Beam Shaping and Permanent Magnet Quadrupole Focusing with Applications to the Plasma Wakefield Accelerator

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1 Beam Shaping and Permanent Magnet Quadrupole Focusing with Applications to the Plasma Wakefield Accelerator R. Joel England J. B. Rosenzweig, G. Travish, A. Doyuran, O. Williams, B. O Shea UCLA Department of Physics and Astronomy Particle Beam Physics Laboratory Los Angeles, CA USA D. Alesini INFN Laboratori Nazionali di Frascati Rome, Italy Workshop on the Physics and Applications of High Brightness Electron Beams Erice, Sicily Oct 9-14, 2005

2 The Plasma Wakefield Accelerator (PWFA) Overdense Plasma n b < n p ; k p! z > 1 current neutralized n b < n p ; k p! r << 1 self-focused Bingham, R. Nature, 394, 617 (1998). Underdense Plasma n b /n p > " 2 unfocused " 2 > n b /n p > 1 ion focused (blowout) Wake Fields in Blowout Regime Blowout Regime Mechanism: Plasma electrons disturbed by drive beam. Longitudinal space-charge wave generated. Ion channel created, pulls electrons back. Ion focusing is linear in r. Accelerating electric field, E acc n 0 1/2 [V/cm] Rosenzweig, et al. PRA, 44, R6189 (1991)

3 Overview of Drive Beam Issues for Blowout Regime of PWFA Longitudinal bunch shape High beam brightness High charge Strong Focusing Betatron matching Creation of a Witness Bunch Chen, P., Su, J., and Dawson, J. SLAC PUB 3662 (1985). Transformer Ratio: E + = acc.field;e! = decc.field R = E + / E! = k p L z R > 2 if L z > 2k p triangle doorstep ideal

4 Overview of Drive Beam Issues for Blowout Regime of PWFA Longitudinal bunch shape High beam brightness High charge Strong Focusing Betatron matching Creation of a Witness Bunch! r,max = Q / e! 4"n 0! N,max = p 2 " 0 r,max z mc B min = 2cQ 2 # eq! N,max " z

5 Overview of Drive Beam Issues for Blowout Regime of PWFA Longitudinal bunch shape High beam brightness High charge Strong Focusing Betatron matching Creation of a Witness Bunch

6 The UCLA Neptune Laboratory Beam Charge: Beam energy: Emittance: Power Source: RF Frequency: Cathode laser: Laser pulse length: pc up to 15 MeV $ N = 6 mm mrad 18 MW Klystron GHz µj at # = 266 nm 5 ps RMS 1.6-Cell Photoinjector 7&2/2 Cell PWT Linac

7 Neptune Dogleg Compressor S-Bahn Compressor S-Bahn is a dogleg or dispersionless translating section. Half-chicane with focusing elements between the bends. Can be operated in a nondispersive mode with symmetric beta function and 2" betatron advance. Like a chicane, may be used as a bunch-length compressor. Nominal first order temporal dispersion (R56=-5cm) is suitable for beam-shaping.

8 Neptune Dogleg Compressor PARMELA Simulation Results: 1000 particles, 300pC Initial Final: Sextupoles Off Final: Sextupoles On $ x,n (initial) =4.9 µm %$ x,n =9.9 µm+12.7 µm = 22.6 µm 2D PIC Simulation 5 GeV/m gradients 6 nc drive beam w/ n 0 =2e16 cm -3 space-charge nonlinear total GUN PWT Pre-Focus sextupoles Final Focus

9 Neptune Dogleg Compressor ELEGANT: Simulated Witness Beam For PWFA application, drive beam needs a witness beam to accelerate. Region of high dispersion in x Strong correlation b/w x and z Insert mask in x to sever beam in z No mask inserted Undercorrected with sextupoles to elongate profile With 1cm mask inserted at above location witness beam ramped drive beam

10 Temporal Bunch Shaping: Diagnostic Deflecting Mode Cavity Courtesy of D. Alesini DEFLECTING VOLTAGE! x x B Lowest dipole mode is TM 110 Zero electric field on-axis (in pillbox approx.) Deflection is purely magnetic Polarization selection requires asymmetry L B x " f x' = RF L B 2P ce / e RF R! DEFLECTOR BUNCH L x B " f = RF LL B 2P ce / e RF R! J.D. Fuerst,, et. al., DESY Report CDR98, 1998 E z = E 0 J 1 (!r)e i" ; J B r = B 1 (!r) 0 e i" ;!r B " = ib 0 J 1 #(!r)e i" ; Pillbox Fields on axis &r = 0 E z = 0 ; B x = B 0 2 ; B y = i B 0 2 ;

11 Deflecting Cavity: Power & Resolution screen deflection: V! >> V min = " x,0u / e L#" t f 2! x, f =! x,0! t,min =! x,0u / e L"V # f 2 +! def! def = 2! z L "V # f cu / e cos($ 0 ) 1 (! 0 " 0) V!,design = 3V min = 545kV! t,min = 545 fs! x, f = beam size at screen with deflector on;! x,0 = 0.3mm = beam size at screen with deflector off; L = 43cm = drift from deflector to screen; f = 9.6GHz = RF frequency; V " = deflecting voltage; R " = 820k# = transverse shunt impedance per cell; P in = input RF power; U = 12MeV = electron beam energy; $ 0 = deflector injection phase = 0;! t,min = minimum resolvable rms bunch length; %x = 30µm = spatial resolution of screen & optics; %t = effective temporal resolution of deflector;!t =!x U / e L" fr # 1/2 np in n=1 n=3 n=7 n=5 45 fs 50 kw n=9 9 cells; 50 kw; 50 fs resolution

12 ELEGANT Simulations ELEGANT Simulation Results Using RFDF element with 9 cells 10,000 macroparticles Shunt Impedance: R T = 6.12 MΩ Power: P = V 02 /R T Initial Current Profile V 0 = 0 ; P = 0 V 0 = 272 kv ; P = 12 kw V 0 = 545 kv ; P = 48 kw V 0 = 609 kv ; P = 61 kw

13 Deflecting Cavity: HFSS Design DIMENSION VALUE [mm] t d a 5 b3 b b2 b b1 b b b b HFSS Geometry of 1/2 structure t 3.0 d X-Band, 9-cell design. Collaboration with INFL Frascatti. Will be built at UCLA; diffusion bonded at SLAC. Powered by a VA-24G X-Band 50 kw. Frequency: GHz

14 Deflecting Cavity: HFSS Design out of phase by 90 E-field H-field P in = 50kW V! = 1 e " F! dz = 528kV R! = V! 2 / P in = 5.6M# Resonance of the #-Mode

15 Deflecting Cavity: Polarization Separation Rods Holes Rods give greater better mode separation but shift the desired mode too much Holes give less mode separation (5 MHz) but only perturb desired mode by 2 MHz (within range of temperature tuning). Holes look like better option: 5 MHz is large compared to the resonance width Undesired Desired Undesired Desired MHz +53 MHz -7 MHz -2 MHz

16 Prototype Cavity

17 Constraints on Brightness & Emittance blowout regime transformer ratio betatron matching n 0 > mc2!e 2 L n b = Q / e! r <! max = k!" 2 r " p = 4!r e n 0! N = "# $ r 2 Q / e 2cQ z 4"n 0! z! N <! N max = "# $ max "1 n b >> > 4n n 0 R > 2! L > 2k p # eq B > B min =! r =! eq = " / (2#r e n 0 ) 2 # 2 r! N max " z Q=300 pc ; L=2mm;! z = 0.5 mm ~110 µm ~50 mm mrad ~250 ma/µm 2 n 0min ~ 2.8x10 13 cm -3

18 Permanent Magnet Quad Focusing standard iron quads PowerTrace 1.08 Simulation PMQs (110 T/m) ELEGANT Simulation Result "=25.7; E=13.13 MeV; Q = 300 pc! x =130 µm; $ x =41 mm mrad! y =57 µm; $ y =15 mm mrad! z =0.51 mm;! ' =1.84% B! 2Q /! t " N,x " N,y = 412mA / µm 2

19 Scaling to Higher Charge: 4 nc n 0 > mc2!e 2 L! r <! max = Q / e! 4"n 0! N <! N max = "# $ 2 max z # eq B > B min = 2cQ 2! N max " z Q=4 nc ; L=4mm;! z = 1 mm ~500 µm ~420 mm mrad ~12mA/µm 2 n 0min ~ 0.8x10 13 cm -3

20 Scaling to Higher Charge: 4 nc scaling applied to laser at cathode:! x,! y,! t " Q 1/3 (Q : 300 pc # 4nC) Q = 4 nc; pt-to-pt space charge UCLA-Parmela 2.0, 1000 particles $ N ~ 25 mm mrad simulation of gun and linac w/solenoid for emittance compensation GUN PWT Pre-Focus Final Focus sextupoles

21 Scaling to Higher Charge: 4 nc scaling applied to laser at cathode:! x,! y,! t " Q 1/3 (Q : 300 pc # 4nC) dispersion killed to 1st Order longitudinal ph. space and profile at end ELEGANT, 1000 particles simulation of sbahn and final focus horizontal dispersion killed to first order (R 16,R 26 ) 2nd order longitudinal dispersion T 566 killed! N,x = 742 mm mrad! N,y = 456 mm mrad tail is 3rd order (U 5666 ) octupoles needed? GUN PWT Pre-Focus Final Focus sextupoles

22 Scaling to Higher Charge: 4 nc scaling applied to laser at cathode:! x,! y,! t " Q 1/3 (Q : 300 pc # 4nC) dispersion killed to 2nd Order longitudinal ph. space and profile at end ELEGANT, 1000 particles simulation of sbahn and final focus horizontal dispersion killed to second order 2nd order longitudinal dispersion not killed! N,x = 96 mm mrad! N,y = 141 mm mrad tail is 2nd and 3rd order (T 566, U 5666 ) GUN PWT Pre-Focus sextupoles Final Focus

23 Conclusions PWFA drive issues: ramped profile, strong focus, high charge Ramped profile: - improved transformer ratio (R > 2) - feasible using dogleg compression with sextupoles - deflecting cavity diagnostic (50 fs resolution) Strong focus: - traditional EM quads + permanent magnet quadrupoles - adequate emittance and brightness (~ 100 µm, 450 ma/µm 300 pc) High Charge: - scaling to high charge (~4 nc) at Neptune has some dilemmas - tradeoff between optimal profile and good emittance - extra sextupoles and octupoles may be required - beam sizes become bigger than the beam pipes - implies complete or partial redesign of the compressor

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