needs.1) with typical units of 1032 cm−2 s−1 . E2 Field Inject O t Flux Bias Eject m1. Phys. McGraw-Hill (1962) [2] By permission. Siberia Cambridge.5 15 + 15 50 + 50 3. Germany CERN. An upgraded Super KEK B [6] at KEK and a new Super B collider [7] to be located near Frascati using parts from the decommissioned SLAC B-factory both project performance levels at 8. USA Name (type[a] ) CBX[b] (e− e− DR) Spear (e+ e− SR) PEP (e+ e− SR) SLC (e+ e− LC) PEP-II (e+ e− DR) AdA (e+ e− SR) Adone (e+ e− SR) DAΦNE (e+ e− SR) Super B (e+ e− DR) VEP-1 (e− e− DR) VEPP-2/2M (e+ e− SR) VEPP-4 (e+ e− SR) CEA Bypass (e+ e− SR) ACO (e+ e− SR) DCI (e+ e− DR) Doris (e+ e− SR) Petra (e+ e− SR) HERA (e± p DR) ISR (pp DR) Sp¯ pS (p¯ p SR) LEP (e+ e− SR) LHC (pp.1 + 2. PbPb DR) RHIC (heavy ion.25 + 0. Europe Brookhaven.5 2. LC: Linear collider.000 + 7. The LHC has begun operation with an initial beam energy of 3.5 315 + 315 104.5 + 2.5 + 8 1.5 3.5 + 31.000 100/u[c] + 100/u[c] 6+6 30 + 30 3. The expected start of commissioning is in the 2014-2016 time frame.5 0. Both projects have been approved by their funding agencies and will take advantage of very low emittance beams made possible by the damping ring technology developed for the SLC.5 + 104.55 2. [a] DR: Double storage ring. [c] 200 GeV per charge unit. [b] Princeton-Stanford Colliding Beam Experiment.7 7+7 3. The LHC collides protons on protons using two separate rings and the Tevatron collides antiprotons on protons in a single ring 13 . and projects an integrated luminosity of more than 6 fb−1 over the next two years. The Tevatron collider has been in operation over 23 years and its current peak luminosity of 4 × 1032 cm−2 s−1 is 400 times its design. France DESY. Location Stanford/SLAC.5 + 8 3. China Fermilab. Japan Beijing.0 0.Ch.5 + 1. The Tevatron collider with a beam energy of 1 TeV has accumulated over 8 fb−1 per interaction region by the end of its operation in FY2011.000 times this unit.8 + 1.25 1.1 + 9.8 3+3 19 + 19 30 (e) + 820 (p) 31.000 to 10.1 + 9.0 0.5 TeV and has already achieved a peak luminosity in excess of 2 × 1032 cm−2 s−1 Beam Energies E (GeV) . Italy Novosibirsk. USA Orsay.1 980 + 980 Damping Ring 7–95 Linac e+ Source Final Focus Final Focus x Collision point Start 1963 1972 1980 1989 1999 1962 1969 1997 2015[d] 1963 1974 1979 1971 1966 1976 1974 1978 1992 1971 1981 1989 2009 1999 1979 1986 1999 2015[d] 1989 2008 1987 Linac Damping Ring e– Source 7993A6 Figure 1: Components of a Linear Collider.5 7.13 0.1: INTRODUCTION Table 1: Colliding Beam Machines.55 + 1. USA Frascati.0 + 3. USA KEK. USA Cornell.5 + 0. [d] Planned.7 + 0.5 1. SR: Single storage ring. pp DR) CESR (e+ e− SR) Tristan (e+ e− SR) KEK B (e+ e− DR) Super KEK B (e+ e− DR) BEPC (e+ e− SR) BEPC II (e+ e− DR) Tevatron (pp-bar SR) points have enabled performance levels in excess of 200 times this unit at the asymmetric B factory at KEK with similar performance at the asymmetric B factory at SLAC.5 + .0 0.5 + 0.13 + 0. on High Energy Acc. Stockholm 225-cm).g. See later. A static and uniform magnetic field B is applied perpendicular to D-shaped hollow electrodes (“dees”). Proc. and are summarized in [3]. The average magnetic field can therefore match the mass increase of the accelerated particle with positive axial focusing provided by the azimuthal variation. Johnsen.pi. U. Conf. K1200) particularly for multi-particle cyclotrons where the energy for an ion of charge Qe and mass Am0 (where m0 is 1/12 of mass of 12 C. The record for classical cyclotrons is β = 0.48 MeV) is given nonrelativistically by E = KQ2 /A. Two electron cyclotrons with sinusoidal azimuthal variation of the magnetic field were built (Berkeley.1 shows the original cyclotron concept [1]. 1950.w. 27 inch.22 (Oak Ridge 86 . Nuovo Cimento 37 (1965) 1228 [4] ILC Reference Design Report: http://media.79.4 Cyclotron H.6: GLOSSARY OF ACCELERATOR TYPES pp and ep Colliders 105 Lepton Colliders 103 Cyclotrons are often referred to by the diameter of the magnet pole (e. (Synchrocyclotrons are exceptions.2 mm-mrad. cyclotrons are characterized by magnetic field and accelerating rf frequency which are constant in time (c. Kerst et al. U-400). Blosser. (≈ proton kinetic energy in MeV) has become a designation (e. It is the collision energy of the constituent particles that can access new particles. M. K500. subclassifications. These effects limit highest ion velocity. Isochronous cyclotron Thomas [4] pointed out that magnets with alternate strong and weak azimuthal regions (“sectors” or “hills and valleys”) provided an additional axial focusing which could offset the defocusing from a radially increasing magnetic field. PANIC 05 Proceedings. British Columbia & TRIUMF Earliest [1] and most numerous of circular accelerators.org/rdr draft v1. The maximum bending power (Bρ) is related to K by K = (eBρ)2 /(2m0 ). SG/64-9 Design Study of ISR (1964) [3] M.pdf (2007) [5] CLIC Design Report: CERN-OPEN-2008-021 (CLIC-Note-764) (2008) [6] T. (1971) p. N z ≈ 5 to 1 mm-mrad. Many cyclotrons are referred to by a local name or acronym (e. LEP LHC 104 102 SLC Ecm (GeV) Petra Tevatron 103 SppS CEA RHIC(pp) Hera 102 SPEAR 10 1 10 0 Adone CBX ISR ACO AdA Tristan PEP VEPP–4 CESR Doris PEPII KEKB DCI BEPC VEPP–2M Daφne VEPP–2 VEP–1 101 '70 '80 1–2006 8355A20 '90 Year 2000 10–1 '60 '70 '80 Year '90 2000 Figure 2: Colliders over the years.it/SuperB/CDR 1. and energy spread ΔE/E typically 10−3 with best value 2 × 10−4 .g. In practice. CERN AR/Int. m0 c2 = 931. Their characteristics are best documented in the proceedings of a series of triennial conferences [2]. using electrostatic separators to provide separation of the beams except at the two IPs.Sec. ORIC. Craddock. sometimes overlapping. U.6. 184 . Typical beam parameters achieved by cyclotrons: normalized emittances N r ≈ 2 to 0.).g. Kageyama. The dees are driven by an rf voltage whose frequency matches the constant cyclotron frequency qB (1) f= 2πm of nonrelativistic ions. Michigan St. 8th Int. PR 102 (1956) 1418 [2] K.1. p. and the accelerating voltage must be high for ions to reach the design energy before they get out of the accelerating phase of the rf cycle (due to relativistic mass increase and to magnetic field decreasing with r). the magnetic field must decrease with r to assure stability in the axial direction.) 14 .589 (2005) [7] Super B Conceptual Design Report (2007): http://www. Super KEKB. Electrons and muons are constituent particles while only the quarks in hadrons are the constituent particles with only a fraction of the total hadron energy. Classical cyclotron (now rare) Fig. Ions from a central ion source are repetitively accelerated in and out of the dees on a spiral path to maximum energy. Cyclotrons have evolved in many. PR 102 (1956) 590.infn. Future colliders are likely to be either linear colliders using e− and e+ to avoid high synchrotron radiation losses or storage rings using muons to get to the highest collision energies.K. AGOR). G. More recently “K”. O’Neill. linearcollider. References [1] D. 2 meter. Tigner. using superconducting magnet coils. “strong-focusing” by spiralling the hills was introduced and designations “sector-focused cyclotron”. A simpler. characteristic is lost and beam current typically decreases by ×1000. Multiple beams can be extracted simultaneously at different energies using suitably shaped foils. ∼230 MeV for proton therapy.w. (Thomas cyclotron is normally reserved for azimuthally sinusoidal fields. RIKEN.1.w. pole tips with a constant gap in the hill region and a larger constant gap in the valleys came into use. “radial-sector” (i. delivers 80-GeV heavy ions. The radial. Over a dozen 210-ton IBA 230MeV cyclotrons have been installed in hospitals worldwide in recent years (Sec.7. Moving the foil to a different radius easily changes the output energy of such a cyclotron i Near r = 0.14). spiral line is trajectory of positive ion. reversing their bending radius and thus sending the beam quickly out of the cyclotron. In the 1950s.6. (2) 240-ton K1200 nuclear physics cyclotron at East Lansing produces beams >10 GeV for heavier ions. Weight and size reduction leads to ∼×0.) More than 800 isochronous cyclotrons have been built (50-590 MeV for nuclear and particle physics. “spiralridged cyclotron”. Examples: (1) 22-ton cancer therapy cyclotron in Detroit produces 50 MeV deuterons. Synchrocyclotrons provided the energy-frontier beams of the 1950s but have now been superseded by synchrotrons for high-energy physics and by isochronous cyclotrons for nuclear physics. magnetic channels) are avoided. at that time.(1)]. Superconducting compact cyclotron This class includes cyclotrons with superconducting main magnet coils or rf systems (e. Synchrocyclotron This largely outmoded form of the classical cyclotron uses an rf frequency which varies with time to track the orbital frequency. the 520-MeV meson-factory cyclotron at TRIUMF requires weak magnetic fields so that this cyclotron is the world’s largest (17 m dia. where high beam currents make extraction especially difficult. 15 . accelerator of any type. To avoid electric dissociation (Lorentz stripping. and 10-100 MeV for commercial production of radionuclides). Sec. At maximum energy a thin foil strips the electrons from the H− ion. The highest beam velocity achieved by a cyclotron is in the 1 GeV synchrocyclotron at Gatchina.g. Separated sector cyclotron This is a subclass of isochronous cyclotrons in which the valley regions are iron free.9 operating costs. The energy limit of the classical cyclotron is relieved. poles).5 construction cost and ∼×0. β = 0. (3) 90-ton Varian/Accel cancer therapy cyclotrons at PSI and Munich produce 250-MeV protons. Bi (r) ≈ (r/G)i where G is magnet gap.1: INTRODUCTION over a broad range. but the c. θ) = B0 (r) + Figure 1: A classical cyclotron.Ch. The H− technique is used in most radionuclide-production cyclotrons. “azimuthally-varying-field cyclotron” are now used largely inter-changeably with isochronous cyclotron. These cyclotrons can be up to ×10 lighter than room-temperature cyclotrons due to the unusual cyclotron scaling law that total flux ∝ 1/B. Auxiliary slow extraction systems were often used to stretch the duty cycle. The 9-T superconducting magnet is light enough to be mounted on a rotating gantry. and first used at PSI in the 590-MeV meson factory (operation 1974). making it the highest energy c. Orbit characteristics Magnetic Field Bi (r) cos[iθ + ζi (r)] (2) B(r. Lanzhou). If magnetic field points into page. TRITRON at Munich). B0 = B0 (r = 0) = 2πf0 m0 /q [Eq.1. providing a more trapezoidal azimuthal field variation. Also. The RIKEN K2600 SRC.5).8) of H− at high velocities. Colorado [5]. non-spiral) formulation of this concept was adopted for the Indiana U. A very compact synchrocyclotron for cancer therapy with 250-MeV protons has been built by Still River Systems. H− cyclotron Cyclotrons to accelerate H− ions were introduced in 1962 at U. separated sector design is also used in large heavy-ion cyclotrons (GANIL.e. The concept was proposed in the late 1950s by Oak Ridge for a 900 MeV isochronous cyclotron. and difficult extraction components (electrostatic deflectors. 200 MeV proton cyclotron (operation 1975). Ilim ≈ 10 mA is typical. 4. A is the full beam height. If sectors are radial (α = 0). The acceleration system consists of dees (2 gap drift tube) or cavities (1 gap drift tube). and V the peak accelerating voltage per turn. Texas A&M. Single-turn extraction uses high accelerating voltage V and narrow rf phase interval at voltage peak to give turn spacing larger than turn width so that the deflector septum can be placed at a low density point between last two turns (extraction efficiency of 99. orbit scallops. so V is critical. . Flutter is defined as 1 B 2 − B2 = fi (r)2 (3) F (r) = 2 B 2 i where fi (r) = Bi (r)/B0 (r).g. 2/2. depends on maximum E/A (energy/nucleon).min where 0 is the permittivity of free space. ⎤ ⎡ gi cos(iθ + ζi )⎦ (4) r(θ) = r ⎣1 + i=1 − 1). γmax ≈ 1. Longitudinal limit In an isochronous device the orbit period is independent of the energy so the longitudinal length of bunch is unchanged but space charge force increases the energy spread of particles in a given turn and is the principal limit for single-turn-extraction (see below). “Flat-topping” voltage by adding higher harmonic gaps is sometimes used.97% at 590 MeV at PSI). Sometimes f is called flutter. tan α = rdζ/dr. N = 3 is the most frequent choice below 200 MeV/A because of the fast rise of B3 near r = 0. the radial tune νr rises faster than γ. This requires highly stabilized magnet and rf (amplitude Choice of sector number N = 3.. The acceleration system often runs on harmonic of beam orbital frequency frf = hf0 . magnetic azimuthal first harmonic) of ∼ 10−5 relative to main field. now usually located in valleys of magnet (in all valleys or. Catania. if N is even. 2 Df V (7) Ilim = 0 (2πf0 )Aνz. N = 2 is radially unstable. hitting resonances. Dees usually operate at 50-200 kV (peak voltage dee to ground). Spiral angle α is the angle between radius vector and tangent line to spiral curve. N/4. νz decreases with r and resonances limit usable energy band.1. Odd numbers other than 3 are too complicated. Df is the fraction of the machine circumference occupied by the beam. With flutter.6: GLOSSARY OF ACCELERATOR TYPES Due to large energy gain per turn and relatively rapid change of ν values with energy. Without flutter. A radius gain of 3-5 mm is typical (limited by axial instability at the nearby νr = 2νz coupling resonance). F (sometimes written F 2 ) called mean square flutter. Precessional extraction introduces coherent radial oscillation (amplitude a) prior to extraction to add precessional component (2πa|νr − 1|) to the acceleration radius-gain-per-turn [dr/dn = r(γ/(1 + γ))(qV /E)(νr )−2 where qV is the energy-gain-per-turn]. m0 γ(r) Bisoc = 2πf0 q −1/2 2πf0 r 2 m 1− (5) = 2πf0 q c /(i2 r dB = γ 2 − 1 ⇒ νr = γ (6) B dr As scalloping increases. Axial focusing tune νz ≈ [−k + F (1 + 2 tan2 α)]1/2 . where gi ≈ fi Field spiral ζN (r) is the angular location of maximum value of the main flutter component. Numerical calculations are required to estimate residual nonlinear component. etc.2 ⇒ 200 MeV/A for N = 3). A scaling law shows that turn separation ∝ V 3 . 6. kisoc = 16 .e. Imperfection resonances are often intentionally used to steer the beam in the central region and near extraction. νz. Multiple dees are sometimes phased by selecting a natural mode of the resonator structure (0-mode or πmode) and sometimes by servoed phase shifters (as in 3 dee h = 1 systems at MSU. 8.min is the axial tune at the radius of weakest focusing. Space Charge Limits Axial limit Assume fully overlapping turns (“current sheet” approximation).. Positive ion cyclotrons use an electrostatic deflector with thin (∼0. Precession usually induces a νr = 1 transition at the edge region using a field bump (i.Sec.1-0. The linear component of space charge force can be compensated by moving beam slightly to side of voltage wave.2 to avoid resonances.. cyclotrons frequently pass through essential betatron resonances at ν = N/3. and imperfection resonances at 1/1. Cavities operate up to 850 kV per gap. Normally one picks α(r) to increase with r to give νz ≈ 0. in alternate valleys). The N/2 stopband limits maximum γ (e.3 mm) septum followed by magnetic channel(s). & AGOR). Beam extraction H− cyclotrons use stripping foils. 3 26. Iˆ is maximum charging current.. 11 12 7 16 15 Chain Idler Wheel Pellet Charging Chain Charging Inductor Chain Drive Wheel Gas Stripper Assembly High Voltage Terminal Dessicant Tray Beam Output Drift Tube 8355A46 Figure 1: 1 MV Tandem Pelletron accelerator.77 29. the Netherlands.H. Final emittance depends on ion mass because of multiple scattering in the terminal stripper. the final emittance will be limited by the acceptance of the high energy acceleration tube to about 20 π mm-mrad (MeV)1/2 .1: INTRODUCTION 2 1. For light ions (p’s and α’s).06 L(m) 2.1 shows tank size versus terminal voltage for tandem pelletrons. 3. D and L are pressure tank diameter and length.5 3 1 and frequency). compressed. by Nissin-High Voltage Co. Science LXXII (1930) 376 [2] Proc. Smythe.3 MW currently the highest power beam from any accelerator. however important heavy ions such as C+3 at 2. V (MV) 1 3 5 10 15 20 25 Electrostatic Accelerator J. RAST 1. Horiz. Horiz. insulating rings sealed 17 . The FWHM of the terminal voltage variation of a Pelletron is ∼500 V without special ripple reduction circuitry. cw or pulsed). 4 5 1 6 7 8 9 10 11 14 13 Pelletron Tank Beam Input Drift Tube Insulating Plastic Support Accelerating Tube-Cutaway view Potential Distribution Ring Generating Voltmeter Discharging Inductor Capacitor Pickup 11–97 9. low outgassing.Ch. Thomas.3 23.K. 5. Int. for a proton beam the FWHM energy spread is 500 eV. NEC An electrostatic accelerator is a single potential drop system in which the high voltage potential is generated by the mechanical transfer of charge from ground to the high voltage terminal.) References [1] Lawrence. Tab.27 5. final emittance is ∼ 3π mm-mrad (MeV)1/2 . Ltd. Vert.org/ [3] M.87 ˆ I(μA) 50 300 1000 300 300 900 900 from the high voltage terminal to ground gaining additional energy. Particles on either side of the minimum-turn-number phase make an additional turn and so on to the edge of occupied phase interval. 12. which strips two or more electrons away changing them to positive ions. R Table 1: Tandem Pelletron basic specifications.E. 65 (2008) [4] L.. i. Flat-topping the rf waveform by adding a third harmonic is used at PSI to broaden the usable phase interval. Vert. 10. Carbon foils of a few μgm/cm2 can also be used. Very high V is required at high currents (∼3. Ferry. 2. 14. Examples: fabric belt charged Van de Graaff accelerators built by High Voltage Engineering Europa B.6. tube of argon or nitrogen gas (microns Hg). Overall multi-turn extraction efficiency ranges from 50% (typical) to 93% (PSI) to 97% (numerical optimization). This tube is made up of dense. Thus. 8. The positive ions are accelerated away Orient.43 18. 15.2-mA beam . and pellet chain charged Pelletron National Electrostatics Corp (Fig. Extraction current is limited by longitudinal space charge spreading of the turn structure. R built by USA.11 8.1). For heavy ions like gold. Edlefsen.13 4.18 5. 6.. K. 16. tandem types. V is terminal voltage. PR 54 (1938) 580 [5] M.e.R.49 8.22 2. At MeV energies. Rickey. Craddock.until recently at 1.4 MV/turn at PSI for a 2. Negative ions are injected and accelerated by a positive dc voltage on the high voltage terminal. 11.V. 66 (1962) 1.23 10. NIM 18-19. (*Folded tandem with 180◦ magnetic deflection in terminal. Conf. Symon. Multi-turn extraction is the default situation when single-turn requirements are not met. 7. the ions are directed through a turbo-molecular pumped [1]. Horiz.6 MeV cause the foils to rapidly thicken and break. For a C+4 beam it is 2000 eV. Most electrostatic accelerators built today are dual acceleration.* D(m) . Particles at turn number steps line up on the septum and a fraction of (septum thickness)/(radius-gain-per-turn) is lost. Vert. 4. http://jacow. on Cyclotrons and Their Aplications. and by Vivirad High Voltage. Japan.* Vert. W. 13. Acceleration tube All electrostatic accelerators must have a highly evacuated tube for the ions to traverse during acceleration.61 1. 6.-14. so an FFAG’s vacuum chamber. IEEE Trans.4). and (usually) to remove the central region — the same steps that convert a classic Lawrence cyclotron into a separated-sector ring cyclotron. Another method uses a chain made up from steel cylindrical pellets linked by stainless steel pins to nylon insulators. A chain carries typically > 150 μA of current [8]. Ferry. are difficult to control precisely. Nature 195 (1962) 1292 [4] F. contact with ground is broken as the wheel turns. as the radial and momentum Charging system Many fabric belts are still in use. Glass insulating rings sealed with polyvinylacetate. Nucl. A.H. The voltage between the electrodes is established by resistors or corona points draining current from the high voltage terminal.L. one can also vary the electric field along the beam path to produce cylindrically symmetric focusing fields that deflect low energy particles into adjacent electrodes [5. Allen. Rose. its beam intensity can be much higher. No. length.E.e. Res. Inst. Rathmell. pressing firmly against a wheel. Raatz.A. The innovations were to break the magnet into radial or spiral sectors to provide strong focusing. 7. Above 6 MV.K. Each chain is surrounded by a long. NIRL/R/21 (1962) [3] R. For most acceleration tubes the electric fields along the tubes are inclined or spiraled so that low energy secondary ions and electrons produced on the electrodes are deflected into nearby electrodes and cannot gain high energies [2.A. U. cyclotron [2]. to metal electrodes.9. NIM A328 (1993) 28 [8] G. NIM B37/38 (1989) 403 Support column Below 6 MV terminal voltage. P.B. Craddock. FFAGs operate just like synchrocyclotrons. 3]. On the other hand.A.Sec. The inductor electrodes are biased up to −60 kV for chain runs to and +60 kV for chain runs from a positive polarity high voltage terminal.6.E. but are capable of reaching tens of GeV. Nat. although no new machines do so. To remove ions and electrons produced on the electrodes. As the grounded chain. The FFAG is the most general type of fixed-field accelerator (i. In this case ceramic cylinders are bonded with aluminum to titanium electrodes to form posts about 18 in. columns with alumina ceramic insulators can be used. although effective. charge transfers to and from the belt must be accomplished via corona discharge or physical rubbing.S. closely spaced inductor electrode where the chain leaves or arrives 18 . Howe. Wittkower. Van de Graaff. It is generally found that a comfortable reliable gradient of about 1. Sec. leading to large terminal voltage ripple and can limit useful belt life.D. The posts can support 1 MV when immersed in pressurized SF6 gas. Nucl. 6]. Raatz et al.1. 1. Sundquist.14. NEC tube uses high density alumina ceramic insulating rings sealed with aluminum metal to titanium metal electrodes. long. moves into the inductor electrode charge flows smoothly onto it.2. N. NIM B259 (2007) 15 [2] W. Sci. Fixed-Field AlternatingGradient accelerators (FFAGs) were proposed independently by Ohkawa in Japan.6. one can use acrylic plastic plates as the insulating mechanical support column for components inside the pressure tank. The chains are charged and discharged by an induction scheme. Aluminum hoops are positioned along the insulating plates and are connected to the acceleration tube resistor divider [7]. modulated rf. J. This construction is suitable for columns up to about 29 ft. Sci.J.D. Some tubes also use low magnet fields to sweep low energy secondaries and electrons out of the beam path [4]. NIM A287 (1990) 87 [6] J.6 FFAG Accelerator M. Contact with the wheel occurs as the charge on the pellet is bound by the inductor to prevent sparks or corona discharges from the chain. Since the fabric belt is an insulator. Then while the chain is still within the inducing field. NIM A244 (1986) 104 [7] J. With fixed magnetic fields. Fixed magnetic fields lead to spiral orbits. R. Terrasi et al. See also Secs.6: GLOSSARY OF ACCELERATOR TYPES at a wheel. References [1] F.1. titanium or stainless steel electrodes are successfully used.3 (1967) 122 [5] M. magnets and rf cavities tend to be larger and more costly than a synchrotron’s. Kolomensky in the USSR and Symon and Kerst in the US [1]. Such methods. together with aluminum. The induced charge is trapped on the chain and carried to the terminal or ground where the chain enters the discharging inductor electrode. British Columbia & TRIUMF Following the discovery of alternating gradient (AG) focusing in 1952. and pulsed beams. Norton et al.6 MV/m can be achieved with a modern acceleration tube. high. Of course. with applications as diverse as treating cancer. Scaling FFAGs operating or under construction Recent years have seen the construction and successful operation of the first-ever FFAGs for protons by Mori’s group at KEK [7. The “circumference factor” R/ρ ≥ 4. whereby the orbit shape.8 for the KEK 150 MeV ring). depending on the sector type: file B(θ)/B. Ten machines have been built and a muon cooling ring is under construction. But proposals for proton FFAGs were not funded at that time. together with injector and booster FFAGs.5 if there are no straights [1].2).sector spiral angle α ≡ r(dθ/dr). im¯ = B0 (r/r0 )k and plying a magnetic field profile B a momentum profile p = p0 (r/r0 )k+1 . To first order the tunes are given by νr2 ≈ 1 + k νz2 ≈ −k + F (1 + 2 tan2 α) (1) (2) where ¯ ¯ .1: INTRODUCTION of F (1 + 2 tan2 α). constant νz requires a constant. without a steel return yoke. An 11-MeV 70-mA 19 . Mori introduced important innovations in both magnet and rf design. constant νr requires k = constant. (b) high permeability.5 GeV spallation neutron sources in the 1980s. and producing neutrinos. allowing broadband operation. Clearly. 6]. Except for ERIT and NHV (FDF). (c) low Q (≈1). The scaling principle was therefore adopted. heavy ions.average field at radius r is B ¯ − 1)2 . forcing the return flux through the D and automatically providing reverse field. value A similar 150-MeV FFAG has been built at the Kyoto University Research Reactor Institute (KURRI). it has become apparent that FFAG designs need not be restricted to the “scaling” approach explored in the 1950s.magnetic flutter F ≡ (B(θ)/B . In addition. but smaller with them (1.if spiral: α constant. and so short cavities with high effective fields. 8] and several more following scaling principles (Tab. boosting high-energy proton intensity. Moreover. Scaling FFAGs Resonance crossing was a big worry in the early days of AG focusing. which offer (a) rf modulation (with a 1. acceptances are larger. optics and tunes are kept the same at all energies. For recent reviews see [5. set purely by rf considerations. sector axis r = r0 eθ cot α . As a large k is usually chosen to minimize the radial aperture. . and culminated in the construction and successful testing of electron models of radial-sector and spiral-sector designs [3]. Dropping this restriction has revealed a range of interesting new design possibilities. and the repetition rate. with improvements in magnet and rf technology.Ch. The DFD triplets are built and powered as single units. FFAGs have become the focus of renewed attention. the radialsector designs employ DFD triplet magnets. electrons and muons.5–4. The rf innovation (avoiding the cumbersome rotary capacitors on synchrocyclotrons) is the use of FINEMET metallic alloy tuners. The world’s first tests of acceleratordriven sub-critical reactor (ADSR) operation were carried out there in 2009. The open structure also facilitates injection and extraction. which have been explored in a series of FFAG Workshops [4]. nor were those for 1.6 MHz sweep) at 250 Hz or more. Kerst and others at MURA (the Mid-western Universities Research Association) in Wisconsin in the 1950s and 60s. ∼15 designs are under study for the acceleration of protons. driving subcritical reactors. MURA’s recipe was to keep the flutter F (r) = constant by using constant pro¯ and. and so high beam-pulse rep rates. The most intensive studies were carried out by Symon. because of the low energy-gain/turn.average field index k(r) ≡ r(dB/dr)/ B ¯ ≡ B(θ) . reverse fields raise the average radius. irradiating materials.if radial: boost F by specifying BD = −BF . Recently. can be several kHz. 15) at J-PARC. Optics measurements have been carried out with αparticles. Figure 1: Scaling and nonscaling FFAG orbits. The muon bunches it collects will be rotated in phase space. acceleration would occur over 6 turns within a stationary bucket (T. with 1. Moreover. Planche et al. positively bending Ds and reverse-bending Fs (Fig.6 GeV stage of the reference scheme of the International Design Study of a Neutrino Factory (IDS-NF) Mori’s group proposes a 161-m radius ring with 225 FDF cells.25 m) would provide 250-MeV protons.1). Scaling can therefore be abandoned. and the orbit length C(p) shortened and made to pass through a minimum instead of rising monotonically as p1/(k+1) (Fig. [9]). 4-. Quasi-scaling FFAGs A novel technique for creating a scaling field with superconducting magnets has been proposed by Machida ([10] p. C(p)’s parabolic variation and its parametric dependence can be derived by treating the F and D FFAG proton storage ring has also been built at KURRI for boron neutron capture therapy using an internal Be target. 20 . 11] who proposes a “vertical FFAG” where the beam follows a helical path at fixed radius in a ring of superconducting magnets. a number of different scaling FFAG designs are being studied [6]. [4] on the NHV 10-MeV electron FFAG. reducing their momentum spread from ±30% to ±3% for ultra-sensitive studies of rare muon decays. This uses nested 2-. allowing the use of high-Q fixed-frequency rf. For the 3.3 m) 400-MeV/u C6+ ions. to medium-sized sources for 230-MeV proton and 400 MeV/u ion therapy (for which the high pulse repetition rates are clinically advantageous).e. These range from a fist-sized prototype of a 10-MeV machine for electron irradiation.112) for the PAMELA cancer therapy FFAG. the high current being maintained by ionization cooling (Sec. PRISM (Phase-Rotated Intense Slow Muon source). Vertical scaling FFAGs A more radical approach has been taken by Brooks [4.2. Scaling FFAG studies In addition. [10] p.3 to 20 GeV for a neutrino factory (see also Sec. using constant-gradient “linear” magnets greatly increases dynamic aperture and simplifies construction. while employing the strongest possible gradients minimizes the physical aperture. 6. and a wider variety of lattices explored. A major advantage of FFAGs over linacs – either single or recirculating – is that their large acceptances in r and p reduce the need for muon cooling or phase rotation.7. the tunes allowed to vary.i.4506). to a chain of four FFAGs accelerating muons from 0.and 8-pole solenoids to approximate the r k law over the beam aperture. The variation in orbit period is thereby reduced. Fixed-frequency acceleration between stationary buckets and by harmonic number jumping (HNJ) have also been considered. a 68 MeV/c DFD storage ring.1. The former “serpentine” method (see below) is possible in scaling √ FFAGs if the orbital period minimum at γ = k + 1 lies within the acceleration range. is under construction at RCNP Osaka for eventual installation at J-PARC (Sato et al.Sec. and a similar second ring (radius 9. Linear nonscaling (LNS) FFAGs In a study of FFAG arcs for recirculating linacs in 1997.6-12. Mills and Johnstone pointed out that the rapid acceleration (<20 turns) essential for muons allows betatron resonances no time to damage beam quality. [12] applied this nonscaling approach to a complete FFAG ring.1.6: GLOSSARY OF ACCELERATOR TYPES A first 12-triplet ring (radius 6.2 (left)). Moreover the accelerators themselves are significantly less costly.4).6.8 GV per turn at a fixed frequency of 200 MHz. and shows that a scaling law Bz ∝ ekz produces skew-quadrupole focusing and constant tunes.and some of radial-sector design. The radial orbit spread would be reduced (allowing the use of smaller vacuum chambers and magnets). Johnstone et al. FFAGs are also of interest for muons. showing that it would be advantageous to use superconducting magnets in which the field strengths decrease outwards . some of spiral. and has been successfully demonstrated by Yamakawa et al. and show that dangerous resonances can be avoided. each with 4 triplet cells. Operation could be either pulsed (100 Hz) or c. and the crossing of many integer and half-integer resonances – a 1020 MeV electron model (EMMA) has been built [16] and successfully commissioned at Daresbury.2 (right)) that stays close to the voltage peak (crossing it three times).1: INTRODUCTION 40 a LNS-FFAG complex of three concentric 48cell rings to produce 250-MeV protons and 400MeV/u C6+ for cancer therapy. providing extra edge focusing. Using a similar lattice Rees has also designed a non-isochronous 4-MW 10-GeV proton driver (C = 624 m) ([5] p. and have built a single straight scaling FFAG triplet for beam tests [4].6-25 GeV stage of muon acceleration (67 FDF cells. Johnstone’s “tune-stabilized” design [18] keeps the betatron tunes constant by using NLNS magnets where the pole gap varies with radius and the sector edges are straight. In order to demonstrate the novel features of such a design – particularly the serpentine acceleration outside buckets. fed by a 3-GeV RCS. ([5] p. and assuming qF = qD = q. They also propose ([10] p.44) have carried out tracking studies without any attempt at fine tuning and find only small losses at a few resonances. and LF D is the (shorter) F–D spacing.115) have proposed Insertions Beam injection and extraction is often a design challenge for FFAGs. to design a muon ring that is isochronous from 8 to 20 GeV – a muon cyclotron. Lattices along these lines have been developed. A similar 1000-MeV proton ring could be added to serve as an ADSR driver. Initial experiments on these two features have shown that the beam behaves as expected [17]. Nonlinear nonscaling (NLNS) FFAGs For cancer therapy.5 tons.02%. Machida ([10] p. first falling and then rising. but not all radial. M´eot et al.84) proposed a chain of 3 LNS-FFAGs in the AGS tunnel as a 19-MW.102). decay loss 7. Berg and Koscielniak [15] have shown that by exceeding a critical rf voltage an acceleration path can be created (Fig. This would be composed of either superconducting or permanent magnet triplets.w. E Scaling Non-scaling 30 20 10 0 10 15 Energy (GeV) 20 -π/2 0 +π/2 Phase Figure 2: Linear nonscaling FFAGs: (left) circumference variation with energy. For NS-FFAGs Rees ([5] p.124) a lightweight LNS-FFAG gantry. (right) acceleration path (yellow) in longitudinal phase space.(2).0% over 11. The extra magnets provide an additional degree of freedom. There are separate 250-MeV proton and 400-MeV/u C6+ rings. capable of accepting the whole extracted momentum range at fixed field. Trbojevic et al. rendering Eq. C(p) = C(pm ) + 12π 2 (p −pm )2 e2 q 2 N LF D (3) where N is the number of cells. because of the regular cell structure.74) also uses nonlinear field profiles but a more complicated dFDFd cell structure.4503) have proposed racetrack versions of the PRISM and ERIT storage rings. the high rf voltage needed to cross resonances quickly would be too expensive. magnets as thin lenses of strength qi (gradient × length) [13]. confirming the viability of the LNS approach. derived for two-component cells. radius 111 m. With the orbit length varying by only 0. Rees ([5] p. as first shown for scaling FFAGs by Meads [19]. no longer applicable. so that spiral edges are not required.74) showed that four 9-cell straights 21 . snaking between neighbouring buckets (rather than circulating inside them) just as in an imperfectly isochronous cyclotron. Insertions providing longer drift spaces can however be designed. with distinct pmin . For symmetric F0D0 or triplet cells. Ruggiero ([5] p. The IDS-NF has adopted a LNS-FFAG for the final 12. 12GeV proton driver. The orbit radii r(p) show similar dependence. and weigh only ∼1. where resonance crossing is of more concern. (requiring harmonic number jumping).Circumference Variation (cm) Ch. ([5] p. The minimum is at pm = (4pc +eqLF D )/6 where the pc closed orbit is such that BF = 0.558) has recently presented a design with 4 straights that are well-matched to the arcs over the full 30-250 MeV energy range. Lagrange and Mori ([10] p.6 turns) [14]. This would operate at 50 Hz. LNS-FFAGs have also been considered for lower-energy applications with slower acceleration. the particle sources and acceleration methods are usually similar. 1138 [14] J. Craddock. In series-coupled systems.S. The contours and strengths of the electric fields are determined by the shapes and spacings of the accelerating electrodes with intermediate potentials.1038/nphys2179 [18] C. 1959) [3] K.) ICFA Beam Dynamics Newsletter 43. PAC’03. Garren. Wan. McMillan. EPAC’04.web. F. High voltage electrodynamic accelerators are also called potential-drop or direct-action systems.cockcroft. Transformers are not needed in the rectifier stages. http://www.6. EPAC’08. T503 (2001). Cleland. Berg et al. PAC’12. while others use an assembly of high voltage transformers [1. focused.K. Aiba et al. The use of multiple overlapping electrodes prevents spark discharges in the acceleration tube. ac power is capacitively coupled in parallel to the rectifier stages. [7] M. 96. 241 [15] J.gov/icfabd/Newsletter43. Cyc’01. M. 3].. ibid. Berg. PAC’83.fnal.org [11] S.3. EPAC’06. 639-786 (Wiley.K. Some of these systems transfer ac 22 .R.pdf [6] M. Craddock. Symon et al. Cole. all stages receive ac power directly from the primary source and the voltage generated under load is the same in High Voltage Electrodynamic Accelerators M. 1 (2010) [17] S. In parallel-coupled systems. matched acceptably to the main arcs at all momenta. http://www.S.6. Particles are extracted from their sources (ions from plasmas. References [1] K. HB2010.R. Craddock. but for higher voltages. 2508.H Prior (ed. High voltage generation The many applications can require potentials from as low as 70 kV to as high as 5 MV. S. 3452 [9] A. Meads Jr. Inc. In Fig. v.6: GLOSSARY OF ACCELERATOR TYPES power from the electric service to multiple rectifier stages through an array of high voltage capacitors. Proc. Barlow et al.jacow.1b. multiple-stage cascaded rectifier systems are needed to insulate the secondary dc circuits from the primary ac power source. 3068 [13] M. C. RAST. Snowmass 2001. 299 [8] S. In Fig.M.1. PAC’03. ac power is capacitively coupled in series from each rectifier stage to the next. ac power is inductively coupled in series from each of the transformer-rectifier stages to the next stage.5) that transport charges mechanically from ground to the particle source. Nature Physics 8.1d. 19-133 (2007). Brooks.1c. A. 3389 [10] Proc. T508 (2001) [16] R. 452 (2003).R. In Fig.1a. in “Experimental Nuclear Physics”. 243 (2012) | doi:10. Koscielniak. http://hb2010.T. the lower stages in the cascaded rectifier circuit must transmit ac power to the upper stages. Johnstone. IBA Industrial. Suppl. PR 103 (1956) 1837 [2] E. S. Koscielniak. 2. Johnstone. Machida et al.1 [2]. 1. A variety of such multiple-stage systems have been developed. so the dc voltage generated under load is reduced in the upper stages. IPAC’10. 65 (2008). 244 1. ac power is inductively coupled in parallel from a common primary winding to all of the secondary windings. Symon.R. the high voltage power supplies in electrodynamic accelerators convert low voltage alternating current (ac) to high voltage direct current (dc) by means of cascaded rectifier circuits. Concentration of the rf allowed the circumference to be reduced from 1255 m to 903 m..Sec. FFAG2003. EPAC’00. electrons from hot cathodes). conventional single-stage transformerrectifier systems can be used. They increase the kinetic energies of ions and electrons by connecting particle sources to high voltage generators and accelerating the particles to a variety of targets at ground potential. For voltage ratings below 300 kV.J. Sato et al. In Fig. could be inserted in his isochronous muon ring. NIM A624. PAC’99.uk/events/ffag11 [5] C. protects the insulating rings between the electrodes from scattered particles and permits the use of high potentials and strong electric fields. 2116 (2011) [19] P. Symon. (2001) [4] FFAG’11 Workshop.7 Particle acceleration Charged particles are accelerated in highly evacuated tubes to minimize collision with residual gases. Although there are several different designs of the high voltage power supplies. www-bd. Machida et al. The dc outputs of each stage are connected in series to produce high voltage dc power. Johnstone et al.1. Proc. PAC’11. The different methods for coupling ac power to all of the rectifier stages are illustrated in Fig.psi. In contrast to electrostatic accelerators (Sec.K. K.ch/ [12] C. W.F. and accelerated by strong electric fields created by the high voltage potentials.ac. 0 MV have been obtained with compressed gas insulation [7.0 MV have been produced with electron beam power ratings up to 300 kW. 3—voltage rectifying and multiplying circuits.5 MV ICTs for irradiating their heat-shrinkable food packaging films. Dynamitrons with voltages up to 5. 17].Ch. 8]. The middle column reduced the ac ripple voltage at the high voltage terminal. Switzerland. The magnetic cores of the secondary windings are separated by thin sheets of solid insulating material. The largest ICT accelerators produce voltages up to 3. All of the dc circuits are connected in series to produce the high voltage at the output end of the assembly [19]-[21]. Emile Haefely & Co Ltd. During the 1950s and 1960s. They produced many accelerators using this type of generator for a variety of research applications such as electron microscopy. simplified the symmetrical cascade circuit by omitting the middle column of capacitors for industrial applications that do not need low ac ripple voltage. Philips. General Ionex Corporation also produced parallel-coupled tandem accelerators called Tandetrons for high energy ion implantation in silicon wafers [18]. the Netherlands. High voltage. Insulation between components is provided with compressed SF6 gas.0 MV [6]. Parallel coupling allows the use of many more rectifier stages.1: INTRODUCTION (a) (b) (c) 3 2 3 1 2 2 3 (d) Parallel-coupled systems The parallelcoupled cascade circuit proposed by Schenkel [11] predated the Greinacher circuit. High Voltage Engineering Corporation developed the Insulating Core Transformer (ICT). Capacitive Cascade generators Series-coupled systems Cockcroft and Walton [4] used a high voltage generator with multiple rectifier stages capacitively coupled to a source of ac power. This is a three-phase. and separation of high energy particle beams. 10]. Parallel-coupled systems During the 1970s. 2— stage. in Japan. 1—Power supply. Inc. Rectifiers and filter capacitors convert ac power to dc at each stage. produced many air-insulated high voltage generators and accelerators based on this concept with voltages up to 3. Radiation Dynamics. Potentials up to 4. The rectifiers are connected in series to produce high voltage dc power. but it was not used for very high voltage generators because of the difficulty of making capacitors that could withstand the dc output voltage. During the 1950s. makes 0. During the 1980s. Their largest accelerator of this type is rated for 30 mA of dc electron beam current or 150 kW of beam power [9. multi-stage rectifier cascade circuit using magnetic coupling to transfer low voltage. developed a symmetrical seriescoupled cascade circuit with three columns of capacitors. the firm Nissin High Voltage Co Ltd. ion injection into higher energy rf accelerators.0 MV have been obtained with compressed gas insulation. Two-stage tandem ion accelerators using this type of high voltage generator have been produced by Radiation Dynamics. the Budker Institute of Nuclear Physics developed 23 . ICTs are now made by Vivirad High Voltage in France and Wasik Associates in the USA. all stages. During the 1930s and 1940s.0 MV with electron beam power ratings up to 100 kW. USA. This type of system is commonly called a Cockcroft-Walton accelerator. reduces the internal impedance of the high voltage generator and increases the amount of current and power that can be provided for particle acceleration. 2 3 1 1 1 1–98 8355A169 Figure 1: Cascade generators. low frequency ac power from the primary windings at the low voltage end of the transformer to an array of high voltage secondary windings. high frequency ac power at about 100 kHz is generated by a triode-driven resonant system consisting of an iron-free transformer and a pair of semicylindrical electrodes which surround the rectifier assembly.V. the firm N. Power is capacitively coupled from these electrodes to semicircular corona rings connected to the rectifier junctions. [16. Their series-coupled voltage multiplying rectifier circuit was proposed earlier by Greinacher [5]. Voltages up to 5. Sealed Air Corp. developed the parallel-coupled cascade circuit used in Dynamitron accelerators [12]-[15]. Similar systems are now made by High Voltage Engineering Europa in the Netherlands. Inductive Cascade generators Series-coupled systems In the 1950s and 1960s. U. A.1-3 (1993) 515 [11] M. Svin’in.0 MV and 400 kW of beam power at 0. 27].526 (1966) [20] R.5-6 (1981) 1353 [27] V. Nos. M. & Chem. 4. Scharf. U. NS-18 (1971) 108 [18] K.394 (1959) [13] M. Vol. Eng. Nucl. Fernald. Vol. Vol.S. GB Patent No. Elektrotechnische Zeitschrift.338.A. Sci.274.40 (1919) 333 [12] M.R.D. & Chem. Chapter in Radiation Processing of Polymers. Charged Particle Accelerator. Kuntke. The Aurora system uses multiple bridge rectifier circuits with lower voltage per stage and can produce 0. Bangerter. 26. Cascade Generators. Van de Graaff.R. Thompson. IEEE Trans. fur Technische Physik. Sci. Vol. The first large IL was the Astron Injector at LLNL [1]. All of the secondary windings are coupled to an external coaxial primary winding which extends the full length of the high voltage assembly. Abramyan.R. Albertinsky. the Budker Institute. & Chem.I.530.3 (1965) 288 [9] K.S.S.R.42. Malone. U. 3. Vol. P. Patent No. 3. Proc. Zeit. Radiation Phys. Insulating Core Transformers..P. 2. Nos.. Nos. Harwood Academic (1986) [2] E.28 (1955) 1. Schmidt. A 2. U.8 Induction Linac R.3-6 (2000) 661 [24] L.Sec. Industrial Electron Accelerators and Applications. and the Institute for High Temperatures in Moscow developed threephase.619 [5] H.875. 589698 (1973). the Efremov Institute for Electrophysical Apparatus in St. Heilpern. Acta. Part 1. Bouwers. Nos. Sci. P. NS-12.C. U. These use continuous long iron cores at ground potential with primary windings on each core.R. Radiation Phys. Patent No.0 MV. Hanley. M. NS-16 (1969) 90 [17] S. Bill. Reinhold. Greinacher. Proc. 23].. Soc. Part 2. Hanser (1992) [4] J.A. Hemisphere (1988) [3] M.4 MV [2. IEEE Trans. Emanuelson. It has insulated magnetic cores inside the multiple secondary windings. Although induction acceleration had been used for 24 . Voltage Multiplication Apparatus.1.18. and pulse lengths that are not easily achieved using rf accelerators. Helvetica Phys. Schenkel.S. multi-stage transformer systems. Patent No. 25. & Chem. More powerful systems have been developed by the Efremov Institute for applications that do not need voltages higher than 1. Salimov et al.1-3 (1988) 267 [10] S. Vol. Vol. No.3 MV dc and 75 kW of electron beam power. Patent No. Vol.657 (1982) References [1] W. Zeit.S. C. beam energy. fur Physik. Cleland. SPIE Vol. Sci. Walton. Purser et al. PhotoOptical Instr.066 (1966) [21] R. 22.P. Vol. J. H. Reginato et al. Radiation Phys. Radiation Phys. [8] G. NS-12. (1985) 14 [19] R. 4. Nucl. Rectifiers connected in three-phase bridge circuits convert ac to dc power. Radiation Phys. Uehara et al. IEEE Trans. During the 1970s and 1980s. Mizusawa et al.. No. transformer-rectifier system without magnetic cores.T. Royal Soc. High Voltage TransformerRectifier Device. The Elita is a resonant pulse transformer with a solenoidal high voltage secondary winding. Vol. The ELT is a low frequency system for generating high voltage dc power. Applications of Accelerators.499.L.5 MV dc system has been made by LBNL [24].016. LBNL Induction linacs (IL) are employed in applications that require combinations of beam current.14 (1979) 343 [22] G.H. & Chem. Patent No.A.18 (1937) 209 [7] W.R. Radiation Phys. Cleland. E. IEEE Trans. The ELV is a similar multistage. Budker et al.R. 1454485 [23] R. The high voltage secondary windings are insulated from the cores and primary windings. NIM B40 (1989) 1137 [16] P.. Cox.75 MV dc and 100 kW of beam power [2. The Teus system uses a single bridge rectifier circuit with three high voltage windings and can produce 0.4 (1921) 195 [6] A. ELV accelerators produce electron beam power ratings of 50 kW with dc potentials up to 2. Lisin et al. transformer-rectifier high voltage systems. Cockcroft.. Svinin. London. Atomizdat (1980) [26] M.3 (1965) 227 [14] M.J. Truempy. AIP Conf.I. C. High Voltage Electromagnetic Apparatus Having an Insulating Magnetic Core.S. Cleland. Cleland.. & Chem.6: GLOSSARY OF ACCELERATOR TYPES several types of single-phase. Emanuelson. Hanley et al. Nucl. Petersburg. SU Patent No.289. Thompson. R.N.C. 392 (1997) 1305 [25] B. Nucl. Particle Accelerators and Their Uses. Accelerator Design..4-6 (1977) 547 [15] C. K..9. Farrell.M..6. Cleland.57.F. Series A136 (1932) p.31. Nos. and DRAGON-I in China [2].1. Ref. The beam is the secondary of this transformer. The Astron Injector originally produced 350 A of electrons (3. the betatron. The large size. treatment of chemical and nuclear waste. originally built for defense studies. Cavity Acceleration Gap Beam Pulser Pulser Acceleration Gap Short Circuit Beam Figure 1: upper: An IL with two induction modules (stages). with a changing magnetic field by V = −dΦ/dt.g. Flash radiography is another important application of ILs.7 MeV. a lithium accelerator designed for basic studies of hot dense matter [5]. the accelerating voltage V is associated 25 . The integral is over the cross-sectional is uniarea of the core. In any case. This quantity is often referred to simply as the volt-seconds of the core. the accelerating electric field is associated with a changing magnetic field.Ch. The core is usually made of ferromagnetic (or ferrimagnetic) material although it could be simply air or vacuum. The beam current is usually < 1 A. a 50-MeV IL. In contrast. or V dt = A ΔB. A pulser (or modulator) provides the power to energize an induction module. e. Indeed. For a comprehensive review with listings of For a comprehensive review with listings of major ILs and their characteristics. while ΔB is referred to as the flux swing.1 (lower). One can also think of an induction cavity as a shorted transmission line as shown in Fig. Heavy ion inertial confinement fusion and high energy density physics are applications that require beams of heavier ions (Li to U).1: INTRODUCTION Core some time (e. pulsed neutron sources. AIRIX in France. allows the induction accelerators to be used at longer pulse lengths than rf accelerators. electron beam welding. The beam is the secondary of a series of transformers. see [2]. induction cores are often large (∼1m dia.6. microwave power generation. In the line-type machines. >10 kA).1 (upper) illustrates the basic concept of induction acceleration. For ILs. ILs produce beam pulses at much lower repetition rates. The line-type cavities usually have very low impedance. Since then more than 40 ILs have been built. One may view the induction module as an electrical transformer. in contrast to the core-type [3]). In both induction accelerators and rf accelerators. If one assumes that B form over the area. The electric acceleration field is confined primarily to the axis of the accelerator by the conducting walls – the induction cavity – surrounding the induction core.2). An IL consists of one or more (often many) induction modules placed in series. currently holds the record for the highest voltage (kinetic energy). The ATA. Sec. pulse length 300 ns.g. However. together with the use of ferromagnetic material. 4]. A ferromagnetic core is not used. · dA is the magnetic flux in where Φ = B the core. food irradiation. a principal function of the core in a coretype module is to provide a high impedance in parallel with the load (beam). lower: Alternatively. These applications use electron or proton beams. rf cavities are often driven at resonance and induction cavities are not. Another way to achieve induction acceleration is by changing the area occupied by the magnetic field rather than the field itself (line-type induction accelerator. Conventional linacs produce long trains of beam pulses at radio frequencies.g. treatment of materials. burst repetition rate >1 kHz) to create a magnetic field in the Astron magnetic fusion device. an induction cavity is basically a radial or axial transmission line. The old hardware from the ATA has been modified to build NDCX-II. Other applications that have been suggested or implemented include FELs. then V = −AdB/dt. The IL concept Fig. one can think of an induction module as a shorted transmission line. Also. and tunneling in rock [2].). but much higher currents (e.[1] is usually credited for the invention of IL. the pulse length lies in the range from tens of ns to tens of μs. Subsequently ILs to produce beams for electron ring accelerators (experimental collective accelerators) were built at Berkeley and Dubna [3. FXR and DARHT in the US. the development of advanced pulsers. ferrite. (2010) [3] J. but IL technology is still not as highly developed as rf accelerator technology. The measured efficiency into a resistive load approached 50%.g. the development of large. the inductive voltage adder. or pulse forming lines. typical losses in iron-based metallic glass are ≈ 800 J/m3 at a pulse length of Δt ≈ 1 μs and a flux swing of 2.5 T do not drop appreciably below 100 J/m3 even at very long pulse lengths. high-gradient insulators is also an important research topic. Magnetic materials used for induction cores include steel tape. and a class of amorphous metallic glasses such as R . Christofilos et al. Leiss. Finally. Induction technology The main components of an IL are the pulsers. For continuous solenoidal focusing the maximum current is approximately IS = 4 × 105 (Z/A)βγ(Ba)2 Amp. since ILs often have relatively large apertures to carry high beam current. and. a reset pulser normally magnetizes the core in one direction before it is pulsed in the opposite direction by the main pulser. For core materials other than ferrite. Also. a subical. the nanocrystalline materials mentioned above appear to be promising. To maximize ΔB.Sec. For example.C.). those using solid state switches can be expected to have a profound influence on IL design and applications. (1) where Z and A are the charge and atomic mass numbers. during construction there were some unanticipated problems involving the behavior of ferromagnetic materials and the distribution of voltages within the induction cavities. Takayama and R. e. Moreover.E.. For electrostatic quadrupoles B is replaced by E/(βc) where E is the electrical field in V/m. With continued development. Briggs (Eds. e. low-cost ferromagnetic materials having predictable. Springer: NY. but quadrupoles appear preferable for heavy ions. The pulser used capacitive storage and an array of field effect transistors. in one experiment [9]. ILs are related to other devices. Lamination is usually achieved by winding the cores from thin tape (thickness ≤ 50 μm). and a is beam size in m. For example.6: GLOSSARY OF ACCELERATOR TYPES losses. and solid-state devices. This example points to the importance of continuing development of low-loss. nickel-iron tape. the losses at 2. The actual current will be less than this maximum because of emittance. where a solid conductor replaces the beam. highly reliable.3870 26 . B is in Tesla.g. For example. the induction cores. (2) where η is the effective occupancy factor (the fraction of the lattice occupied by quadrupoles). although DARHT has now achieved its design goals. spark gaps.. There has been research on neutralized and collective focusing systems [6]. The beam transport system of an IL must be capable of carrying high current. For a magnetic quadrupole transport system the maximum beam current is approximately IQ = 8 × 105 (βγ)2 (ηBa) Amp. Switches for the pulsers include thyratrons. particularly at the high velocity end of the machine. Core losses are an important consideration. A detailed calculation is required in each individual case. The losses scale approx.J. some IL applications such as high energy density physics and inertial fusion will likely require the development of novel beam transport systems such as compact. K. pulse forming networks. PAC 79.5 T. consistent properties. particularly for lower beam currents. as ΔB 2 /Δt. ILs may become competitive with rf accelerators for high average power applications. p). originally produced by Allied ChemMetglas R Inc.) A newer class of nanocrystalline materials such as Hitachi’s Finemet and Vacuumschmelze’s Vitroperm has losses that are typically several times lower than those of the older metallic glasses [7]. One can estimate the maximum current that a transport channel can carry by setting the beam self force equal to the applied focusing force of the lattice. Depending on the voltage.. an uncooled induction core was run for a few weeks at a repetition rate of approximately 100 Hz. (Because of hysteresis. inexpensive. the core must be laminated to minimize eddy-current References [1] N. pulse length. magnetic switches. the beam transport system. multi-beam arrays of superconducting quadrupoles. but now produced by Metglas sidiary of Hitachi Metals. RSI 35 (1964) 886 [2] Induction Accelerators. and other characteristics. In this regard. the pulsers may be based on simple switched capacitors. p.1. Research on this topic is in its infancy [8]. Solenoids are usually preferred for light particles (e− . in the case of a core-type machine. Research topics Many ILs have now been built. produce x-rays for cancer treatment up to 0. a potential distribution exists. Only one bunch at a time can be sent through this accelerator. Molvik et al. These so called “dees” are connected to a source of alternating voltage.21.1: INTRODUCTION 2.5 – 1. One third is used in medical applications. LINAC98.1.6. Faltens. Jr.4. see Sec.3410 [7] A. In the cyclotron the beam is bent into a circular path by a magnetic field and the particles orbit inside two semicircular metal chambers.Ch. electrical-insulation. In column 2 a suggested technique/method is given.4. In the synchrotron the massive magnet (in cyclotrons and synchrocyclotrons) is replaced by a ring of bending magnets. 1. LBL-35960 (1994) 1. two-thirds are used for industrial applications. see Sec.7. see Sec. 3. today mostly by a chain of metal cylinders connected by insulating links). p. textile.6. Friedman et al.6.6. 7. The cascade accelerator (also called high voltage accelerator) in which the highvoltage unit consists of a multiplying rectifier-condenser system (first used by Cockcroft and Walton).6. Ion beam accelerators are used for a broad variety of industrial applications like micro-machining and for national security applications. The RFQ accelerator has a symmetry corresponding to that of an electrostatic quadrupole. (An alternative to a synchrocyclotron is to modify the cyclotron and divide the magnetic field into sectors of alternating high and low fields. wire and cable. rubber goods.. which include x-ray inspection of cargo containers and stewardship of civil and military nuclear materials. Electron beam processing is utilized by many major industries. Keefe. Along the Widerøe principle the electrodes are connected alternatively to opposite poles of an rf-supply. D.W. in over the energy range 0. automotive. Linac Conf. Of the more than 20 000 accelerators in operation around the world only a few hundred are used in (applied) physics research.5. In a linear accelerator (or linac) the beam travels through a series of hollow tubular electrodes.6. see Sec. The rf-field and the magnetic field strength are varied to keep the orbital radius of the beam constant.1.1. Physics of Plasmas 17. The years around 1930 can be taken as the starting point of the accelerator era when people conducted development work along different principles. Inside each resonator tube. Humphries. Lund U. This is called a sector focusing or azimuthally varying field cyclotron. Sabbi et al.1.9 Industrial Accelerators R. 2. 5. bunching and acceleration.6.12. Tables 1. 4. 056704 (2010) [6] S.18. In column 3 the necessary accelerator parameters are to be found. Only one bunch at a time is sent through the accelerator. Barletta et al. New isotopes will be developed for the PET-technique. The different types of accelerators used in industrial applications are: 1. 6.320 [8] G. packaging and pollution control industry. petrochemical. PAC 81. In the electrostatic accelerator a charging system conveys the charge from ground to the insulated high voltage terminal (originally by an insulating belt. [4] A. p. In the gap between the dees. It combines the action of focusing.01 C/kgair per mA beam current.1. Proc.) See Sec. In the synchrocyclotron the frequency of the applied rf-field between the two dees is slowly decreased as the particle energy increases to compensate for the relativistic ion mass. semiconductor. and 4 present some examples of industrial and medical applications of accelerators. LA-9234-C (1981) p. see Sec. Industrial and medical applications of accelerators will increase in the future and new applications can be foreseen [1]. NIM A 544 (2005) 285 [9] W.1. the particles feel an accelerating voltage and gain energy twice during each circle. Hellborg.2 MeV and electron beam up to 3 mA. including the plastics. In food industry electron beams are used for sterilization. In column 4 suggestions for more readings are given.205 [5] A. In 1937 the first accelerator for applied use was constructed. Today accelerators are applied in very diverse fields.6.11. The applications are given in column 1. LANL Report. The isotope 27 .6. This accelerator could. 3. see Secs. et al. Along the Alvarez principle the structure consists of a set of resonator tubes having an rf-voltage of the same phase applied to them.1. g. An excellent depth dose can be reached 28 . 99m Tc will be produced with energy. 3 He.1. el stat = electrostatic accelerator. The need for 99 Mo from nuclear reactors will therefore be reduced. A number of hadron (p and 12 C) therapy facilities are under construction. Industrial/medical tions applica- Suggested technique/ method to be used Accelerator parameters: typea /particle /current /energy Casc. ch. For detailed descriptions of different types of accelerators see sections in this handbook and [4].25 in [4].17 in [2] Material (nanoscale) engineering in fields like biomedical tissue engineering.14. 140–400 MeV u−1 [5] Mutogensis of seeds for plant breeding Irradiation by keV – MeV ions Casc.Sec.g.g. d.g. treatment with heavier hadrons (12 C and 20 Ne) offers great potential benefit. Irradiation by MeV ions Casc. el stat /p. Hadron irradiation offers better dose distribution than conventional photon and electron beams do and for relatively radio-resistant tumors. It involves very sophisticated/complicated detection equipment. linac (rare cases RFQ) /several different /a few μA to 100 mA /hundreds of keV (or even less) to MeV To learn more.19 in [4]. 4 He /0.7 in [2]. a demand for MEIS (Medium Energy Ion Scattering) facilities can be foreseen. either inside the body “branchytherapy” or close to the body “teletherapy” Mainly cycl but even linacs are used/ mostly light ions like p. MEIS is performed at projectile energies of 100–300 keV. N2+ :30 keV [6] Clinical use of radio nuclides for therapy Radio nuclides produced by nuclear reactions and placed close to the tumor. [7] 12 C: a The abbreviations used for different types of accelerators are: casc = cascade accelerator.6. synchrotr /p. cycl = cyclotron (and synchro-cyclotron).4 in [3].1 in [3] Fabrication of semiconductor devices and materials Ion implantation of dopants and other ions Filter and permeable membrane production Irradiation of thin films with heavy ions. el stat /heavy ions /e. He. several chapters in [2] Treatment of cancer tumors by radiation Irradiation with high doses of ions Cycl. light and heavy ions up to Bi /1 fA – 100 mA /0. by accelerators.1 keV – 20 MeV ch.1.6: GLOSSARY OF ACCELERATOR TYPES Table 1: Material processing by a high energy Ion Beam. quantum devices. el stat. linac = linear accelerator. N2+ :1018 ions cm−2 /e. el stat /heavy ions /tens of μA /10–100 MeV ch. 12 C / e. see Ch. Sec. optical and magnetic information storage technology etc. ch. To get quantitative information about sample composition and surface structure of nanometer technology products.1 – 10 mA /mainly 10 – 20 MeV ch.and intensity-modulated beams using 3-D scanning. RFQ = Radio Frequent Quadrupole accelerator. synchrotr = synchrotron. followed by chemical etching of the films Casc. see e. d. el stat /protons /1 – 10 μA /2 – 3 MeV [9] Geophysical exploration in the petroleum industry. see e. 36 S.5 in [3] Pollution control (e.g. [8] Dating extremely small samples (down to 1 μg or even less) for geological. cosmological and archeological purposes Accelerator Mass Spectrometry (AMS) Quantifying extremely low concentrations of traces in small samples (down to 1 μg or even less) for e. PIXE. fissionable material etc. combustion emissions. el stat/10 Be. 3 He. single or tandem casc. [7] Material analysis with bulk or depth sensitive nuclear methods Ion Beam Analysis (IBA) including methods like RBS. el stat /10 Be. ERDA.g. 4 He /0. 36 S./extremely low/tens of MeV or higher To learn more.g. mainly for imaging and for tracking physical or biological processes in for example plants or animals Radio nuclide production by suitable nuclear reactions Mainly cycl but even linacs are used /mostly light ions like p.6 in [3] Biomedical use of radio nuclides.1 – 10 mA /mainly 10 – 20 MeV ch. PIGE.1. /extremely low /tens of MeV or higher [8] Industrial use of radio nuclides.19 [4]. Detection of neutrons or gamma-rays emitted from a neutron initiated nuclear reaction Casc /neutrons produced in a target after acceleration of p or d to a few hundred keV ch.6 in [3] Safeguard inspections for explosives. 3 He. see footnote in Tab.4 in [3].Ch. CPA etc. 14 C. [7] a For the abbreviations used for different types of accelerators. welding dust. transport) Analyze with the PIXE-technique casc. ch. moisture content measurements in timber and construction industry Detection of gammarays emitted from a neutron initiated nuclear reaction Casc or sealed tube generator /neutrons produced in a target after acceleration of p or d ch.1: INTRODUCTION Table 2: Material characterization by a high energy Ion Beam.22 in [4]. 26 Al. 41 Ca etc. d. mainly for imaging and radiotracers to track physical or biological processes Radio-nuclide production by suitable nuclear reactions Mainly cycl but even linacs are used /mostly light ions like p. biomedical and environmental purposes Accelerator Mass Spectrometry (AMS) tandem casc. 29 in . 4 He /0. el stat /light ions /μA /a few MeV ch. chemical weapons. 14 C. 26 Al. 41 Ca etc. Industrial/medical tions applica- Suggested technique/ method to be used Accelerator parameters: typea /particle /current /energy tandem casc.1 – 10 mA /mainly 10 – 20 MeV ch. x-ray or neutron irradiation a For Accelerator parameters: /particle /current typea /energy Synchrotron producing xrays of 1 eV – 100 keV (far infrared to hard x-ray) To learn more.2 in [3]. see footnote in Tab. 2009 [3] R. Ion Beams in Nanoscience and Technology.7 in [3].g. el stat /electrons /10 μA – 100 mA or more /up to a few MeV To learn more. G.46 [2] R.8 in [3]. air cargos. see e.1. cutting. [13] the abbreviations used for different types of accelerators.6: GLOSSARY OF ACCELERATOR TYPES Table 3: Material processing by a high energy Electron Beam. 27:5. ch.). References [4] R.1. vulcanization and several other similar industrial processes Irradiation by an electron beam with doses up to 100 kGy Material processing like welding. T. Hamm (eds. H. see footnote in Tab. Industrial Accelerators and their Applications. el stat /electrons /up to 1 A /up to 200 keV (in rare cases MeV) ch. Springer.W.Sec. ch. Springer. quality control and control of regulatory requirements Spectroscopic and imaging technique by x-ray irradiation Computed tomography (CT) or 3-D scanning of industrial products. Metrology of internal structures of complex parts or assemblies.W. Zhang (eds. Brown. Hellborg (ed. Vienna (2007). Table 4: Material characterization by a high energy Electron Beam.J. disinfection. 22-24 (2010) [6] Introduction to ion beam biotechnology. p. Y. Physics Today.E. June 2011.28 in [4] Electron beam irradiation casc.E. hazardous waste etc. Skog. K. Hellborg. [10] Irradiation with high doses of electrons or by x-rays obtained after the electron beam has collided with a target linac /electrons /doses up to 2 Gy per treatment /10 – 20 MeV [11] the abbreviations used for different types of accelerators. Atomic Energy Agency. see e. Hamm. Mass Spec Rev. Industrial/medical tions applica- Suggested technique/ method to be used Production.g. Hamm.). Trans. Intern. heat treatment and melting Treatment of cancer tumors by an external beam a For Accelerator parameters: typea /particle /current /energy casc. Whitlow. Vilaithong. drilling. 398 (2008) [1] R. L. Non destructive testing and inspection of e. Springer. I. Electrostatic Accelerators – Fundamentals and Applications. Industrial/medical tions applica- Suggested technique/ method to be used Sterilization. CERN Courier 50:5. 2005 [5] IAEA-TECHDOC-1560. [12] linac /electrons /absorbed dose up to tens of Gray/up to 10 MeV (quite low xray energy for micro and nanotomography) ch. Yu.g. M. Hamm. World Scientific (2012) 30 . M. Hellborg. polymerization. Noda.1. 2006 [7] IAEA Technical report Series 468 (2009) [8] R.). Vol. In this frequency regime.G. more general “structures”. It is now under study. Radiation Therapy.1: INTRODUCTION [9] S. UCLA The rf linac has evolved continuously from its birth after the World War II. The success of these devices is undeniable. Rosenzweig. many inspired by optical sciences. Power et al. Particle-Induced X-ray Emission Spectrometry (PIXE).A. to obtain high powers at short λEM new sources must be considered. While the IFEL has shown more experimental progress than the DLA. Wiley. OH (2000) 1. 7 (2007) [13] R. The problem of miniaturizing the linac has been recognized and has stimulated research aimed at reinventing the accelerator scheme based on new physical principles that use lasers. P¨aa¨ kk¨onen). Malmqvist. IFEL staging was shown at BNL [4]. Further. K.. D. for sub-GeV applications. Pub. These structures. which has extended the utility of IFEL for micro-bunching [6]. showing laser injection and asymmetric (flat) accelerating beam. Brune.E. Campbell. Scandinavian Sci. 20-4. Outdoors and in the Workplace (eds. American Soc. from [2].1. arguing for diminishing λEM by at least an order of magnitude.6. in Radiation – at Home. C. when P is a limiting consideration. metals are too lossy to be of use. J. with 14. Axisymmetry. its application to high energy physics accelerators is limited by synchrotron radiation. with DLA-based acceleration demonstrated [3]. Bossi et al (eds. the first giving micro-bunching and the next accelerating the beam with small energy spread. Synchrotron Radiation News.R. This experiment also displayed the higher harmonic IFEL interaction. photonic band-gap structures. High energy gain was shown later at UCLA [5]. both the size and cost of these “big science” machines has reached the billion-dollar level. Persson and R.R. Advanced accelerators aim to enhance field gradients to >GV/m (allowing a TeV machine in a km). essential 31 . To exploit higher fields. which rotate the laser’s transverse electric field to give longitudinal acceleration. Such devices have undergone testing at SLAC.4.10 Figure 1: Schematic of laser-structure accelerator. the limit on maximum power and stored energy available and.g. by structure breakdown.5 MeV injected beam accelerated to ∼35 MeV peak in 25 cm. Present rf linacs are limited in acceleration gradient to < ∼100 MV/m by two effects: first. With such high P . Welding Journal. Persson. however. The IFEL interaction for micro-bunching is now a common tool for injection into optical accelerators. the paradigm for accelerating structures may be changed. as in the inverse free-electron laser (IFEL). Columbus.R. however. 79-2.Ch. These studies have recently concentrated on pre-bunched beam injection. are fabricated of low loss dielectric that gives breakdown limits in the GV/m range.R. power and field energy considerations have yielded an optimization at shorter rf wavelength λEM . with the insistent demand for increasingly high energy.E. Non-destructive Testing Handbook. 35 (2000) [11] B. Johansson. for Non-destr. B. Dielectric laser accelerator (DLA) structures have been developed in a wide variety of designs.L. DLAs promise more control and Laser. the particle trajectory may also be bent to have a periodic transverse component. To reach present limits. second. with the optical-scale bunching provided by an upstream IFEL. Testing. 1995 [10] D.). in X-band. Wakefield and Plasma Accelerators J.H. Nasta. R. which easily produces copious infrared-to-optical power P . an innovation made possible by the development of high power microwave sources for radar. plasmas and wakefields (advanced acceleration techniques) [1]. Oslo 2001 [12] K. such as inverseCompton scattering (ICS) production of MeV photons for nuclear materials identification. Kao. to >TW. can be relaxed in favor of structures that closely resemble laser resonators [2]. two stages of IFEL were synchronized. the present approach to accelerator design must be abandoned in favor of new. On the other hand. as in Fig. e. Hellborg.-C. The most obvious coherent EM power source available is the laser. e.7. Further.96 n0 (cm−3 ) V/cm. this is ∼100 GV/m. kp σr < 1). The use of slab structure with asymmetric beams permits acceleration of higher charge trailing beams. a UCLA-SLAC-BNL-Penn State consortium. Further.1. for a modest plasma density of 1018 cm−3 . and also strongly suppresses transverse wakefields [12]. The scenario in which a drive beam excites plasma waves that support large Ez is termed the plasma wakefield accelerator (PWFA) [13]. i. This need has stimulated the invention of wakefield acceleration. there is no readily available EM power source that can generate Ez > GV/m in a THz-scale structure. In the linear regime. For Ez > 5 GV/m. BNL ATF. and are now developing asymmetric (slab) structures [11]. in the mm-THz regime. 32 . the dynamics requirements are relaxed. with a structure. in the N ∼10−9 m-rad range. and a key breakdown mechanism in dielectrics. where the plasma density n0 greatly exceeds the beam density nb . as relevant time scales are 4 orders of magnitude smaller than in current devices. As many schemes utilize geometries that are subλEM in one transverse direction. the drive beam pulse (or train) must have significant Fourier components at this frequency. and scale to high-energy application well. the wake wave is an electrostatic oscillation with plasma frequency ωp = kp c = 4πe2 n0 /me . the normalized emittance in this direction must be very small. Here. Simultaneously. avalanche ionization. This drive beam may be of lower quality and energy than a trailing. DLA research presents many challenges. while much shorter λEM is still demanded. When nb ≈ n0 Ez approaches EW B . With sub-100 fs beams available in recent years. Thus. accelerating beam. is mitigated. To excite a high frequency mode.3.6: GLOSSARY OF ACCELERATOR TYPES The first DWA experiments in the high frequency rf regime (∼30 GHz) at ANL [8] achieved field gradients up to 100 MV/m. Subsequent experiments at UCLA have demonstrated that the CCR exiting a DWA tube is quite narrow band [10]. coherent x-ray source. yielding a unique high power THz source for frequency-specific applications. When one uses a dielectric structure in such a scheme (Fig. the drive beam may be specially shaped (in. The first PWFA was performed at ANL [14]. where the wave breaking field EW B ≈ 0. this combination is now under study to give compact. the excited field Ez ∼ = Nb e2 kp2 /2∼(nb /n0 )EW B .13) with extreme focusing strength for a linear collider final focus. First measurements at SLAC FFTB have shown that > 5 GV/m fields can be excited in a SiO2 DWA before breakdown [9]. in which the EM fields of the accelerating wave are created inside of the structure itself by an intense. However.g. these advantages are shared with many optical accelerator structures. Ultimately. GV/m DWA fields became accessible. it is called a dielectric wakefield accelerator (DWA). a rising triangular current profile) to give much larger acceleration in the trailing beam than deceleration in the driver. These programs will explore breakdown mechanisms. and the nascent SLAC FACET facility. where Nb is the number of beam charges and ω is the EM frequency. options midway from rf to optical. Indeed. that is to be plasma. are attractive. relativistic particle beam. As long as the wake is efficiently excited (kp σz < 1. the GALAXIE project. The case with kp σz > 1. These may be most attractively obtained from a laser structure or IFEL accelerator. it was proposed to use plasma wakefields for creating lenses (Sec. the longitudinal dynamics is very challenging. The field scaling of the coherent Cerenkov radiation (CCR) emitted in a DWA is Nb ω 2 . an optical undulator [7] may be built that permits an x-ray FEL using < 500 MeV beams. one must consider the accelerating “structure” to be broken down. DWA research is continuing in many laboratories: the ANL AWA. resonant multi-pulse excitation.2). both the DLA and DWA are limited by breakdown.e. kp σr < 1 and nb > n0 (underdense plasma lens) is most attractive. all optical. acceleration in multi-GV wakes. enhanced transformer ratios. Figure 2: Schematic of dielectric wakefield accelerator showing drive beam hollow dielectric tube generating Cerenkov wakes. this relationship is termed the transformer ratio. producing nearly aberration-free focusing in flexibility than IFELs.Sec. Nature Physics 5. Nature 741. Ion column focusing in the blowout regime was first shown at ANL [18]. high charge (3 nC) beams at the SLAC FFTB. Rosenzweig et al. Byer. 826 (2009) [24] E.P. 21 (2008) [10] A.B. Rosenzweig. Leemans et al.01. Rosenzweig et al. Hairapetian et al. It will explore wakefield acceleration with positrons. Hogan et al.3. 44. Schoessow. 154801 (2005) [6] C. Kimura et al. R6189 (1991) [18] N. 445 (2007) [21] J. Mod. Rosenzweig. PRST-AB 9. Sears et al. Gai et al. Gold. References Figure 3: PWFA field Ez excited by 2 fs. 095003 (2009) [11] G. as the currents supporting the (pure EM) wave lay outside of the bubble. Phys. R. doi:10. and acceleration at > 100 MeV/m observed at FNAL. Esarey. PRL 94.1016/j. Schroeder. 1299 (2010) [2] T. underdense plasma lensing has been observed at FNAL [16]. Nusinovich. Overdense plasma (nb < n0 ) lensing was demonstrated at UCLA [15].H. 20 pC beam. PRL 103.g. W. Plettner et al. PRL 100. PRL 108. New experimental work in PWFA at FACET has begun. S. Ez (see Fig. Tremaine. with fields linear in r and independent of ζ = z − vb t. 81 (1998) [19] M. Indeed. Eds. 81.3). Rev. G. Rosenzweig et al. Murokh.D. including betatron-oscillation x-ray production. 244801 (2012) [12] A.Ch. Leemans. These studies demonstrated a wide variety of effects.J. and a doubling of the beam energy at the drive beam tail [20]. PR E56. 030704 (2008) [8] W.C. 2467 (1995) [3] T. With even shorter beams available at the LCLS (σz ≈ 0. 171 (1985) [14] J. 073105 (2010) [17] J. >kA beams up to ∼1 GeV [22]. Chen. This option is under study [21].6 μm. > 5 orders of magnitude stronger than a conventional magnet. With the advent of short (σz ≈ 20 μm). Pletter. Blumenfeld et al. 696 (2006) [23] M.B. PRL 95.M. 134801 (2005) [4] W. these beams may create a “table-top” FEL [23]. PRL 61. Plettner et al. A. 1229 (2009) an electron-evacuated ion column. Pellegrini. Musumeci et al. NIM A. PA 20. PRL 72. 054802 (2005) [20] I. along with a DWA program. trapping and accelerating plasma electrons to yield N ∼mm-mrad. P. Nature Physics 2. PRL 74. the laser-driven version of the scheme (laser wakefield accelerator. as well the creation of ramped beams and separate 33 .nima. For the example of a n0 = 1018 cm−3 plasma the equivalent quad strength in the lens is 2πen0 = 30 MT/m. with n0 ≈ 8 × 1019 cm−3 . peak Ez in the blowout regime at 10100 GV/m could be reached [19]. Andonian et al. J. 194801 (2005) [7] T. kp σr < 1) where electrons are expelled from the beam channel has considerable advantages [17]. Thompson.S. [1] See. the Advanced Accelerator Concepts series proceedings. Phys. Cook et al.7.S. Further information on LWFA and other laser-driven plasma accelerators is found in Sec.1: INTRODUCTION witness beams. PWFA operation with nb n0 (and kp σz < 1. In addition to the linear ion-column focusing inside the blowout “bubble” region. LWFA) has done so. C. AIP Proc.2011.3) is independent of r just as in a standard rf linac. e.B. While the PWFA has yet to produce a low energy spread and low N beam.B. Fuchs et al. the last being 14th Advanced Accelerator Concepts Workshop.M. PRA – Rapid Comm. 1244 (1994) [16] M. 2756 (1988) [9] M. PRL 92.13 and [24].P. J. 7204 (1997) [13] P. PRL 61. 054801 (2004) [5] P. σx = 77 nm.C.073 [22] W. 98 (1988) [15] G. Barov et al. PRL 95. 111301 (2006). PRST-AB 11. Plasmas 17. PRL 80. PRL 95. Q = 20 pC) a blowout regime PWFA with Ez > 1 TV/m may be created (Fig. Thompson et al. With some improvements in beam quality. C.B. Loew. with typical injector. These linacs rely on rf (typically 0. single-powersource linac. (Secs. however. producing emittance growth and eventually beam break-up and particle loss. Fig. The Brillouin diagram [4]. Δφ is bunch length in units of rf phase.2). The irises or other periodic obstacles create an infinite family of space-harmonic modes (Fig.11 Linear Accelerators for Electrons G. For a given amount of pulsed rf peak power P0 injected into an accelerator section. see below) in that their cell geometry is invariant with respect to longitudinal translation. 2. and accelerate it to a desired energy [1. and what little compression remains to be done occurs during the first few MeV of acceleration (Fig.3). exhibits a second upper-branch (there are an infinity of such higher-order modes.6. when entering the linac. 7. Because a standing wave can be decomposed into two oppositely moving traveling waves. there are also losses and while some power is reflected from the end. Most linac structures are made out of high quality copper which. it is not economical to extend its length beyond the point where ∼70% of the power has been dissipated.6). In both cases.1). corresponds to a TW structure in which this fundamental mode has vp = c at a phase shift of 2π/3 per cell.4.6: GLOSSARY OF ACCELERATOR TYPES 1. The gridded triode gun is sometimes replaced by a laser-driven photocathode or an rf gun where the cathode is embedded inside an rf cavity. The periodic loading is necessary because a smooth waveguide would have vp > c.1. Generally. the structure is designed so that the phase of the wave is synchronized with the beam.6. The rf energy is used to launch a traveling wave (TW) or a standing wave (SW) in an array of microwave cavities or cells (Fig. Above a few MeV. The input is matched so that there is no reflection at the source. In a SW structure. 3].12. Multisection linacs are simply constructed by adding sections linearly beyond the first one.5-30 GHz) energy to produce the accelerating electric field. particles are already considerably bunched. The fundamental mode (n = 0) generally has the largest amplitude and is used for acceleration.A. has a finite loss which causes attenuation. 2. The structures shown in Fig. The bunches can then ride at a constant rf phase and corresponding acceleration field.3.6. the remaining power is dumped into a load. (b) Standingwave structure with total reflection at output end and matching input iris (steady state).3. above a few MeV. In a TW structure. the p Load P 3–98 8334A1 Figure 1: (a) Traveling-wave structure with matching input iris and matched load at output.Sec. The wakefields then cause particles later in this bunch or subsequent bunches to be deflected transversely. SLAC High Voltage Modulator Electron (positron) linear accelerators (linacs) are axially rectilinear structures which capture a beam from an electron injector (positron source). the needed rf phase velocity vp ≈ c. or by cell detuning (see below). dc machines no longer work because cumulative high voltages are difficult to obtain. which means that both traveling waves are confluent and produce acceleration (in reality. This problem can be controlled by appropriate solenoidal focusing (at low energy) and quadrupole focusing (at higher energy). Because of the small rest mass of e± . 34 . These modes are commonly called wakefields when they are excited by a beam bunch. the only efficient way of operating a SW structure is in a mode with a πphase shift per cell on axis.1 are periodic (or quasi-periodic. for mode stability reasons. Fig.1. it is possible to match the input so that there is no power reflection in steady state. HOM) which intercepts the vp = c line at a point with negative slope (backward-wave HEM11 mode). Progressive bunching is graphically illustrated.3 (a) (b) High Power Klystron Peak Power P0 ~c/2 Triode Gun 3c/4 c Load Buncher Accelerator Velocity In Out Modulating ~30° ~5° Prebuncher 2–98 ° = ~ 8334A2 Δφ 70 Figure 2: Schematic of a single-section. Advantages and disadvantages of TW vs. instrumentation and control [3]. While the accelerator structure is the heart of the linac. Other important subsystems include rf drive and phasing.7). A further variation of this 35 .e. For a given total energy.9). modern linacs sometimes use rf pulse compression systems (Sec. the structure can sometimes suffer from a parasitic resonant phenomenon (multipactor) in which a surface-emitted electron gets accelerated. If the linac consists of N identical sections. The steady-state no-load energy acquired by a particle riding on top of the synchronous fundamental wave is (1) V = K P0 r where the proportionality constant K < 1 for a TW structure depends on the attenuation of the section. Fig. alignment. water cooling.g. there are other essential components and subsystems.Ch. Because of the high peak power required (typically 4-80 MW). SW structures are discussed in [5]. The first is the constant-gradient structure in which dimensions are tapered so as to decrease the group velocity linearly with length. Fig.6. prebuncher and buncher.2 shows a high power rf source which in most machines is a klystron (magnetrons are used in single-section low energy machines) with its associated high voltage modulator. Typical machines use gradients from a few MV/m up to proposed ∼100 MV/m. All periodic linac structures are characterized by a figure of merit called the shunt impedance per unit length. To increase the peak power. the SW sidecoupled structure invented at Los Alamos [5] is π/2). then the total energy gain is N V . With a peak beam current I. which temporarily accumulate the rf energy in a storage device. assuming no appreciable field reduction due to beam loading.2 also shows an injector with its triode gun. actual phase-shift per cell in e. as is the case in regular constant-impedance structures.1: INTRODUCTION 11–97 8355A44 Figure 3: Typical Brillouin diagram for a disk-loaded waveguide. and then ejects new secondary electrons which produce an avalanche condition (Sec. TW structures may be designed to be quasiperiodic. Two examples stand out. ac power. these klystrons have low duty cycles (∼100 Hz) and pulse lengths ∼ a few μs. focusing. and K = 1 for the perfectly matched SW structure. and one branch of a higher-order HEM11 deflecting mode. after the appropriate filling times) is reduced by a subtractive term ∝ rI. vacuum. thereby enhancing the peak power emitted in a pulse at the expense of its width. The second one is a variation of the former where the cavity dimensions are varied so as to keep the accelerating fields approximately constant while giving the HOM frequencies a Gaussian distribution which causes them to decohere rapidly in time after their excitation by the beam. showing fundamental accelerating mode operating at 2π/3 phase shift per cell. r..6. At low gradients. the length of a linac can be reduced by increasing its accelerating gradient. hits the surface elsewhere (or returns to the same point). the steady-state energy (i. scheme is to equip every cell with four symmetrical side-openings which enable the HOMs with both horizontal and vertical polarizations to leak out into manifolds while leaving the fundamental accelerating mode undisturbed [6]. The fields are thereby caused to be constant as opposed to exponentially decaying as a function of length. 6. Neal et al. up to a point. Energy (GeV) Gradient(MeV/m) frf (GHz) klystron #/linac peak power(MW) pulse length(μs) e− /bunch (1010 ) N x (mm-mrad) N y (mm-mrad) σz (mm) σδ (10−3 ) [a] SLC 50 17 2. proton linear accelerators [2. SLAC-474 (1996) [9] V.856 NLC 2×250 57 11. injectors for high-energy synchrotrons for nuclear and particle physics. Conf.K. etc. Tab.5 4 45 5 1. the international particle physics community is still assessing the possibility of building an e+ e− linear collider in the TeV CM energy range. Electron and positron linacs are used for many purposes [10]. Sec. The largest number of electron linacs (many thousands) are radiotherapy machines which can be found in hospitals worldwide (energy ∼4-30 MeV. Proc. References [1] Linear Accelerators.H. 3] find use as dedicated linacs for nuclear physics. p.14). Beam energies extend to 1 GeV and duty factors to several percent. AIP Conf. darkcurrent producing spurious radiation and backgrounds.7.13). Proc.6. North-Holland (1970) [2] G.. SLAC-R-606 (2003) after full compression. A. Loew et al. Proc. and contamination. Brillouin. At high fields. Talman.1 [3] R. Second Report. and eventually rf breakdown which can make the linac inoperative.6.A.03 to β 0. x-ray radiography.. by proper surface fabrication. Rev.200 [6] R.H. P. Benjamin (1968) [4] L.A. Bharadwaj.0 4 0.1. among the many options proposed in 2003 [12]. SLAC-303 (1986) p. and drivers for spallation neutron production. H− ions (Sec. ORNL First demonstrated in 1947 by Alvarez and coworkers at Berkeley [1]. FNAL A. Septier. Comm.5 1. PAC 97 [10] G. Conf. Proc. Linear Acc.1. treatment and cleaning (Sec. Henderson. ed.15 3.18) or Cockroft-Waltons (Sec. Acceleration is provided by TM010 -like fields (Sec.6) 36 . Linacs of higher energy (50 MeV50 GeV) are used in laboratories for nuclear and particle physics and as injectors into e± storage rings of various types [11]. Lapostolle. and therefore provide acceleration for particle velocities of β 0. electron field emission takes place. one (ILC) using 1. As this article is being written.12 Linear Accelerators for Protons S. Tab. Most of these linacs consist of single sections and power sources. Low energy linacs are also used in industry for sterilization of various materials and products.1.6. Proton Linear Acc. (Sec.1. Wave Propagation in Periodic Structures. x-rays produced by electrons impinging on targets.1 summarizes parameters of existing proton/H− linear accelerators. R. Conf. dust. Proton linacs generally utilize RFQs (Sec.5 0. and LCLS (design) [9]. Dover (1953) [5] R.3 GHz with superconducting technology. The Stanford Two-Mile Linear Accelerator. Linear Collider Tech.Sec.1 gives the parameters achievable by the full SLAC e− linac. NLC (design) [8]. (1996) [7] P.1. (1976) p. Field emission is caused by a variety of surface irregularities. Miller et al. Loew.5 3270 75 1.0 1. Clendenin et al. Aleksandrov.6. which can have a variety of deleterious effects: parasitic absorption of energy.606 [8] Zeroth Order Design for Next Linear Collider. 105 (1983) p.M.04 0.9.63 1. Miller.0 0.6. Peak beam currents reach ∼200 mA for protons and ∼50 mA for H− beams. as well as originally proposed design parameters for the NLC and the LCLS. wakefields. or direct electron radiation.B. Two main designs.6.856 224 65 3.0 70 65 3. impurities.9). and can be controlled.A.6: GLOSSARY OF ACCELERATOR TYPES Table 1: Linac parameters for SLC (achieved) [7]. Another type of structure damage more recently discovered at high magnetic fields is excessive rf pulse heating resulting in copper melting. Often.7) as injectors. and the other (CLIC) using 12 GHz with room temperature technology. Compendium of Scientific Linacs (1996) [12] G.424 LCLS 15 17 2. Linear Acc.03[a] < 1[a] an rf frequency of 1.1. are still being considered. Loew. PAC 95. with pulse lengths ranging from ∼10 μs to 1 ms.4) are accelerated instead of protons to make use of charge-exchange injection in a downstream synchrotron or accumulator ring.0 1.217 [11] J. Int. Emma. 2.25 805 425 201.5 324 324 972 402. the distance between cavities is fixed.0 201. is the most common structure for acceleration of proton/H− beams in the velocity range 0.i is the synchronous phase for cell i and βi is the velocity at the exit of the cell.06 201.4 (∼0. In the second.5 12.i+1 − φs.5).1: INTRODUCTION − Table 1: Parameters of operating proton/H linacs (taken from [4] except where noted).5 148. 13]. In the first.5 MeV to ∼100 MeV) and so constitutes the low-energy portion of nearly all proton linacs.25 805. 37 . DTLs generally operate in the frequency range ∼200-400 MHz. The physical spacing between cells varies along the length of the structure in accordance with the design particle velocity profile. An often stated loss criteria [14. See Sec.5 202.7. and relative beam/rf phase is adjusted by varying the rf generator phase. a long structure with tens or even hundreds of cells is excited by a single rf power source.25 201.3.56 202.6 for a description of the beam dynamics in proton linacs.4. Facility Species Design Energy [MeV] Structure (energy [MeV]) RF Frequency [MHz] IPNS/ANL [5] FNAL [6] H− H− 50 400 Indiana U.07 433 202.03 < β < 0.25 201. 15] demands particle loss rates less than 1 watt of beam power per meter in order to limit residual activation dose rates to less than ∼100 mrem/hr at 30 cm after 4 hr cooldown. placed with a nominal spacing of βλ.0 Peak Beam Current [mA] 12 50 Beam Pulse Length [μs] 90 60 Rep Rate [Hz] 1 17(p) 11(H− ) 37 40 18 0.6 20 50 400 825 5 120 530 150 80 50 30 80 7. DESY MMF/INR H− p H− p H− p/H− 200 35 40 7 50 600 I-2/ITEP ISTRA/ITEP I-100/Protvino URAL-30/Protvino [8] Linac 2/CERN ISIS/RAL J-PARC [9] p p p p p H− H− 25 36 103 30 50 70 400 SNS/ORNL[10] H− 1000 DTL DTL (116) CCL DTL DTL (100) CCL DTL DTL DTL DTL DTL DTL (100) DAW DTL DTL DTL RFQ-DTL DTL DTL DTL (50) SDTL (191) ACS DTL (87) CCL (186) SCL 200. 12. The length of cell i is φs. Drift tubes.5 20 180 1 100 200 150 100 100 180 25 50 20 10 100 10 120 500 500 2 1 1 16. The accelerating field in each gap oscillates at the same phase and frequency (the zero-mode).6 2 50 50 38 1000 60 30 15 Rf structures Drift tube linac The Drift Tube Linac (DTL) (Sec.i + 1 βi λ (1) li = 2π where φs.0 805. each excited in a TM010 like standing wave mode. LANSCE/LANL H− p/H− 7 800 BNL [7] IHEP/Beijing KEK Kyoto U.0 297 297 148.5 805.2 991. The principal challenge in modern highintensity proton linac design and operation is the minimization of beam loss due to halo growth [11.Ch. A full DTL system consists of one or more cylindrical pillbox resonant tanks. provide a field-free drift region during the decelerating portion of the rf cycle.56 198. established in accelerating gaps (or cells) which are arranged in standing-wave multicell cavities of two types. SNS DTL tank 6 (length 6. A seperated drift tube linac structure (SDTL) consisting of short five-cell tanks with quadrupoles between tanks. the FNAL linac [17] and the SNS linac [18]. are gained in application to proton/H− linacs as well. T is the transit-time factor and P is the rf power. Typical requirements are less than 38 .81 provide acceleration in the velocity range 0. and which follow a ∼100 MeV DTL. so that the beam traverses every other cell in the long array of coupled cavities. high accelerating gradients. At higher energy. the effective shunt impedance begins to decrease. The accelerating gradient is usually constant from cell to cell. compact designs. where E0 is the peak axial electric field. for acceleration from 186 to 1000 MeV [21. These include the CCDTL structure [23].4) makes these structures useful for acceleration of a beam delivered by a DTL.6: GLOSSARY OF ACCELERATOR TYPES is in use at the Moscow Meson Factory [19]. The Disk and Washer structure Rf setpoint determination To ensure good quality of the accelerated beam. and PARMILA [28] for generating the linac layout and performing beam dynamics computations. while adjacent cavities are unexcited. therefore making the structure less sensitive to construction tolerances and tuning errors.25 MW to establish the field. Efficient acceleration is achieved by placing the nominally unexcited cells off the beam axis. so that the DTL structure begins to become less efficient than other structures above ∼100-200 MeV. The relative rf phase shift between accelerating cells is therefore π. A high shunt impedance at higher velocity (β > 0. is used at the J-PARC facility for acceleration from 50-190 MeV [25]. Two structures with βg = 0. Either permanent magnet or electromagnetic quadrupoles are contained within drift tubes to provide transverse alternating gradient focusing. although a field ramp is sometimes included to maintain smooth longitudinal focusing. Segments are coupled one to the next by off-axis “bridge couplers” that span the intercavity drift spaces where quadrupoles and diagnostic devices are located. large aperture. Other structures A large number of other structure types have been studied and several have been built. The benefits of SC cavities realized in other applications.55 < β < 0.3. The synchronous phase at each cell (the “phase law”) is selected to provide adequate longitudinal focusing (typically between −30◦ and −20◦ ) and may also be ramped to adjust phase acceptance. and iii) rf losses produce a cavity amplitude decrease only in second-order. A single klystron powers a long coupled cavity linac (CCL) module. has ZT 2 = 39 MΩ/m. and the (excited) cell spacing is nominally βλ/2.34 m). Coupled-cavity structures The various “highenergy”’ rf structures exploit the remarkable properties of the π/2 mode of excitation in a biperiodic array of coupled resonant cavities [16]. the phase and amplitude of the rf cavities must be set and maintained very close to their design values (Sec.10) with geometric-beta (the synchronous particle velocity) βg < 1. and therefore do not contribute to beam acceleration. For a shunt Rf power considerations impedance defined by Rs = V02 /P . An Annular Coupled Structure (ACS) is being built for J-PARC [20]. and so requires an rf structure power of 1. Elliptical superconducting cavities The SNS utilizes elliptical SC multicell cavities (Sec. namely. The cavity is excited in the π mode with cell spacing equal to βg λ/2. The π/2 mode has the following properties: i) the field amplitude in excited cells is independent of cell frequency errors in first order. A DTL with space-periodic RFQ focusing (a RFQ-DTL) operates at IHEP Protvino [8]. The most common coupled cavity structure is the sidecoupled structure used at the LANSCE linac [16]. the shunt impedance per unit length is Z = E02 /(P/L) and the effective shunt impedance per unit length is ZT 2 = (E0 T )2 /(P/L). In the π/2 mode.90. For example.8 MV/m. Design codes The most commonly used design codes for rf cavities and proton linac structures are the POISSON/SUPERFISH codes [27] for electromagnetic field calculation. or for longitudinal matching.7. lower rf power requirements. which consists of many multicell tanks or segments (each of which may have ∼10 accelerating cells) forming a long chain of as many as 200 coupled oscillators.6). SC spoke resonators are under consideration for the lowenergy portion of future high-power proton linacs [26]. all of which operate at 805 MHz. etc.4. every other cavity is excited..Sec. ii) rf losses do not produce a phase shift in excited cavities.1. and the crossed-bar H-cavities (CH-cavity) under study for the FAIR project [24].2. Additionally.61 and βg = 0. E0 T = 2. 22]. 7 0. and less than 1% amplitude error. Wangler.1: INTRODUCTION 1 RFQ transmission [rel.6).W. DTL tuning The rf phase and amplitude must be set for each DTL tank.. Principles of RF Linear Accelerators.] 1. An example is shown in Fig. The solid curves show measured data and the points show results of the model-based fit. Beam-based tuning techniques that make use of model-based methods are best suited. The set points are calculated using the measured data and coefficients derived from the model [32.8 0. In the DeltaT scan method.75 0. An example is shown in Fig. The rf set points and energy of the incoming beam are obtained by comparing the measured curve to the model.95 0. CCL tuning The rf phase and amplitude have to be set for each CCL module.1 [29].9 0. and the cavity field amplitude [34]. 1◦ phase error. Curves with larger phase width correspond to higher rf field amplitude.9 0. so that only properly accelerated beam current is measured with a faraday cup.1 1.85 0.75 0. A phase scan analogous to the one described for the DTL is used to determine the input beam energy and phase. One method. the acceptance scan. 33]. Linear Accelerators. Phase scan signature matching analogous to that described for the DTL can also be used. eds. u. A fit of the measured beam transmission vs rf power to a curve calculated from the model allows the correct set point to be determined.8 0. Low-energy particles are absorbed in an energy degrader. determines set points by comparing the measured beam transmission vs rf phase to the phase width predicted by a model (Sec. Figure 3: Measured difference in beam phase recorded by two beam phase monitors vs SNS DTL rf phase for two different DTL rf amplitudes. An example SNS DTL acceptance scan is shown in Fig. makes use of the measured beam phase at one or two locations downstream of the tank vs the tank rf phase and amplitude.65 0. the beam phase at two locations downstream of the module is measured vs the module rf phase with the rf on and off. Septier.15 Figure 2: Measured beam current vs SNS DTL rf phase for several different DTL rf amplitudes.3 [31].85 Unom = . RSI 26 (1955) 111 [2] T. A.Ch.2. References [1] L. Figure 1: Measured transmission vs rf field amplitude for the SNS RFQ compared to a model prediction.95 1 RFQ field [rel. North-Holland (1970) 39 .2. Lapostolle.4.172 I = 22. u. A second method. SCL tuning The rf phase and amplitude have to be set for each cavity in the SCL. Wiley (1998) [3] P.] 0. phase scan signature matching [30].7mA 0. Alvarez et al. RFQ tuning RFQ tuning requires setting the rf field amplitude only.05 1. Paromonov.1655 [18] J. p.285 [9] Acc. p. p. LINAC 04. Clendenin et al. p.601 [17] C.Sec.6: GLOSSARY OF ACCELERATOR TYPES [4] J. p.ch/Linac96/ Compendium/COMPENDI. McGraw-Hill (1962) 1. The x-ray depth-dose relation is basically exponential. Crandall. X-ray therapy [5. Dooling et al.13 Figure 1: Livingston Chart. KEK Report 2001-14 (2001) [21] C.PDF [5] J. p.42 [25] Y. Treating a tumor deep inside a patient involves significant doses up. LA-5115. Andreev et al. Schmidt. Billen et al. J. Livingston. LINAC 04.3423 1. LINAC 96.773 [8] Yu. LANL LA-UR-98-4478 [29] A. The chart is named after Stanley Livingston who first used this method of showing this history.L.6. Budanov et al. Particle Accelerators.619 [22] G.1) [1]. p. in [3].H. Kim. as is dosecontrol to the percent level. PAC 01. LINAC 1972. Fig. Beam Dyn. JAERI-Tech 2003-44 [10] N. Billen. AIP Conf Proc.1104 [19] V. 1515 [13] F. Nath et al. radiation is now highly effective for cancer therapy [1]-[4]. These doses can be mitigated by multi-port treatments in Livingston Chart D.and down-stream of the treatment field.W. Technical Design Report for J-PARC. Blewett. PAC 05. p. Galambos.1 Medical Applications of Accelerators J. 693 [12] S. (Fig. Alessi et al. PAC 05.97 [30] T. beam-delivery systems must work within these constraints to achieve 3-D conformation of dose to the tumor and avoid unacceptable damage to nearby healthy tissue. PAC 05.cern. LANL Report LA-6374-MS (1976) [33] A. LINAC 04.web.1. Hartill. J. LINAC 02.V.1013 [16] E.3) References [1] M.H. PAC 01. Holtkamp. PA 48 (1994) 169 [31] J. private communication [32] K. Allen et al. LINAC 96.1491. Cornell U. Gerigk et al. Aleksandrov. CERN/PS 96-32(DI). p. PAC 93.554 [26] S. HALO 2003. Precise tumor definition with CT and MRI imaging is crucial. p.C. The historical rise of the beam energy of accelerators when new technologies were developed to accelerate particle beams can be graphically illustrated by the Livingston Chart. A. PAC 03.6. LINAC 04.1 shows energydeposition characteristics of radiation modalities used.1653 [6] L. p. Groening et al.569 [14] 7th ICFA Mini-Workshop on High Intensity. PAC 01. Wkshp.549 [27] POISSON/SUPERFISH.P.341 [24] L. 6] is the most widely used radiation treatment. where the center of mass energy is twice the beam energy for equal energy beams (Sec.6. The chart in Fig. http://linac96.G. p. LBNL Radiation therapy Ionizing radiation in sufficient doses kills cells. Owens et al.837 [11] Proc.484 [23] J. LINAC 94.114 [20] V. EPAC 02. High-Brightness Beams (1999) [15] N. Catalan-Lasheras et al. The important parameter for new particle production and interactions is the center of mass energy which depends on the fixed target particle mass in addition to the beam energy. p. Alonso.3064 [34] S.329 [7] J. p. Knapp. As a result of much biological and clinical research.1.6. Henderson et al. p. LINAC 04. Feschenko et al. PAC 01. Galambos et al. LANL LA-UR-961834 [28] H. p. p.14. Ciovati et al.14 1.H. p.A.1 assigns an equivalent beam energy for the colliders 40 . Rode. p. PAC 05. p. 29th ICFA Adv. Takeda. p.S. Yamazaki. so heavier ions in addition to having sharper stopping points are more lethal to malignant cells. Ionization density for charged particles varies as Z2 . Average beam current of a few nA yields dose rates adequate for treatment times of ∼1-2 min for all but the largest therapy fields.1 reveals the advantage of using heavy-charged particles (instead of e− ) for therapy. A continuous beam is preferred. Initial ion treatments used neon. Elekta. The more advanced delivery systems now being developed require energy variability. the primary hurdle to widespread application has been limited availability due to its high cost. With overall lengths of 1-2 m. X-rays are produced by electrons striking a heavy-metal target. and are now in clinical use at several facilities. but today carbon is the ion of choice for sparing of normal tissue on the entry path and good cell killing in the stopping region. GE. The wider proton curve arises from the higher multiple Accelerators for proton therapy Proton energy of 250 MeV allows penetration to 30 cm in tissue. The first hospital-based proton therapy accelerator was the synchrotron at Loma Linda. Accelerators for x-ray therapy 5-30 MeV Sband electron linacs are the mainstay of radiation therapy today (∼5000 worldwide. Even with less sophisticated delivery systems. with a duty factor > 25%. and successful clinical programs with these beams have been ongoing for more than 50 years. The development of the isocentric gantry (patient lies stationary while the xray beam is rotated around the tumor) facilitates IMRT. requiring only a fast and reliable beam cutoff system. Uppsala). precise beam-intensity control and above all high stability and rapid response. Computer-controlled IMRT (Intensity-Modulated Radiation Therapy) adjusts the entry angle. dose distributions of protons and ion beams are considerably better than even the best x-ray systems. principal manufacturers: Varian. Harvard. The control systems for beam-delivery and accelerator must be tightly coupled. dose per field and field shape (with multileaf collimators) to achieve excellent 3-D conformation for fields as large as 30 cm. which beams are brought in from several angles and overlap at the tumor. These “passive” delivery systems are decoupled from the accelerator. Toshiba). Mitsubishi. The well-defined stopping point also makes it easier to conform the radiation dose to an irregularly-shaped tumor by independently varying the position and energy of stopping particles. Figure 1: Energy deposition vs depth for various radiation modalities. Powered by either a magnetron or a klystron. these accelerators operate at repetition rates up to 1 kHz. the large therapy fields (≈ 20 cm dia. First recognized by Bob Wilson in 1946. Interfacing an advanced delivery system with a short-pulsed beam presents difficult problems. Proton and ion-beam therapy [7]-[13] Fig. The very broad bremsstrahlung spectrum is “hardened” by using absorbers to filter out contributions from lower energies. In these first facilities. 41 . Pencil-beam scanning systems have been designed for this purpose. very compact accelerator and beam transport systems are possible. the Bragg Peak at the end of the particle’s range can provide a significant concentration of dose into a tumor. the range of the beam was varied by energy degraders in front of the patient. Early proton therapy was performed with fixed-energy synchrocyclotrons (e.Ch. efficiency and reliability have been key to their acceptance for clinical applications.1: INTRODUCTION scattering and range-straggling of protons. the tail of the carbon curve comes from nuclear breakup of the projectile into lighter (longer-ranged) fragments.g. treatment port orientations were adjusted by moving the patient. Up until recently. and low rigidity of the electron beams. Their compactness.) at the required uniformity (≈ 5%) were produced using sophisticated scattering foil techniques. S-band linacs are a highly successful spin-off from high-energy and nuclear physics programs. starting in 1997 treated 440 patients with carbon. or oblique for their carbon beams. Beam is transported to two fixed-beam rooms and three gantry rooms.6: GLOSSARY OF ACCELERATOR TYPES stallation of units started in 2012. Isocentric delivery is now standard. Because of the high rigidity of the proton beam (up to 2. Several thousand patients were treated with π − in the 70’s/80’s at LAMPF. is now running. p¯ is out of economic reach for today’s technology. It has two fixed-beam rooms. The CPACLLNL high-gradient DWA (dielectric wall accelerator) induction linac aims for 100 MeV/m accelerating gradient. Operating on a 2-s cycle. corresponding to a magnetic rigidity of 6 T-m. injected by a 2 MeV RFQ with a single-turn kicker. completed in 2001 has treated 4000 patients with carbon and protons. Treatments with helium beams began in the mid 1950’s at Berkeley’s 184 Synchrocyclotron. employing a sophisticated scanning system with control of all accelerator parameters for each pulse. Linac energy-boosters are being developed in Italy. The field is advancing rapidly. from ion source out. and to more are under construction. As much as 3 m between the last bending magnet and the patient (isocenter) is needed for treating large fields. and beam-lines serving several independent treatment rooms delivered as a “turnkey” system) IBA (Belgium) leads the pack with ten or more installations of their 235-MeV cyclotron-based system. PSI but disappointing clinical results halted trials. adjustments take a few seconds. All these offer fixed field orientation: either horizontal. Hitachi and Mitsubishi have between them eight slowcycling synchrotron-based systems in operation.5 T-m) gantries are very large (10-13 m dia). Noteworthy is the Mevion 9T superconducting synchrocyclotron. Developing compact accelerators for reducing size and cost of proton delivery is a hot topic today. mounted directly on a gantry in the treatment room. This is a synchrotron-based facility with a 7 MeV/u RFQ/IH linac injection chain and two ECR-based ion-source front ends. while trials with neon (and other ions) at the Bevalac took place between 1978 and 1993. the half-integer resonant extraction provides reasonably flat spills with a 25% duty factor at any desired energy up to 250 MeV. Synchrotronbased systems are capable of pulse-to-pulse energy variation. It has a weakfocusing lattice. For “conventional” layouts (one accelerator. Japan completed in 1994 has two 16 T-m synchrotrons (over/under) capable of 30 cm range with silicon beams and has treated 7000 patients with carbon. Ion source current in the cyclotron must be increased (by up to 103 ) to maintain brightness (dose rate).1. TRIUMF. Cyclotronbased systems use a degrader and collimated energy-selection channel in the transport line. Next major technological hurdle is patient/organ motion during treatment. Delivery and in- Accelerators for ion-beam therapy An energy of 400 MeV/u is needed for a carbon beam to penetrate 30 cm tissue.Sec. but this increases the size and weight of this magnet. and locating dosimetry and field definition equipment. Isocentric delivery presents a formidable challenge. and rapid-cycling compact synchrotrons could provide cost savings. built by Fermilab. FFAG’s (Sec. GSI. and one gantry room capable 42 . but are a long way from meeting clinical-beam specifications. While passive (scattering-foil spreading) systems still account for the majority of installed delivery systems.6. HIT in Heidelberg treated its first patient in 2010.6) could provide energy variability with cyclotron-like beam quality. for clinical intercomparisons. Accel Gmbh developed a compact superconducting cyclotron (based on a Henry Blosser design) and has two operating facilities now. Energy changes in today’s facilities are mostly done outside the treatment room to avoid quality degradation and neutrons. Accel’s cyclotron rights have been purchased by Varian that is now marketing this technology.1. Gantry diameter can be reduced by starting the spreading process before the last magnet. but some do have gantries for proton delivery. The HIMAC facility in Chiba. All existing facilities are synchrotron-based (slow-cycling). The Italian CNAO facility in Pavia came online in 2011. Proton beams generated by highpower lasers are being developed. A third Japanese carbon facility at Gunma. vertical. compact enough to also fit in the treatment room. Most now strive to deliver both proton and carbon beams from the same accelerator. active scanning is rapidly advancing. California. requiring online imaging instrumentation and live tracking by beam. The “star dose” boost from capture of stopped π − and p¯ excites interest in the physics community. Hyogo. However.g. LANSCE (LANL) and iThemba LABS (South Africa)]. Also still operating today are the neutron therapy programs at Fermilab (60-MeV protons deflected onto a neutron target partway down the injector linac). Few remain today because of maintenance issues and recognized need for higher-energy neutrons. the tumor area is flooded with epithermal neutrons which are selectively absorbed by the boron causing more radiation damage to the tumor tissue.5 MeV) proton beams producing neutrons via the {p-Li} reaction. Critical to success is the tumor- 1.g. Neutron therapy Fast neutrons (14-70 MeV) have been used for therapy for over 50 years. using a 66 MeV extraction port from their 200 MeV separated sector cyclotron. Interesting options exist for accelerator-production of this isotope using highcurrent SC linacs producing milliampere beams of > 200 MeV protons.2 Radioisotopes Radioactive isotopes are widely used in both diagnostic and therapeutic applications [14]. IBA has designed a superconducting cyclotron capable of 400 MeV/u Q/A = 1/2 beams (C6+ . Mitsubishi built the Gunma facility. 111 In). Accelerator-produced isotopes are made with proton (or alpha) beams of 35 MeV or lower from cyclotrons (e. delivered either by uptake of injected/ingested material (e. At this time there are no active projects in the US. PET isotopes are short-lived. BLIP (AGS-BNL). over 50. research continues.6. none of which are located on US soil.14. Initiatives now look to high-current (10-100 mA) low-energy (2. Of these. alpha and beta emitters find therapeutic applications. 43 . iodine in thyroid treatments) or by surgical implantation of radioactive seeds (brachytherapy). 201 Tl. the very high ionization density (owing to low-energy proton knockons from nuclear scattering) produces favorable results in radioresistant tumors. detecting activity or hyperactivity concentrations in tissues. While diagnostic isotopes emit hard gammas to minimize absorption in the body. Slow neutron “capture therapy” (BNCT) has a small though faithful following. D-T generators (14 MeV neutrons) were widely used for many years. or single photon emitters and suitably collimated gamma-ray detectors (SPECT). particularly salivary-gland tumors. located at shallow depths.1: INTRODUCTION specificity of the pharmaceutical. isotopes either alone or attached to physiologically relevant molecules. only the U. 67 Ga. 25 m long. are used for functional imaging. Cyclotrons producing neutrons via either {p-Be} or {d-Be} reactions in the 60-70 MeV range were employed in the 1970-80. and iThemba LABS. Reactor neutrons have been principally used in these studies. tumor-seeking pharmaceuticals are administered to the patient. 123 I. Though clinical success has been sparse.g. 99 Mo/99m Tc is the workhorse of nuclear medicine today.or dual-particle (H or H/D) cyclotrons (≤ 18 MeV) close to the end-use clinic. but may restart in the future. offering significant cost reduction and reduced facility size for ion beam therapy. of the full rigidity beam from the accelerator. Two new European projects: MedAUSTRON in Austria and ETOILE in France are under construction. and is actively pursuing further projects around the world.000 procedures are performed daily in the US.Ch. and are produced with small single. Washington machine remains. South Africa. 100-800 MeV protons from TRIUMF. Boron-loaded. Tracers. Research isotopes are also produced at higherenergy accelerators [e. The supply of this isotope is not secure today owing to the age and reliability of the few production reactors. 18 F. Interest in this modality is not widespread in the medical community. It is a prominent fission fragment from HEU (highly-enriched uranium) reactor cores. With depth dose similar to lower-energy x-rays. Protons are extracted by stripping foil dissociation of the hydrogen molecule. maximizing dose to the volume close to the isotopic application. weights over 600 tons and has its scanning magnets upstream of the last 90◦ magnet. Also studied is driving subcritical reactor assemblies with high-current proton beams from FFAG structures. Imaging is possible using positron emitters (PET) such as 11 C. This machine at Harper-Grace Hospital in Detroit is currently off line for economic reasons. localization of dose into a well-defined volume is difficult. H+ 2 ). A 60 MeV SC deuteron cyclotron mounted on a ring in the treatment room provides a compact source of neutrons from dissociation of the deuterons striking an internal target. Commercial production is concentrated in a few centers with elaborate distribution networks to provide rapid delivery of short-lived isotopes. The gantry is 13 m diameter. jsp?query id=0&page=0&osti id=10163935 [13] A. Sessler. TRIUMF (500 MeV) has a maximum field of 5 kG.n) reactions with low-energy (11-15 MeV) cyclotron beams.A.sc. Karzmark.de:8080/dspace/handle/2128/659 [9] Ion Beam Therapy. where Bave is the average ring bending field in T. Biomedical Particle Accelerators. Williams & Wilkins (1994) [7] Particle Therapy Cooperative Group (PTCOG) (http://ptcog. Chomicki. Thomlinson.5. Storage rings e− or e+ beam energies > ∼ 2. Sec. A notable example is the coronary angiography program started at SSRL and continued at NSLS (BNL) and HASYLAB (DESY). Erice. The higher-energy cyclotrons used for production of longer-lived isotopes push the limits of current (up to 1 mA).it/programme.fzjuelich. BNL The idea of muon colliders was introduced by Skrinsky et al [1]. ed. A. Relevant reports: http://www. World Scientific (2009) [5] C. allowing larger emittances for given luminosity. but for higher energies the magnetic field must be reduced to avoid Lorentz stripping (Sec.gov/bridge/product.A.8) of the H− ions. producing a detailed image of coronary arteries with little contrast agent. Chu et al. Scharf. Linz.H. O. mechanical and activation problems associated with beam extraction. [1] R.Sec. the muon bunches collide many times.1. Renner. U. on Hadrontherapy (1993). The number of such collisions is limited by the muon lifetime to nturns ≈ 150 Bave .biblio. http://erice2009.6.psi. Small cyclotron technology has been revolutionized by the development of high-quality H− ion sources. Chapman & Hall (1995). LBL-33749 (1993). Workshop on Hadron Beam Therapy of Cancer. and totally automated. Palmer. magnetic fields in the cyclotron can be high. http://juwel. AIP Press (1993) [3] W. Numan. For energies up to 30 MeV.J.1.gov/np/nsac. Symp. Chu.T. convenor.3).doe. Physica Medica XII (1996) 199 [4] Reviews of Accelerator Science and Technology. requiring high energy electron colliders to be linear and long.7.15 μ+ μ− Collider R. TN).html.2. E. Manufacturers include CTI (Knoxville.gov/mep/NSACI/. Biological and Medical Physics series (2012) [10] Hadrontherapy in Oncology. Elsevier Excerpta Medica. is suppressed. Beam currents for the PET isotope systems are modest (e. 2nd Ed. Springer. http://www. ed. B. Neutrino Factories [2] use many of the same components. Int. Targetry and autochemistry units are usually included. Scharf. Ludewigt. NIM A319 (1992) 295 1. Relevant x-ray energies are in the 10’s of keV range. W. Radiology 47 (1946) 487 [2] W.T. For lower energy rings. self-shielded. IBA (Belgium) and Ebco (Vancouver). The commercially-available cyclotrons are compact.. ed. http://www.osti. References • Because circular. ∝ E 4 /m4 . U. Chou. 50 μA).6: GLOSSARY OF ACCELERATOR TYPES Accelerators for isotope production PET isotopes are most commonly produced by (p. McGraw-Hill (1993) • Synchrotron radiation. phy. C. Vol.anl. resulting in much smaller collision energy spreads.5 GeV are adequate for this purpose. leading to very compact structures.htm [14] NSAC Isotopes Subcommittee. highly reliable. as opposed to electrons. RSI 64 (1992) 2055 [12] W. and “Isotopes for the Nation’s Future” (Nov 2009) [15] W. which solved the thermal.15.g. Medical Electron Accelerators. so that a muon collider can be circular and smaller. [6] F.1 Collider The main advantages of muons for a collider. Chao. are: • Synchrotron radiation. “Compelling Research Opportunities using Isotopes” (Apr 2009). Congress Series 1077 (1994) [11] W.M. Khan.web. in which an exposure taken with x-rays just above and just below the K edge are subtracted.R. Linz. T. 1st Int. Tanabe. Proc. is suppressed. The Physics of Radiation Therapy. high magnetic field dipoles and wigglers are required. 2009. 44 .R. Wilson. as bunches cross (beamstrahlung.ch/) [8] Ion Beams in Tumor Therapy.6. 1.S.2.M.na. providing complete hands-off preparation of isotopes in a form ready for administration. Advanced radiography [15] The advent of high fluxes of high quality x-rays from synchrotron radiation sources has opened up opportunities for diagnostics with monochromatic x-rays.infn. Representative parameters of colliders at 1.1. while only the longitudinal momentum is restored by rf.1 .087 2 5.4 5 0. mμ is the muon mass in MeV.1 12 ≈4 25 72 • S-channel Higgs production is enhanced by a factor of (mμ /me )2 ≈ 40000. LR is the material radiation length. For 6-D cooling. Muons passing through an absorber. the lattice must have dispersion and an absorber geometry that yields greater energy loss at higher momenta than lower.1 & 2. the transverse emittances in the sequence of beam manipulations prior to muon acceleration. Combined with transverse cooling this gives 6-D cooling. are 1. A high intensity 8 GeV proton source.4) appears feasible. But there are challenges: selecting polarized muons is very inefficient. and. Fig. 2. A system of rf cavities bunch the muons and phase rotate [4] them into a train of both muon signs. The initial muon 6-D emittance (2⊥ ) is ∼ 4 × 106 times the specified final value. In the linear case.Ch. This reduces the longitudinal emittance. transverse emittances in beam manipulations prior to acceleration. mμ dγ/ds is the energy loss per unit length. Figure 2: Longitudinal vs. where β⊥ is the beam Courant-Snyder parameter. but increases the transverse.7.5 1. at higher energies. the equilibrium emittance in this process is β⊥ 1 14. A liquid metal target.1 2 1 o ≈ βv 2 mμ LR dγ/ds Figure 1: schematic of Muon Collider. βv = v/c. 3. 45 . A tapered solenoid transports them to a lower field decay region.5 and 3 TeV CM energies are given in Tab.1 15 ≈4 25 72 3 4 .1: INTRODUCTION Table 1: Parameters of Collider Rings. The schematic of the most complete conceptual design [3] is shown in Fig.8 10 0. but ionization cooling (Sec. able to withstand the 4 MW beam. giving ‘emittance exchange’. neutrino radiation is a significant hazard. All components of this scheme have been simulated at some level. Efficient cooling requires β⊥ to be tapered to lower values as the emittance falls.2 gives the longitudinal vs. electron. ring magnets and detectors must be shielded from decay electrons. numbered as in Figs. acceleration and cooling must be fast to avoid decay losses.2. C of m Energy TeV Luminosity 1034 cm2 sec−1 Beam-beam Tune Shift Muons/bunch 1012 Ring <bending field> T β ∗ at IP = σz mm rms momentum spread % Repetition Rate Hz Proton Driver power MW ⊥ Trans Emittance μm Long Emittance mm 1.1. and stochastic cooling are too slow. lose momentum in 3 directions. and a buncher that forms intense short (∼2 ns) bursts. The main components. Synchrotron.087 2 8. Hydrogen is the best absorber material. in a 20 T hybrid solenoid (water cooled copper coils inside superconducting) to capture the pions. 3c) is an alternative 6-D cooler.3 8.2 Muon storage ring neutrino factories The main components of a neutrino factory [6] are the same as for a collider.15. rf in high pressure hydrogen gas does not [16] show the problem. An experiment to demonstrate ionization cooling [13] is under construction at Rutherford Appleton Lab (RAL) in the UK. Final 4D transverse cooling to the required transverse emittance is achieved with liquid hydrogen in high field (30-40 T) solenoids. Chromaticity from the IP is locally corrected to allow low β ∗ insertions. Technical challenges A liquid mercury target has been tested [12] in a proton beam at CERN and has demonstrated multi-megawatt capability.6: GLOSSARY OF ACCELERATOR TYPES 4. showing severe damage of copper surfaces. the loss of rf power appeared acceptable [17]. The collider ring [11] must be isochronous to allow very short (1 cm) bunches. Instead of a collider ring. 11. and low energies.3b). no emittance exchange. whose orientations and tilts are such that one of the long straight sections points to distant neutrino detectors. 2. 6-D re-cooling. ∼ 106 ).6. The Helical Cooling Channel (HCC) [8] (Fig. Merging in the transverse dimensions is done by kicking different bunches into transports of differing lengths (a trombone[9]) to bring them at the same time to differing transverse positions. in fields [14]. 1. with frequencies first low. one of each sign. at 805 [14] and 201 [15] MHz. Figure 3: 6-D cooling lattices: a) HFOFO Snake. but rising as the bunches become shorter. Initial acceleration is in linacs. A cavity with all beryllium end walls is under construction to test if this is a solution.6. Merging in longitudinal phase space is done by phase rotations using rf and drifts. With a small admixture of an electro-negative gas. where the longitudinal emittance rises rapidly from the adverse dependence of energy loss on energy. and the effects of a relatively low intensity proton beam did not cause breakdown [17]. c) HCC. Tests. Tungsten shielding is needed to keep the decay electrons from heating and quenching the ring’s SC magnets. Several possible solutions are under study: 9. 10. 7. It is filled with high pressure hydrogen gas that acts as the absorber and suppresses rf breakdown. 5. Experiments with rf in magnetic fields.75-1. the beam is injected into one or two long race track shaped storage ring. 1. But this is acceptable. 6. far less cooling (a factor ∼ 10 vs.Sec. and reacceleration in vacuum rf cavities. have shown little or no damage on beryllium surfaces. The transverse emittances at this point are still ∼10 times worse than those required. b) Guggenheim. of the now larger combined bunches. The linacs are followed by Recirculating Linear Accelerators. The detector also requires special shielding from these electrons. 46 . By 200 MHz.15. causing damage by cyclic heating. but the longitudinal emittances are ∼100 times better than needed. and then one or more pulsed synchrotrons [10]. 1. It is proposed [18] that field emitted electrons are accelerated by the rf and focused by the magnetic fields. are continued to the lowest technically feasible transverse emittance. with suitable spacing. Energy loss is in wedge shaped liquid hysdogen absorbers.5 TeV). Separate 6-D cooling of each sign in periodic lattices following slow (Guggenheim) helices [7] (Fig.1. and acceleration to lower energies (440 GeV vs. The multiple bunches are merged into single bunches. 0. Charge separation in a bent solenoid. but the requirements are less severe: more smaller muon bunches. focusing and bending by tilted solenoids. have shown damage and/or limited acceleration gradients. the cavities should be superconducting. The muons of the two signs can now be recombined. B. sometimes with focusing properties.web. The target-moderator-reflector design is optimized. Examples: the 800 47 .M. Phys. Hanlet et al. P.bnl. charged-particle reaction.cern. Derbenev.LA May 21-25. PRST-AB 8. In contrast to reactor sources.Ch. fusion (accelerated deuteron beam bombarding deuteron or tritium targets). and using a pulsed time structure. Skrinsky. and spallation [1]. beam intensity. Alexahin. Fermilab-Pub00/108E (2000) [3] R.2)[6. Another challenge is to build the small bore 30-40 T ‘all superconducting’ solenoids for the final cooling.fnal. • Increasing the n target yield. Improvements in surface treatments. New Orleans. Chem. 100. A.16 3. Example: the isochronous-cyclotron of PSI. Sov. and there are plans to test this. Proc. Targets are surrounded by a moderator-reflector layout matched to produce neutrons in the desired energy range (cold. 8]: • C.S. Pavel Snopok.py/access? contribId=65 &sessionId=28&resId=0&materialId=slides &confId=2854 [10] D. Neuffer. J. PRST-AB 8 (2005) 061003.fnal. 12th Int. NFMCC-DOC-553 • Increasing the power of the incident beam.edu/ [14] A. Skrinsky. Klaus. n-scattering is an intensity limited field. Ankenbrandt. Beam channels bring moderated neutrons to the experimental stations surrounding the shielded target station. Summers et al. Palmer. THPMS082 [11] Y. • Sources with long (ms) pulses driven by high-intensity linacs.ppt [12] http://proj-hiptarget.B.cap. Parkhomchuk. PRST-AB 9 (2006) 011001 [7] R. there are three types of accelerator-driven sources (Tab. Muon Collider. Michigan State U. A test that could reach 40 T is under construction [20]. PRST-AB 8. which delivers a c.V.iit. CERN Neutron production methods include fission (reactor-based). Gianfelice-Wendt. 041002(2005) [9] C.W. 072001 (2005) [15] A. isotope and excited-state decay. and is a strong function of the target material and incident beam type. According to the incident beam’s time structure.3 MW at 590 MeV [9]. including Atomic Layer Deposition [19] should suppress the initial electron production. http://www. 12 (1981) 3 [2] N. H. J.B. MUC-NOTE-269 (2003) [5] Y. Holtkamp. realized by increasing the beam energy. et al. eds.gov/mumu/conf/collider -091201/talks/YAlexahin-2-091201. Bross. Finley. there are efforts in: References [1] V. Because of the weak interaction of neutrons with matter and the engineering heat transfer limit on n production methods..w. which are essentially c. Lower fields give somewhat lower performance.w.bnl. 7. The latter three accelerator-driven sources rely on charged particle beams bombarding metal targets to produce n beams. Yonehara. e− -bremsstrahlunginduced photon production and photonuclear reaction. http://indico.cap.6.1: INTRODUCTION 1. Palmer et al. R.http://mice. Conf. Lengeler. acceleratordriven sources have the advantage that they can be pulsed. V. Johnson.bnl. • Increasing the n transmission efficiency. guides with high-reflectivity. D. proton beam of 1. Weggel et al.w. Neutron yield increases significantly with the incidentparticle energy. Berg et al. J.ch/proj-hiptarget/ [13] MICE. Proc.pdf [8] Y. http://www. High peak flux is of interest for most n-scattering types of measurements. Proc. EPAC 2006. thermal. Wei. http://www. George. PRST-AB 12.W. A. Palmer et al. Ott. Moretti et al. Parkhomchuk. Accordingly.cap.gov/mumu/conf/ MUTAC090406/talks/PSnopok1-090406. A.N. MOPPC036. 13121 (1996) [20] R. AHIPA09 [4] D. PAC 07.N. (1983) 485. are used. http://www. HTS materials have sufficient current density for even higher fields. TUPCH147 [17] K. 2012 [18] R.gov/mumu /conf/collider-091201/talks/YAlexahin-1091201.J. IPAC12. epithermal).ppt [6] J. E.V. of Nucl. sources driven by high-intensity electrostatic accelerators or cyclotrons. 031002 (2009) [19] S. Neutron Sources J.gov/getFile. Alexahin.gov/projects/muon collider /FridayMeetings/ (2009) [16] P. Phys.. but it has not been demonstrated. on High Energy Acc. Time of flight measurements require small repetition rate (≤ 60 Hz). in a typical lead target a 1 GeV proton produces 20 neutrons.2-10 GeV.. To keep average linac losses low (∼1 W/m) emittance growth and halo generation have to be carefully controlled at all stages of the linac. and for retuning and operational robustness.3. up to 200 mA peak current is at the limit of present-day technology.w. 4) DTL or CCDTL. 8) target with moderators and reflectors. 3) chopper. The 1-GeV SNS linac consists of H− source. beams of currents up to 350 mA are accelerated with a voltage typically from 60 to 120 kV. Low loss ring injection requires new ways Compact neutron sources In fusion-based (DD. Pulsed sources allow time-of-flight correlation of the incident neutron energy. Long-pulse (ms) facilities have the advantage of a simpler driver layout (i.2) [5. depending on the goal beam power. This avoids the monochromatization needed in c. air. they require an H− linac combined with an AR or RCS filled by multiturn injection and emptied by fast one-turn extraction (Fig. neutrons are produced by the interaction of high energy (GeV) protons with a target. up to 100 mA peak current and down to ∼0. (a) 1 2 3 6 5 4 9 7 p i(t) • Sources with short (μs) pulses driven by a combination of high-intensity linacs and rings. low-emittance H− for low-loss charge-exchange injection into the ring. SCL is preferred to non-SC options especially for duty cycles higher than 5%. A dominant design criterion is ultra low beam losses for avoiding component. 1) H− source. D-T. RFQ. The n yield covers a wide range from 106 to 1011 n/s.1. 9) neutron channels. 5) nc or sc high energy linac. effects of Lorentz detuning. However. and potentially higher integrated n-flux. For a pulsed p beam with its velocity changing during acceleration. A linac starts with a proton or H− source (Sec. Different options for linac and ring energies have been used or proposed (Tab. beam transients and injecting-energy offsets require careful rf amplitude and phase control [2].5).1 π mm-mrad normalized rms emittance are at the limit of present-day technology. SDTL. a pulsed linac with high proton intensity). and the proposed 2. The number of n produced is proportional to the proton energy in range 0. Example: the J-PARC 3 GeV proton rapid-cycling-synchrotron (RCS) supplied by the 181 MeV H− linac and the SNS 1 GeV proton accumulator ring (AR) supplied by the 1 GeV H− linac.1. The SNS’s SCL (6% duty) starts at 186 MeV with each cavity driven by its own klystron and rf control. Linacs for short-pulse sources accelerate high-intensity. Existing and planned spallation sources use a proton energy range 0. (b) Time structure of beams at linac and at ring. LEBT. in order to avoid the overlap of slow n from one pulse with fast n from the next. RFQ (Sec. sources which greatly reduces the useful n-flux. microphonics. DTL.18).1). and tunnel activation and for allowing maintenance and repair on short notice.6: GLOSSARY OF ACCELERATOR TYPES – H MeV LAMPF p-linac at Los Alamos [5].4) followed by one or more sections of SC and/or non-SC accelerating or transport structures. coupled target-moderator configuration. in particular at structural and rf frequency transitions.6.5 GeV ESS p-linac in Lund. MEBT.Sec.7. Duty cycles of up to 100% has been demonstrated for RFQ and superconducting rf linac (SCL). 6. LEBT. Spallation neutron sources In spallation sources [5]. A typical guideline is to limit the average uncontrolled beam loss to be below 1 W/m. The 400-MeV J-PARC linac consists of H− source. Linac Linacs for long-pulse sources accelerate high-intensity protons.7.1). and SCLs of two different β’s. 6) AR or RCS with H− -H+ charge exchange injection. Short-pulse (μs) facilities have the advantage of much higher peak n-flux. 48 . T-T) n generators. DTL (Sec. 7) beam transport to target.1. the 13 MeV LENS p-linac at Indiana University. MEBT. Compact sources based on electron and proton linacs produce yields up to 1014 n/s (Tab. 2) RFQ. 8].e.5-5 GeV. 8 i(t) (b) 1 ms 20 ms t 1 μs 20 ms t 10–97 8355A36 Figure 1: (a) Schematic of a short-pulsed neutron source. and ACS. constr.2. planned Ta. At high injection energies. Extensive space-charge analysis of resonance and equipartition conditions and comprehensive Monte-Carlo simulations (including nonlinear space charge forces) have to be applied with up to 107 macro-particles for a realistic layout between H− -source and ring injection [17].45 1 cw - - 0.0075 Rep.1 25 1. 45MeVe-linac 13MeVp-linac 13MeVp-linac W+Pb Be Be Ave.RAL [10] SINQ. Stripping foils have of halo containment.3 (1) 25 8.6 GeV RCS 2.27 1 60 10 0. n-yield (1013 ) (n/s) 0.Tsinghua operat.7 0. Name Status Accelerator type & energy Target type IPNS. Pulse beam rate length at power (Hz) target (kW) (ms) 1 50−100 10−8 −3×10−3 13 20 2 16 50 0.5 GeV linac Average beam power (MW) 0.12) is identified to be a loss mechanism for H− beams and studied at the SNS linac [18]. 12] J-PARC [13] Tokai CSNS [16] Dongguan ESS Lund operat. 49 .7. constr. rate (Hz) 30 Protons per pulse (1013 ) 0.4. collimation and beam cleaning.08 20 3 0. Upon charge-exchange injection using a stripping foil.g. Name Status Accelerator type & type energy Target Hokkaido LENS.Ch. >5 MW) the use of multiple rings may become mandatory. low magnetic fields have to be used to avoid magnetic stripping (Lorentz stripping.1: INTRODUCTION Table 1: A few existing and planned compact sources.3 1 0.6 0.3 Pulse length at target(μs) 0. 8-GeV linac proposed by Fermilab). Rings [19] The SNS AR of 248-m circumference accumulates 1 MW p-beam (2. 35 A peak current). U Zr. The average uncontrolled beam loss is ∼1 W/m limiting the performance. Intrabeam stripping (Sec. The J-PARC RCS presently accelerates 300 kW p-beam from 181 MeV to 3 GeV.16 50 2. At very high beam power (e. elaborate painting with correlated 4-D or 6-D phase space fills the ring acceptance as uniformly as possible. ORNL [11. diagnostics.Indiana CPHS.5 Ave. Sec. The ultra low injection losses also require the transport (HEBT) between linac and rings to have a precise control of energy (energy-deviation correction by a rotator cavity and energy-width spreading by ramping or a spreader cavity) and a removal of halo particles by betatron and momentum scraping. Rep.16 4 5 Table 2: A few existing and planned spallation sources. 1985− operat. black-body stripping further limits the maximum field strength of the magnets [3].1 0. Large ring acceptance (typically >400 π mm-mrad) and good magnetic field quality (∼10−4 deviation level) are needed for keeping effects of space charge and magnetic resonances at a tolerable level.ANL [5] 1981− 2008 operat.g.PSI [9] LANSCE LANL [5] SNS. W.1. Pb W 800 MeV linac AR 1GeVlinac(nc/sc) Hg AR 181(400)MeVlinac Hg 3 GeV RCS 80 MeV linac W 1.8 5 20 62 2000 At ultra-high energies (e. operat. 50 MeV linac 500 MeV RCS 70 MeV linac 800 MeV RCS 590MeVcyclotron U ISIS. 1996− 1985−PSR 1975−linac operat.5 0.9×10−6 duty.8) of H− s. white neutron source applications. Herling.7. Neutron targets [5] For spallation sources.4.2. depleted U) and liquid (Hg.99 (Academic Press) [2] J. Long straight sections are used for rf. high reliability and short down-times are essential. Pb. Momentum scraping is essential for RCSs to control the beam loss during rf trapping and ramping.14). Effects of any beam-induced electron cloud are mitigated by vacuum-chamber surface coating.2.4. low impedance beam lines are essential.6. The coupling impedance of extraction kickers and the pulse-forming network is minimized [21. (ii) ramp up tunes to minimize effects of space-charge depressions during beam capture. Methods of Experimental Physics. solenoidal magnetic fields. Remote handling devices are used in areas demanding frequent maintenance. accelerator production of tritium.7) are needed to avoid beam losses at extraction. Y. J.000 appm – atomic parts per million – of He produced by transmutation). At ISIS. and (iv) lower tunes to avoid coupling resonances at extraction. The efficiency of rf trapping can be increased by using a low frequency. Radiation resistant materials are used in areas of high radio-activation. G. For RCSs with ceramic vacuum chambers either internal rf-cages or external metal stripes are used [10. Particles are brought to the target station with large acceptance transfer lines which may contain multipole elements to flatten the beam density profile at the target. The ring lattice is generally based on a high periodicity and transition energy (Sec.9 should not be passed.6: GLOSSARY OF ACCELERATOR TYPES supply neutrons to a large number of experiments (∼1000-2000/yr).a. and Ga-liquid-metal cooling has been proven out [26]. Adequate shielding. the tunes are adjusted to (i) compensate for the natural chromaticity and the varying magnet field at injection.15). dual-harmonic rf-system and by chopping the injected H− -beam (at the linac front end) at the ring revolution frequency.23. Carpenter. Betatron scraping efficiency is improved by a two-stage system with acceptances significantly smaller than the rest of the ring.H. 319 [3] H. p. water-cooled Li and Be targets are in use. and 10. transmutation of nuclear waste. 8] (Sec. High availability. W. Ch. 23.C. Wei et al. muon storage rings (Sec. for the production of radioactive beams or muon beams. Fast kicker magnets (< 200ns) (Sec. Optics 53 (2006) 45 50 . Liquid targets in pulsed operations suffer cavitation-induced pitting damage to the surfaces of target vessels. an efficiency of about 98-99% so that a high intensity of partially stripped H0 particles has to be handled in the injection region.g. Bryant.2. 13]. Its use for irradiation facilities is also being considered. Rotating solid targets are studied for multiMW class sources. For compact sources driven by lower energy proton beams. (iii) reduce tunes during the time from 2 to 4 ms after injection to avoid transverse resistive wall instability. Stainless steel specially treated and hardened by the kolsterizing process is in use. 8]. 24]. This combined load and the absence of corrosion and tritium production linked to cooling water circuits are the main reasons for developing liquid targets. and high intensity radioactive beams. water-cooled solid (Ta.Sec. The short stopping range of lowenergy p beams causes complications. For MW targets this can become comparable to the range expected in Tokamak fusion reactors (> 100 d. proton radiography.1. Large spallation sources have to References [1] J. but larger than the beam core [24]. Yelon. For short pulses an additional load stems from shock/stress waves produced by the high energy content (up to 100 kJ) of proton pulses.p. Mod. PAC 2001. accelerator driven subcritical nuclear power generation. – displacements per atom – produced by p and n knock-on. Pb-Bi) heavy metal targets with horizontal or vertical injection are in use up to MW range. This low emittance beam presents an interesting source of high energy protons which can be used e. and clearing electrodes to reduce the secondary emission yield [22. beam dumps and fast beam loss monitoring acting bunch-to-bunch are essential. Beam-in-gap cleaning reduces the beam loss at extraction for ARs [25.M. Vol. Collective effects and instabilities are most relevant. Targets have to contain the nuclear cascade produced by protons and withstand high radiation damage. injection. Other applications The accelerator and target technology necessary for spallation sources in the MW-range has requirements which are in many respects similar to the ones needed for future high power proton accelerators envisaged for neutrino factories.B.1. extraction and scraping systems. the Z-machine at Sandia uses 36 modules in parallel). p. In ultra high current devices the load is connected to the transmission line by a Magnetically Insulated Transmission Line (MITL). the current in the MITL produces a sufficiently large transverse magnetic field between the line conductors to cause the emitted electrons to flow parallel to the electrodes instead of across the electrode gap. 010101 (2001) [25] R. PAC 93. Wang et al. Abingdon. 3 (2000) 080101 [12] N. Davino et al. Letchford. p. Three commonly used loads are: (i) Vacuum diodes with field emission cathodes that produce electron beams. Simple systems of this type produce output pulses of 1-10 MV with pulse durations of order 20-100 ns.2250 [26] B. Modest changes in the pulse duration and the generator output impedance are achieved through the use of tapered transmission lines connecting the pulse line to the load. J.94-025. 2] was first developed by J. The discharge of the transmission line.W. NIM B139 (1998) 82 [16] IHEP Report IHEP-CSNS-Report/2004-01E (2004) [17] K. Adams et al. 975 [11] J. Pulsed High Voltage Devices J. The charging and discharging of the transmission line occurs in ∼1 μs and ≤ 0. into a transmission line. depending on the dielectric used in the pulse line. More recent extensions of the technology produced ∼30 MV Transmission line loads The load depends on the application. RAL Proc. Rees. or water dielectric transmission line as a lumped parameter capacitor. p. J. Macek et al. Bryant.A. which is accomplished by the the use of water-dielectric transfer capacitors as an intermediate low inductance circuit element between the Marx generator and the transmission line. Catalan-Lasheras et al. MIT Thesis (2002) 1. D. p. at impedances of a few to 50 Ω. Witkover et al.S. The transmission lines use deionized water (for low impedance) or transformer oil (for intermediate-to-high impedance) as the insulating material. Cornell U. EPAC 94. The engineering science of Pulsed High Voltage devices [1. UK (1993). Pabstand.241 [20] R. EPAC 00. Rees. through triggered spark gaps. now as a distributed line. p. ICANS XII. Hammer. or oilfilled. Gabriel. NIM A451/1 (2000) 287 [18] V. A. Lengeler. Wei.731 [7] P. ICANS XIII (1995) PSI Proc.6.g.H.Ch. Collaboration on Advances SpallationSources (ICANS).322 [8] J. The transmission line is usually connected to the load by an overvolted gas or water spark gap.1 μs respectively. Aldermaston. UK). ESS-96-53M (1996) [15] H. Breakdown strengths of the dielectrics are ∼100 and 300 kV/cm respectively for pulse durations ∼1 μs and increase slowly (∝ t−1/3 for sub-μs pulses) with decreasing pulse durations.L. p. Int. Vol. EPAC 02. KEK Report 2002-13 (2003) [14] ESS Study Final Report.C. by an order of magnitude and hence increased the available power correspondingly.688 [21] D.A. p. Linac 2010. p. Haines. Very short duration high power pulses require low inductance power feeds.J. Bongerdt. The latter can be charged with a faster rise time from the water capacitor than directly from the Marx generator. Materials 318 (2003) 1 [5] Proc. Nation. Applications of this technology include x-ray generation and inertial confinement fusion. sub-1 Ω impedances. PAC 97 [10] D. Nucl. PRST-AB.A. PRST-AB. 95-02 [6] G. compared to the charging time of ∼1 μs. Blackburn. EPAC 04.J.R. T. M. Lebedev et al. connecting the transmission line to the load. Martin of AWRE (Atomic Weapons Research Establishment.1804 [23] L. PRE 036501 (2004) [24] N. and hence low series impedance..1467 [22] P.837 [13] JAERI/KEK Report JAERI-Tech 2003-044. Electron beams were produced by field emission cathodes.H. PAC 95. [4] T. 4. PAC 01. and power levels of tens of TW. an evacuated transmission line in which the wave electric field causes electron emission from the negative line conductor. Bauer et al. Linac 04. He used a Marx generator to impulse charge a solid dielectric.929 [19] G. p.1: INTRODUCTION output voltage. He et al. leading to a more compact system as well as to the formation of multiple channel discharges. However. McManamy. In sub-1 Ω impedance generators the basic Marx generator-pulse line configuration may be repeated many times (e. (ii) Diodes with 51 . Holtkamp.17 Marx generators/Pulse lines The typical Marx Generator uses plus/minus charged columns of capacitors that are charged in parallel and discharged in series. Wei et al. RMP 75 (2003) 1383 [9] G. PAC 99.III. into a vacuum diode reduced the pulse duration. g. Diodes naturally generate electron beam currents when a suitable polarity high voltage pulse is applied across the diode. especially in the beam production mode of operation. i. plasma electrodes that are used to produce electron or ion beams.18 Radio Frequency Quadrupole J. Pulse transformers Many of the above devices are not well suited to high repetition rate operation.g. Staples. This is accomplished by applying a transverse magnetic field in the diode such that the electron excursion from the cathode is less than the anode cathode gap spacing. square voltage and current waveforms are of secondary importance compared to the peak power output.1.A. e. with the load in the center. Inductive addition Induction accelerators are discussed in Sec. pulse transformers offer the preferred modulator configuration. For applications requiring more modest beam currents. Nation. high power microwave generation. Martin. such as a Z-pinch. [4]. much lower and a degree of tuning is possible. This is especially true in multi-TW devices where the low impedance of the generator leads to a relatively slow increase in the load current. LBNL A Radio Frequency Quadrupole (RFQ) is a compact and versatile accelerator operating over a mass range of protons to low charge state heavy ions. to the dynamics of the imploding Z-pinch.6. Such circular arrays can then be stacked in series in order to drive a higher impedance load. as has been done in the design for the next larger Z-pinch driver by Stygar et al. inertial confinement fusion research and for the generation of intense soft x-ray pulses. klystrons). many such modules are switched in parallel in a circular array using a large. Thyratron switching permits high repetition rate use more readily than that achievable with pressurized gas switches. The voltage of the cathode is then equal to the sum of the secondary voltage outputs of each of the modules. and (iii) Z pinches. Rise times of 100-200 ns are achievable with step-up ratio’s of < ∼ 8. Ion beams can also be generated if there is a suitable ion source. 26 MA. uses 20 1-MV induction modules to produce a 20 MeV electron beam in a single diode. In order to achieve a very high current in a low inductance load.1. Proton and other low atomic number ion beams have been produced this way.Sec. accelerating from a few keV/n for heavy ions with a total voltage integral of up to several MV. For electron beam production the increased injector energy allows larger space charge limited beam currents. The fluctuations in the output of higher impedance devices are. References [1] J. the conductor adds the voltages from the modules. the high voltage output is essential for efficient use of the accelerator power. Pulsed Power.7. For example. 100 ns current rise-time pulse to a Z-pinch. but the ion generation efficiency is low unless the electron current is suppressed. 050402 (2009) [4] William Stygar et al. and reduced beam divergence. The Hermes III accelerator at Sandia. however. 030401 (2007) Linear Transformer Driver (LTD) The fundamental unit of LTD technology is a capacitor switched into a low inductance circuit with soft iron core isolation. Several 1 MA pulsers with rise times of 150-300 ns have been built using this approach [3].8 for a given high-Z target material.6. PA 10 (1970) 1 [3] A. The device is well matched.C. Recent experiments at Sandia have reported the production of 2 MJ x-ray pulses with peak powers of up to 280 TW. Duty 52 . which scales as I·V 2.e. except in burst modes. on the anode. For hard x-ray production. Voltage and current fluctuations For many pulsed power applications.3. The voltage fluctuations can be ∼ 50% and the current rise time is comparable to the pulse half width. Advances in Pulse Power Vol.A. Plenum Press (1996) [2] J. or in series-parallel arrangements to reach ultra- 1. (e. The operating frequency ranges from 6 MHz (for Bi+2 ) to over 400 MHz (for protons). the Z-machine delivers a ∼5 MV. circular iron core to isolate all of them. Pulse durations are typically ∼1 μs and output voltages in the range 300-500 kV. The achievable rise time is strongly affected by the transformer step-up ratio and the core material selection. The above arrangements are commonly used for hard x-ray production. Kim et al. such as a plasma.6: GLOSSARY OF ACCELERATOR TYPES high power. PRST-AB 10. High voltage pulses for radiography or for use in electron beam injectors are frequently produced by the use of a single central cathode conductor as the secondary of several induction modules. however.. PRST-AB 12. and q/A the charge-to-mass of the ion. is of use in determining an optimum parameter space for high-current. the transverse focusing strength and the clear beam aperture decrease. and transmitted current to greater than 200 mA of protons. factors range from 0. giving wide design freedom of the capture and acceleration sections. followed by a short shaper section that initiates the formation of the bunch. input beam is matched at the RFQ entrance to the time-varying transverse beam profile by the radial matcher. f is the frequency in MHz. LIDOS [3] and RFQtrak [4]. The KT formalism is suitable for the design of high-current RFQs. where κ is the field enhancement factor. TOUTATIS is based on PARMTEQM. κ ≈ 1.8 kilpatrick. The sustainable field is expressed in units of kilpatrick. low emittance-growth designs.55. Shortpulse RFQs may be safely pushed to greater than 2. To reduce the truncation error of the two-term field expansion. None of these approaches is straightforward.25 − 1. limiting geometric acceptance. PARI adds higher-order terms and adjusts the cell parameters to maintain the acceleration of the reference particle. the surface field in MV/m. As m and thereby Ez increase. The peak surface field on the vanetip is Es = κV /r0 . The alternatinggradient electric-quadrupole field provides velocity-independent focusing and will transport unaccelerated or partially accelerated beam to the exit. but rather ad-hoc.Ch.5/Es ) for Es . which illustrates bunch resonances as a function of betatron phase advance and tune depression. The transverse limit It scales as βλ2 V 2 φx q/(a2 A) and the longitudinal I as V φ2s a/λ. Beam dynamics codes RFQ design and simulation codes include PARMTEQM [1].7 MV/m. indicating that a low-frequency machine is 53 . φs the stable phase. lower emittance growth and shorter structures may be generated using other design approaches. Depending on the detailed vanetip geometry. without a specific design recipe. The d. typically oc- Space charge The KT approach used in PARMTEQM uses the helper code CURLI to optimize the beam dynamics design at the end of the gentle buncher section where the bunch is formed. restricting output beam energies to less than 2-3 MeV for protons for efficient designs. followed by an accelerating section.643Es2 e−(8. Jameson [5] presents a lengthy summary comparing the above codes.1% to 100%. The helper code RFQUIK assembles a cell table for use in PARMTEQM. The TOUTATIS code. where the displacement of the vanetip from the axis varies from a to ma along the length of the cell. The upper limit of m is constrained by the minimum longitudinal radius which sets the size of the tool used to cut the vane profile. RFQ.0 kilpatrick. PARMTEQM uses the Kapchinskii-Teplyakov (KT) design procedure where the beam is bunched adiabatically with a long gentle buncher section. with a the minimum vane tip radius. The transverse and longitudinal current limits It and I are defined as the current that depresses the tune by typically 60%.4 MV/m at 400 MHz. but greater bunching efficiency. so the tune depression is at a maximum. V the vane-to-vane peak voltage. and treats transverse beam loss on the physical location of the vane boundary.1: INTRODUCTION cupying more than half of the physical length of the RFQ. used during the design of the IFMIF c. adds field maps. The Hofmann diagram [6].w. typically 4-8 cells. PARI uses a look-up table for a limited number of vanetip profiles. One kilpatrick at 200 MHz is 14. Ez (z) scales approximately as (m−1)2/3 . the shunt impedance drops off as β −2 in the accelerating section. RFQs held to less than 1. The Ez (z) profile may be chosen arbitrarily. the charge density is high and the energy is still low. found by solving the implicit equation f = 1. but removes the paraxial approximation. The transverse phase space acceptance of an RFQ increases rapidly with the design field gradient. The LIDOS and RFQTRAK codes also include field maps for a more accurate evaluation of the beam characteristics.w. and a PIC formulation of the space charge forces. allowing arbitrary cell shapes and gaps in the vane. V is the peak rf voltage between vanetips. with c. requiring significantly more computational resources. solves the boundary-value problem for the actual vanetip geometry in each cell. As a Sloan-Lawrence accelerator. TOUTATIS [2]. and r0 is the average vanetip displacement from the beam axis. Ez (z) is controlled by the vane modulation parameter m ≥ 1. as well as the magnitude of the multipole components of the fields. Beam dynamics An RFQ comprises an alternating-gradient time-varying electric quadrupole strong focusing transport channel with an accelerating field Ez (z) added as a perturbation by modulating the vanetip profile. and 19.c. HFSS [10]. However. moving the TE110 where δf0 (z) is the localfrequency variation due to mechanical errors and (δf0 ) = 0. producing a quadrupole E-field. A program that specifies tuner settings by solving 54 . the dielectric bead only E-field stored energy. or π-mode stabilizers for high duty-factor RFQs. Several methods have been used to increase the dipole-quadrupole frequency separation. The 4-rod structure avoids the TE110 mixing problem by supporting opposing vane pairs on quarter-wave stubs. which may be estimated with 2-D codes such as SUPERFISH [1] or URMEL. The metallic bead removes both E. A typical frequency range is 100 to 425 MHz. or even lower. Example codes include CST-Microwave Studio [9]. shortened due to the additional capacitive loading of the vanes themselves. CAD modeling codes such as ANSYS [12]. Rf structure codes The 4-vane RFQ operates at the waveguide cutoff frequency. used at JPARC and SNS. but a high-frequency machine would have a higher longitudinal current limit. increase the local resonant frequency by removing H-field energy. particularly ones that employ various types of stabilizers and tuners.and H-field.1. The LEDA RFQ uses resonant coupling between longitudinal RFQ regions to effectively shorten each section. require a large range of mesh density to include small details over a large cavity volume. Advances in computational capabilities have resulted in the development of powerful finiteelement and finite-difference codes that permit the characteristics of complex rf structures to be determined. and Omega3P [11]. Opposite vanes may be strapped together with vane coupling rings (VCRs) in low dutyfactor structures. The split-coaxial structure has been promoted for even lower frequency accelerators for lowcharge-state heavy ions and for superconducting RFQ structures. the presence of mode stabilizers and vane end cutbacks require a full 3-D calculation for accurate estimate of the resonant frequency. This restricts the practical length of an RFQ to less than about 5 free-space wavelengths above which mechanical tolerances become severe.Sec. Tuning The 4-vane RFQ is a standing-wave structure where the deviation of local field dE0 (z)/E0 as a function of the local detuning δf0 (z)/faverage is given by the solution of 8π 2 δf0 (z) ∂ 2 δE0 (z) = (1) ∂z 2 E0 λ2 faverage preferred for a large transverse current limit. The field profile may be modulated by the periodic structure of the support stubs. The operating frequency of heavyion RFQs may be in the 50-200 MHz range. Rf structures All RFQs have in common a time-varying electric quadrupole focusing field on axis. The electric field energy is almost entirely within the vane region. The choice of rf structure will depend on the operating frequency. This structure is more compact than the 4-vane structure and has been frequently applied to lower-frequency heavy-ion accelerators. Field errors scale as the square of the length of the RFQ.6: GLOSSARY OF ACCELERATOR TYPES dipole modes higher in frequency and away from the quadrupole mode. which have been used to model RFQ mode structure and surface power density. the 4-vane structure is modified with large cut-outs in the vane base that modify the mode structure. reducing the field perturbations due to local frequency error. The field distribution is usually determined by pulling a metallic or dielectric bead through the RFQ and noting the change in resonant frequency. Both of these potential problems are manageable. affecting bunching. Tuners are introduced along the outer walls of 4-vane RFQs usually in the form of pistons which when moved inward. field distribution and wall power density. and the magnetic field energy mainly around the stubs. Sensing loops may be placed along the RFQ and calibrated by the bead pull to measure the fields during operation. A major drawback of the 4-vane structure is the presence of almost degenerate dipole TE110 modes which may mix with the TE210 quadrupole mode. and there may be a non-zero potential between the ends of the vanes and the endwalls. RFQs. length. Maintaining an adequate focusing phase advance for mass greater than proton requires a longer operating wavelength λ. Here. and power efficiency required. as the vane voltage V and aperture a are already at a practical limit. which also include 3-D electromagnetic solvers as an additional module are used to model the time-dependent thermal and thermally-induced stresses in the structure. The 4-vane structure excites a waveguide in the TE210 mode. adding vanes to concentrate the electric field near the axis. Multiple couplers driven from the same rf source should be isolated from each other to ease balancing the power flow through each. p. p. Proc. Young. Project-X(PXIE) [7] and many others. Abs.839 B.2947 L. The first magnet is usually of a different size as the beam is not yet relativistic. p. At 400 MHz. High average power RFQs RFQs designed for c. Pisent [15] describes several specific designs.cst. Jongen. Energies below 3 MeV are still well served by electrostatic accelerators (Sec. lowering the local frequency. Beam acceleration The Rhodotron is a recirculating rf accelerator based on a unique beam pattern that looks like a flower. operation include LEDA [8].1: INTRODUCTION Eq.A.1. PAC 1981. p. EPAC 2008. is a novel accelerator principle suitable for electron acceleration up to 10-12 MeV. PAC 1997.com K. ORNL/TM-2007/001 I.19 Rhodotron Y. Machines performing up to 12 crossings have been manufactured.5). Linac 2010. the vanes and the RFQ body are supplied with separate coolant temperatures [16] to differentially control the vane length from the body dimensions to hold the frequency constant.6. or in the case of LEDA and the SNS RFQs. Linac 2000. Ko. The beam crosses a number of times at different azimuths a half wave coaxial cavity in its median plane. eases tuner adjustment.(1). (Belgium) developed a range of 5 to 10 MeV Rhodotrons with average beam power ratings from 25 kW to 700 kW at working frequencies of 107 MHz and 215 MHz.1 and 2. an isothermal copper cavity shifts 7 kHz per degree centigrade. Loop couplers are easily adjustable. even if pulse operation is possible. The central conductor of the cavity has two cones at the extremities thereby improving the Q and avoiding HOMs to be excited by the beam References [1] [2] [3] [4] [5] [6] [7] H. Virostek et al. 1987. The field distribution in 4-rod RFQs concentrates the magnetic field energy in the volume around the support studs.ansoft. raising the local frequency. IPAC 2012 55 . This seems to be a practical limit.372 S. Designs tend to lower frequency to reduce the wall power density to keep it below the 15 W/cm2 range with larger aperture to reduce beam loss in the structure. XX Int’l Linac Conf. Hofmann. Active tuners may be required. Pisent et al.de www. The big accelerating cavity has a fairly high Q factor (50.5 MHz) and so has a relatively low power consumption thus enabling c.3542 A. Pisent. This new accelerator principle was the answer to the needs of high power electron beams of more than 2-3 MeV for industrial applications or for intense x-ray production. S. IFMIF [14].com A. p. IBA The Rhodotron. PAC 2001. PAC2001. based on bead pull measurements.69 A. Ion Beam Applications. Each time the beam crosses the cavity it gains up to 1 MeV. Pisent et al. The high power density at the edge of the iris will require special attention. but are limited in the peak rf power that can be introduced in each coupler to the few hundred kW range. See Figs. ACES 2002 Conf. The measured Q-value of typical 4-vane structures runs from 50 to 80% of the theoretical value calculated by the electromagnetics codes. operation.908 http://laacg1. Bondarev et al. Li et al.w. High duty-factor RFQs with high average wall power densities (in excess of 1 W/cm2 ) may change shape due to thermal expansion.2752 R. which couple with the rf H-field. 000 @ 107. At more than 3-5 MeV industrial linac’s have been used so far but with a relatively poor electrical efficiency and limited beam control and intensity. resulting in a redistribution of the field profile. Higher average power may require the use of iris couplers. Thirty machines have been sold so far. Vernon. CEA.ansys. TRASCO [13]. p. maximum at the wall of 4-vane RFQs. M. Jameson. p. Rf power couplers The rf may be introduced through multiple or single loop or iris couplers. invented by Jacques Pottier. Linac 2004.3297 www. Tuners may be in the form of capacitive plates near the rods.6.A.gov R. p.Ch. Smith et al. 2002 www.lanl. The beam is then reinjected by external DC magnets towards the center of the cavity. [8] [9] [10] [11] [12] [13] [14] [15] [16] 1. or in metallic blocks in the vicinity of the support studs. Duperrier et al. The magnets’ position and field are chosen in such that the beam is re-injected with the right phase with respect to the rf field. p.2399 D.w. The electron train must be pulsed at working frequency to allow the beam transmission ∼100%.1).0 × 1012 eV (LHC. This is due to the 56 . This means that the injected peak current is 8 to 10 times the average current. light and heavy. The injection energy is 30-60 keV.6. The kinetic energy of the stored particles ranges from 10−6 eV [2] to 4. Particles stored in rings include electrons and positrons. The beam must be injected into a storage ring but may not be extracted (Fig. Peak current up to 1 A. A beam current control accuracy of 0. Parameters for storage rings such as particle species. atomic. and protons were stored.6. the number of stored particles from one (ESR [4]) to 1015 (ISR [5]).6: GLOSSARY OF ACCELERATOR TYPES fact that the magnets lengthen the beam trajectories and shift the phase when the energy increases. Accelerator rings such as synchrotrons (Sec. Beam focalization Unlike linacs.1% precision in less than 500 μs • Electrical efficiency: up to 55% at full beam power 1. the phase stability is of synchrotron type. positrons. BNL Storage rings are circular machines that store particle beams at a constant energy.1% is easily achieved. To store beam in rings requires bending (dipoles) and transverse focusing (quadrupoles). as well as for experiments in chemistry. The IBA e-guns are based on commercial cathode-grid assemblies that allow good beam control in time and amplitude. Storage rings are used in highenergy.1). molecular and cluster ions [1].1. 7 × 1012 eV planned). and store time vary widely depending on the application. The electromagnetic focusing forces due to the rf field have limited effects except on the first crossing.21) are used as storage rings before and after acceleration. harmonics.20 Figure 2: Vertical section showing the tapered central conductor. beam size. protons and antiprotons. positive and negative atomic ions of various charge states. No other elements are needed to control the beam size.1. and molecular physics. and neutral polar molecules. beam intensity. material and life sciences. muons. Beams are stored in rings without acceleration for a number of reasons (Tab. Spin polarized beams of electrons.Sec. making the machine simple and robust. nuclear. with average currents up to 100 mA. Figure 1: Horizontal section of the cavity showing the beam path and magnet positions. Machine properties summary • Energy range: up to 10-12 MeV per accelerator (more cavities can be put in series to increase energy) • Energy spread: < 300 keV at 10 MeV • Beam current control < 0. The cavity that is excited by an external power amplifier chain based on tetrodes does not require a tuning element. neutrons. Fischer. The extraction of the beam is obvious and allows placing different exits at different energies by selecting to switch off certain magnets. has been successfully injected in the most powerful model. The vertical and horizontal focusing is ensured mainly by the magnets. The small resonance frequency drifts due to thermal changes in the cavity dimensions are followed by the rf generator based on phase measurements on the final amplifier. Storage Rings W. The typical phase acceptance is large and around 60◦ . energy. Beam injection The injection of the beam into the cavity is done with an external electron gun. An amplitude regulation is required to maintain the accelerating field stable at better than 1% as the beam power is changed. Phys. RR. BEPC.7. TSR.7). With strong focusing the beam pipe dimensions became much smaller than previously possible.1). SNS Beam quality improvement: LEIR. HERA. K¨ugler.1267 (1995) [2] K. DIAMOND.12). often leading to an increase in the store time. HERAe. Spring-8 Collision with internal target: COSY.3. PIA. Distributed pumping with warm activated NEG surfaces or cold surfaces in machines with superconducting magnets are ways to provide large pumping speeds and achieve low pressures even under conditions with dynamic gas loads.2. Large storage rings have millions of control points from all systems. For a given circumference superconducting magnets (Sec. Vol. τ can be dominated by a variety of effects including lattice nonlinearities (Sec. W. IUCF.4). beam-beam (Sec. CR. pEDM. the beam lifetime measurement itself can be the purpose of a storage ring experiment [1]. Storage ring light sources are continuously improved and will remain the dominant form for the foreseeable future [7]. respectively. KEKB. The magnetic lattice and rf system are designed to ensure the stability of transverse and longitudinal motion (Sec. p. SLS.2. RHIC. Magnetic multipole functions can be combined in magnets.2.4. and planned machines. UMER Figure 1: Small storage ring (CRYRING at the Manne Siegbahn Laboratory) with main components labeled. MIMAS. In hadron colliders and ion storage rings store times of many hours or even days are realized.72. and to compensate for nonlinear field errors of dipoles and quadrupoles. Issue 3. to suppress instabilities. space charge (Sec. INDUS. 58. and the beam quality. Rep. New technologies allow for better storage rings. KSR Synchrotron light source: ALS. The time dependent beam intensity I(t) can often be approximated by an exponential function I(t) = I(0) exp(−t/τ ) where the decay time τ and. Beam accumulation: AA. U.[3] is the first proposal for a collider storage ring. ISR.2.2. Prog. CLS. TARN. corresponding to up to 1011 turns and thereby target passages. PSR.4. the store time ranges from a few turns to 13 days (ISR [6]). Paul.7.3).-J.3. B. and an ultra-high vacuum system may be needed (Sec. a storage ring allows to reuse the accelerated beam many times if the interaction with the target is sufficiently small.5.9) allow for efficient replenishment of synchrotron radiation losses of large current electron or positron beams. slow extraction: ELSA. ILC DR Stretcher. A number of storage rings exist where the beam itself or its decay products are the object of study.6. Beams are stored bunched with radio frequency (rf) systems.5. In this case. HESR. The largest application of storage rings today are synchrotron light sources (Sec.2. References [1] M. Higher order multipoles are used to correct chromatic aberrations.21). Nuclotron Collider: AdA. PLS. intrabeam and Touschek scattering (Sec.2. RESR.1). LHC. PAR.422 (1978) 57 .1. MIT-Bates. Trinks. AR. correspondingly.4) make higher energies possible. or the lifetime of the stored particle. ESRF. interaction with the residual gas or target (Sec. Ref. existing. Storage rings have instrumentation to monitor the electrical and mechanical systems. Lett.7. and unbunched. APS. Tevatron.2.1: INTRODUCTION Table 1: Storage ring applications with examples of past. The beam size and momentum spread can be reduced through cooling (Sec.2. SOLEIL. For long store times vacuum considerations are important since the interaction rate of the stored particles with the residual gas molecules is proportional to the pressure.3. ESR. In experiments where the beam collides with an internal target or another beam (Sec. Computers are used to control the operation (Sec. p. g − 2. Larsson.1. VEPP-2000 Stored beam experiments: ASTRID. EPA. Phys. and superconducting rf systems (Sec. BESSY.Ch.7).3). AS.10). of which about 50 exist world wide.5).6. The main consideration in the design of a storage ring is the preservation of the beam quality over the store length. NSLS. so that beams may circulate along stationary orbits and be continuously accelerated. Goward and D. Particle beams can be accelerated to higher momentum in synchrotrons. Particle Accelerators and their uses’. ρ is orbit radius. Another requirement in synchrotrons is for the frequency of rf field frf to synchronize with circulating frequency f0 of the particle beam. Phys. The nonsynchronous particles will be lost in the accelerator if there is no longitudinal focusing. [3] [4] [5] [6] G. ρ stays constant if variation of B matches the increase in p. F. where the phase slipping is avoided for synchronization and magnets get less massive as in cyclotrons (Sec. i.6. Barnes at the Telecommunications Research Laboratory of UK modified its small betatron to operate as a synchrotron [1]. π) above the transition energy. the faster it moves and the longer is its orbit.6: GLOSSARY OF ACCELERATOR TYPES the magnetic field ramps along with the beam momentum increase. Harwood (1986) [7] M. bending and focusing magnets confine the particles to move along and around the central orbit.21 Synchrotrons C. Veksler [2] in the USSR and McMillan [3] in the US independently discovered the principle of phase stability in synchrotrons. This shows that there is a transition energy γt : higher energy particles circulate faster when γ < γt . π/2) below the transition energy and (π/2. PR 102. Nucl. Figure 2: Phase oscillation in synchrotrons. Figure 2 illustrates the phase oscillation. Below transition. where p is particle momentum. In 1944.X. microwave as well as their control and these became possible after World War II. In 1952. Synchrotrons posed technical challenges to magnets. and slower when γ > γt . below and above the transition energy. Scharff. the ejection elements extract the beam when it reaches the desired energy. a team at General Electric Co. there are energy and phase deviations in reference to the idealized synchronous particle. 518 (2010) 1. and Ze denotes particle charge. In 1946.(1).6. Figure 1 shows the schematic of a synchrotron. In a synchrotron. IHEP Synchrotrons are characterized by the magnetic field synchronizing with momentum of particle beams and the electric field synchronizing with their circulating frequency.Sec. Bei et al. speed and orbit length: the higher the energy of a particle. As seen in Eq. while orbit length dominates when approaching the speed of light. particle beam is injected into the vacuum pipe through a deflector. As the energies and the arrival times to the rf cavity of the particles in a beam are slightly different. NIM A 622. the particle “b” circulates with higher frequency for Eb > Ea and gains more 58 . an rf cavity installed in a straight section accelerates the beam. or synchrotron oscillation. A 756 3 (2005) K.A. In the following year. BNL finished a proton synchrotron of cosmic ray energy range. Zhang. As shown. There are two factors affecting the revolution frequency of particles in a synchrotron. the 3 GeV Cosmotron. Johnsen. S. There may have up to h synchronizing particle bunches in a synchrotron.4). Litvinov et al. constructed a dedicated 70 MeV electron synchrotron.1.1. stable phase is in the range (0. Fang. the guide field B varies with time as p(t)c (1) B(t) = Zeρ Figure 1: Schematic of a synchrotron. 1418 (1956) Yu. CERN 84-13 (1984) W. O’Neill. c is speed of light. frf = h · f0 (2) Here h is harmonic number (integer). The speed is dominating factor at low energy.e. which in turn can provide high effective interaction energy (Sec. The typical size of vacuum chamber is 800-mm wide by 200-mm height.6. In a strong focusing synchrotron. Synchrotrons are used to make collisions between oppositely directed beams. The light emitted from electron synchrotrons was harmful in the history of e+ -e− colliders. PR 88 (1952) [5] N. and serve as booster injectors for higher energy accelerators. For the electric and magnetic fields to be modulated in synchronism with beam momentum.14). while in the latter case dipoles and quadrupoles play roles of bending and focusing separately. and the BNL’s Alternating Gradient Synchrotron (AGS) of 30 GeV completed successively.1. with d distance between two lenses. the CERN Proton Synchrotron (CPS). Dokl.M. Synchrotrons are applied for nuclear and particle physics experiments of fixed targets. 413 [2] V. Veksler. Courant. Barnes.e. Patent no. Dozens of synchrotron radiation sources have been constructed in the world. The idea had been visualized by Chritofilos in an unpublished paper [5].6.1: INTRODUCTION are combined in the same magnets. 393 (1944) [3] E. Their magnetic gaps are only 70-80 mm. the overall focal length F = d/f 2 > 0. βs and Es are relative velocity and energy of the synchronous particle respectively. Akad. which allowed using smaller magnets and reaching higher beam energies. H.736. Nauk SSSR 43.D. CERN immediately abandoned its 10 GeV weak focusing plan and constructed a 25 GeV strong focusing proton synchrotron.E. PR 68 (1945) 143 [4] E. synchrotrons are operated in pulsed mode with typical average beam current of the order of μA’s. the bending and focusing References [1] F. energy for φb > φa than the synchronized particle “a”.1. 2. In the same year when Cosmotron was completed. i.C. Chrostofilos.5). U.16). known as colliders. In 1959 and 1960. so that it is more flexible providing even stronger focusing. Similarly. Courant.5) and a variety of other instabilities. The transverse focusing was explored in cyclotrons (Sec. In case when Δφ = φ − φs is small enough. The strong focusing opened a new era of synchrotrons. Goward.Ch.e. and also by beam-beam interactions in colliders (Sec. ΔVrf = Vrf (φ) − Vrf (φs ) ≈ 2πfrf V cos φs · Δφ. D.6.2. 1 1 d 1 = + − (6) F f1 f2 f1 f2 If the lenses have equal and opposite focal lengths. M.2. The maximum beam current in synchrotrons is limited by space charge effects (Sec. this constant-gradient focusing is rather weak which makes the beam’s cross section large and leads to bulky vacuum chambers and massive magnets. horizontal focusing and defocusing (vertical focusing and defocusing) magnets are alternatingly arranged to make a global strong focusing like in an optical system.799 (1956) 59 .S. In the former case. McMillan.S. i. f1 = −f2 .4. combined function and separated function.3). so that it oscillates around the particle “a” anticlockwise in the φ-ΔE space when γ< γt . it has now become an important tool for scientific research (see also Sec.I. the “restore force”.1. while the total weight of magnates gets to ∼10000 tons in weak focusing synchrotrons of GeV scale such as the Cosmotron.S. There are two catalogues of strong focusing.1. E. Snyder. is nearly constant and the synchrotron oscillation behaves as a simple pendulum.1. Proton synchrotrons are used as spallation neutron sources (Sec. d2 Δφ + ωs2 Δφ = 0 (3) dt2 with oscillation frequency f0 ωs hη cos φs eV = − (4) fs = 2π βs 2π Es where η = 1/γt2 − 1/γ 2 . 346 and 44. M.20). Particles get focusing in both horizontal and vertical planes if the guide field index n satisfies 0 < n < 1 with ρ ∂By )r=ρ (5) n=− ( B0 ∂r However. The alternating gradient focusing quickly superseded constant focusing in synchrotron design. 158 (1946). Natrure. Proton and heavy ion synchrotrons are also widely applied for medical treatment (Sec.4).6. Livingston. particle “d” oscillates around the particle “c” clockwise when γ> γt . Snyder proposed the concept of strong focusing (or alternating gradient focusing) [4]. Livingston and H.6.K. The high energy frontier accelerators constructed in recent years are all collider type. 6. 60 .4 GHz) and high accelerating gradients (≥ 100 MV/m). Delahaye. Two-Beam Accelerator J. low-energy drive beam is used to generate rf power that is applied to a high-gradient acceleration structure. In addition. where a low-current beam is accelerated to high energy (Fig. gyrotrons. these structures have to be damped to reduce long-range transverse wakefield effects. 6] is based on a relativistic drive beam which is not reaccelerated to avoid active elements in the main tunnel. However.1. For the sake of beam stability. CERN Novel schemes of Two-Beam Acceleration (TBA) have been proposed [1.1). different time pulses in the train are used to power different sections of the main linac.4 GHz from the drive beam. with early work [1] centered on using FELs to extract rf power from the drive beam.P. The structures to extract the power from the high-intensity drive beam are referred to as PETS (Power Extraction and Transfer Structures) [8]. The structures are passive microwave devices in which the drive beam bunches interact with a large aperture (25 mm diameter) structure with a shallow periodically corrugated inner surface to preferentially excite the synchronous TM01 mode at 12 GHz. low energy (2. In the process. The bunch spacing is then reduced to 2. Two main approaches of TBA research have been pursued so far: The relativistic klystron approach (RK-TBA) [4] developed by LBNL/LLNL uses induction acceleration of the drive beam and to maintain the energy at 10 MeV throughout most of the device.2 [7]. 2] as power source for high-energy facilities and especially for e± linear colliders. Operating the linac in the fully-loaded mode enables the beam to be accelerated with an rf-power-to-beam efficiency of ≈ 96%.5-m structure extracts a rf power of 130 MW from the 100 A drive beam.22 Up to 90% of the beam energy is transformed in rf power after which the remaining beam is dumped.5 cm in three successive stages in a delay loop and two combiner rings using funneling techniques to repetitively interleave 240 ns-long slices of the trains. A fullyloaded normal-conducting linac operating at a low frequency (1 GHz) is used to accelerate the drive beams to 2. wake-field) can be configured into a TBA. and the method of drive-beam acceleration. Drive beam generation The drive beam generation complex is shown in Fig. PETS are made of eight octants separated Figure 1: Conceptual layout of Two-Beam Accelerator (TBA). A klystron-like output structure extracts power at 11. The rf power for each drive-beam accelerator is supplied by efficient 15 MW multi-beam klystrons with long rf pulse at low frequency. There are also several choice options for the drive beam source. This energy travels along the structure with the mode group velocity and the rf power produced is collected at the downstream end by a power extractor and conveyed to the main linac structure by rectangular waveguides. Rf power production By initially sending the drive beam trains in the opposite direction to the main beam. As a result.4 GeV) and high current (100 A). most rf extraction concepts (FELs.Sec. Acceleration of the main beam is pursued in a following sector using a fresh drive beam. Many variations of the TBA concept have been investigated. a high-current. A particularly attractive and cost effective feature of the CLIC scheme is that energy upgrading of the collider only requires a pulse lengthening of the modulators which drive the klystrons and not an increase in the number of klystrons. The Compact Linear Collider (CLIC) scheme [5. In the TBAs. TBAs scale [3] favorably to high frequencies (≥ 11. The drive beam is characterized by a 12 GHz bunch structure. The drive beams are generated as one long train with a bunch spacing of 60 cm. The TBA has the great advantage of high efficiency for power conversion from the drive beam to rf power. the bunch repetition frequency and the beam intensity are multiplied by a factor of 24. It produces one after the other all required drive beams for each linac. The primary technical challenge of the RK-TBA lies in propagating the intense drive beam (hundreds of amperes) at low energy (10 MeV) over long distances.4 GeV.6: GLOSSARY OF ACCELERATOR TYPES 1. Successive drive beam trains supply power to a linac sector 876 m long. the beam kinetic energy is converted into electromagnetic energy at the mode frequency. Each 0. klystrons. These experiments resulted in a total rf output of > 200 MW.3). vacuum. the power generated by these structures is turned off by a remotely adjustable external reflector.5 GW of 12 GHz power in a 20-m Test Beam Line decelerator in order to carry out beam stability studies by HOM damping slots connected to broad-band SiC rf damping loads. At LBNL a RK-TBA version [12] was designed as a power source for a linear collider with 1. Experiments The earliest TBA experiments [9] were performed on ETA-I addressing issues of power extraction. alignment & stabilization (Fig. using the ARC facility. bunched beam transport through two reacceleration induction cells and three traveling-wave extraction cavities. Two generations of CLIC Test Facilities (CTF1 1990-1995 and CTF2 1996-2002) have demonstrated the technical feasibility of the CLIC scheme. a string of four power-extracting structures driving five accelerating structures increased the energy of a single electron bunch of the probe beam by 55 MeV [13]. Reacceleration experiments [11] were performed on ATA that demonstrated 61 . In particular CTF3 has demonstrated the generation of a 130ns 150-MeV 28-A drive beam with 2 cm bunch spacing using a fully-loaded linac and two stages of bunch interleaving resulting in an intensity and frequency multiplication by a factor 8 [15]. In CTF1. quadrupoles. Figure 3: Two Beam Acceleration module. a peak power of 76 MW was extracted from the drive beam by a highimpedance 30-GHz traveling-wave section. In CTF2.1: INTRODUCTION Figure 2: Layout of CLIC RF power generation scheme. with phase and amplitude stable over a significant portion of the beam pulse. and used to reaccelerate the same beam. These experiments [10] used a 1-MeV 1-kA 70-ns induction accelerator beam to produce 300 MW of rf power level at 11. beam instrumentation.Ch.4 GHz. Work on the RK version started shortly after. Main beam acceleration The main linac is made of a succession of two beam modules integrating all necessary components including rf structures. In case of problems. Both the high intensity drive beam and the probe beam were generated by laser-illuminated photo-cathodes in rf guns. This beam will be used to produce up to 1. A new CLIC Test Facility CTF3 [14] has been built at CERN to address the major key CLICtechnology-related feasibility issues.5-TeV CM collision energy. T.A. Conf.nrc. Houck. Mod.edu/accel/ilc/codes/..html and http://irs. http://pbpl.B. and upgrades.web. see www. The latter reduces mainly to standard eXtensible Markup Language (XML). 2997 (2011) • Self-Describing Data Sets (SDDS): SDDS is a self-describing file protocol that has been widely adopted in the light source modeling community.H. Snowmass Workshop (1996) [4] T. Braun.7 ACCELERATOR COMPUTER CODES R.anl.com/p/ual/source/browse/ trunk/doc/adxf.stanford.shtml 1.gov/index. IPAC10 [16] J.L.cern. 2439 (1987).slac. J.) and compatibility with modern software tools.S. The first. it is important to accelerator modelers who integrate online accelerator codes into control systems. http://code.ucla.bnl. Beams (1994) [12] Zeroth-order Design Report for Next Linear Collider. It will also be used to power accelerating structures at their nominal gradient of 100 MV/m in prototype Two Beam modules thus addressing the feasibility of Two Beam Acceleration [16]. 24 (1996) 938 [5] The CLIC Conceptual Design Report. A. see. Lidia et al.cornell.ca/software/egsnrc/ The following tables list some widely used (noncommercial) codes and contact information.aps. On Plasma Sci. Lett. 228 (1984) 15 [2] A. so community standards for lattice descriptions are important to facilitate sharing of lattice information among codes.aps.disp allcat/.M. Greece (2005) [9] D. Tomas et al. including: http://oraweb.cern.gov/mumu/ In the future it is expected that a list of accelerator codes will be maintained at the website for Physical Review Special Topics Accelerators & Beams. PRST-AB 13.cap.7: ACCELERATOR COMPUTER CODES Community standards and benchmark simulation codes. http://clic-study. 62 . Kalamata. Phys. An overview of accelerator description formats can be found at http://cern. etc. Westenskow.ch/AccelConf/ICAP06/PAPERS/ THM2IS01. Proc.925 [13] H.edu/∼dcs/aml/ References [1] D. Ryne.A. High Energy Part. Given the ubiquity of EPICS. CTF3 design report. Houck. Geschonke et al.014801 (2010) [7] The CLIC RF Power Source. Syratchev.lns. http://mad. • Accelerator Lattice Descriptions: Complex accelerator lattices may contain many thousands of elements. CLIC note 364 [8] I. Hopkins.g. Vol. A Universal Accelerator Parser has also been developed that parses several formats. preferably disciplined by an XML Schema.592 (1991) [3] S. NIM Phys.PDF.anl. Westenskow.gov/Accelerator Systems Division /Operations Analysis/SDDSInfo. Delahaye et al. Hopkins et al.ornl.10th Int. commissioning.1. and most widely used. SLAC-474 (1996) p.L.php [6] R. http://prst-ab. Sessler et al. Skowronski et al. Sessler. errors.B.edu/Computing/Code Overview/. Information about EPICS is located at http://www. 7th Workshop on High Energy Density and High Power RF. LBNL Simulation is essential to accelerator design. operation. A. G. see http://www.A.40.gov/epics/ and http://www-csr. NIM A 306. Appendix A. PRL 58.google.de/epics/ • Radiation safety modeling and standards: See http://rsicc.org/accelerator/CLICConceptDesignRep.ch/pls/hhh/code website.physics.P. this is described in the documentation for the MAD-X code. http://www.Sec.26. CERN-PS-2001-008 [14] G. Wurtele. No. standard for the specification of lattices is the Standard Input Format (SIF).inms. e. IEEE Trans. At the present time several web sites maintain lists of codes used by various groups.bessy.M.ch/mad. SPIE High Intensity Laser Processes 664 (1986) 73 [10] M. PRL 63 (1989) 2472 [11] G. Res. For realistic analysis (as contrasted with idealized design) two extensions of SIF have been found to be important: full instantiation (where every element has its own parameters. http://www. Allen et al. aps. CERN/PS 2002-008 [15] P.org/ • Experimental Physics and Industrial Control System (EPICS): EPICS is widely used in accelerator control systems. The SIF definition of beamline elements has been very widely adopted. PIC refers to codes with particle-in-cell space-charge capability.) ǡ .1: INTRODUCTION Beam Dynamics Codes: (Below.Ch. . . Ȁ . . Ȁ. Ǧ . . . . . . . ǤǤȀ̱ ǤȀ Ȁ Ȁ ǤǤ ǤǤ ǤȀ̱ ȀȀ Ǥ Ǥ ǤǤȀǦȀ ǤǤȀǤ ǦǤǤȀ Ǥ ̷ Ǥ. Ǥ. ǤǤ ǤǤ Ǥ ǤǤȀ̱Ȁ ̷ ǤǤ Ȁ ͵ǡ Ǥ ǣǡ. ǡ Ϊ Ǧ ͵. Ǣ ǢǦ Ǣ ǡǢǢǢ ǡ ͵Ǧ . . . ǡǡǡʹȀ͵ ǢǢ . ǦǢ Ǣ Ǥ ǤǤȀ Ȁ Ȁ ǦǦǦ Ǥ ǤǤȀ ǡǡǡǡ ǤǤ ͵. Ǣ Ϊ. ǤǤ Ǥ Ȁ ǤǤȀ̱ ΪΪ ǤǤǤ ͵. Ǣ ǡ ǡ Ǣ ǦǤ ̷Ǥ Ǥ̷ Ǥ ͵. Ǣ Ǣ Ǧ ǤǤȀȀǤ ǡǡƬ ǤǤȀȀ ͵. Ǣ ǡ ǤǤ Ǥ ȀȀ Ǣ ǦǤǤȀȀ Ȁ ǣȀȀ ǤǤȀ ͵. ǣ ǡ ̷Ǥ Ǣ ǢǢ ǤǤǤȀȀ ͵. sourceforge.net/ ǤǤǤ ͵.ǡ libtracy. ǢǦǦǦ ǤǤ ȀȀȀ ̷Ǥ ͵. e. ǤȀ ȀȀ ǢǢ ǢǦ Beam Dynamics w/ emphasis on specific phenomena (beam-beam.-cloud. spin): . ǡ ͵ ǡ. Ǧ . . ǡ . . . Ȁ. ǦǤǤȀ̱Ȁ. ȀǤ ̷ǤǤ ǦǦ ǤǤ Ǥ ȀǦǦ Ȁ ǤǤ ǦǦǤǤ Ǥ Ȁ ǦǦ ̷ǤǤ ǦǦ ǤǤ Ǥ ȀǦǦ Ǧ ǦǦ ǤǤ Ǥ ȀǦǦ Ǧ ̷ǤǤ ̷Ǥ ǤǤȀȀ Ǥ ̷ Ǥ ̷Ǥ ǡ ǦǦǦ ǦǦ ǢǦǢǦ ǢǦ. ǢǦ ǢǦǢ Ǣ Ǧ . Ǧ ǢǦ ǦǦ ǦǢǦǡǢǦ Ǥ ǢǦǡǦǦ Ǣ. Ǧǡ ǢǦ ʹǦ Ǣ Φ ǡ Ǥǡǡ ͵Ǧ Ǧ Ǣ Electromagnetics: . ͵ . . ǡ . Ȁ . . ǤǤ Ǥ ǤǤȀȀ̴ ȀȀ ǤǤǤ ǤǤǦ ǤȀǤǫαʹ͵ͷ Ǥ Ǥ ǤȀ Ǥ ǤǤ ǤǤȀȀ. Ȁ. Ǥ Ǥ ȀȀǤ 63 ʹǤͷ ͵ Ǣ͵Ȁ͵ǡ͵ǡ ͵ǡ ͵ǡ͵ ͵ Ǧ Ǧ ǦǦ ʹ ͵ Ǣ ͵ Ǣ . Sec.1.7: ACCELERATOR COMPUTER CODES Free Electron Laser Codes: . . . Ǥ̷Ǥ Ǥ ̷Ǥ ̷Ǥ ǤǤ ̷ Ǥ ǤǤǤ ǤǤǤǤȀȀ ͵Ǧ ͵Ǧ ǡ ǦǦǢ͵ǢǤƬ Ǥ ͵Ǧ Ƭ ǢǦ Ǧ Ǣͳ ͵Ǧ ǡ . Ǧ Synchrotron Radiation Modeling Codes: ʹ Ȁ͵ ǤǤ ȀȀ Ǥ ǤǤǤǤȀ Ǥ ̷Ǥ ǤǤȀȀ. Ȁ Ǥ̷ Ǥ Ǧ ǡ ǡ Ǥ Ǥ ǤǤȀ ȀȀȀ ȀʹǤ͵ Ǧ Beam/Material Interactions: Ͷ Ͷ . ǤǤ ǤͶǤȀͶȀ ͶǤ Ǥ ǤǤȀ̱Ȁ Ȁ ǦǤǤȀȀ ǦǤǤȀǤ Ͷ . ͵ Pre-. Parsers. Auxiliary Codes: Ȁ ͷ ǤǤ ǤȀ̱ ȀȀ ͷǤǤ ȀǡǤǤȀ ǤǤ Ǥ Ȁ Ǧ Ǥǡ Ǥ ͷǡ. Post-Processors. http://cdsweb.jacow.aps. Physical Review Special Topics . 64 .ch/.cern.Ȁ Other Web Resources Since 2006. they are accessible and searchable at http://www.org/. the proceedings of the International Computational Accelerator Physics (ICAP) conference series have been administered by the Joint Accelerator Conferences Website (JACoW).Accelerators and Beams is planning to be a resource for information about accelerator codes. As of this writing.org. see http://prst-ab. Another searchable resource is the CERN Document Server.