Beam Shaping and Permanent Magnet Quadrupole Focusing with

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

The Plasma Wakefield Accelerator (PWFA) Overdense Plasma n b < n p ; k p sz > 1 current neutralized nb < np ; kp sr << 1 self-focused Bingham, R. Nature, 394, 617 (1998). Underdense Plasma nb/np > g 2 unfocused g 2 > nb /np > 1 ion focused (blowout) Wake Fields in 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, Eacc ≈ n 01/2 [V/cm] Rosenzweig, et al. PRA, 44, R 6189 (1991)

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: triangle doorstep ideal

The UCLA Neptune Laboratory 1. 6 -Cell Photoinjector Beam Charge: 100 -300 p. C Beam energy: up to 15 Me. V Emittance: N = 6 mm mrad Power Source: 18 MW Klystron RF Frequency: 2. 856 GHz Cathode laser: 60 -80 µJ at l = 266 nm Laser pulse length: 5 ps RMS 7&2/2 Cell PWT Linac

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 2π betatron advance. • Like a chicane, may be used as a bunch-length compressor. • Nominal first order temporal dispersion (R 56=-5 cm) is suitable for beam-shaping.

Neptune Dogleg Compressor PARMELA Simulation Results: 1000 particles, 300 p. C Initial Final: Sextupoles Off x, N (initial)=4. 9 µm GUN PWT Pre-Focus Final: Sextupoles On 1. 6 11. 5 D x, N=9. 9 µm+12. 7 µm = 22. 6 µm space-charge sextupoles • 2 D PIC nonlinear Simulation total • 5 Ge. V/m gradients • 6 n. C drive beam w/ n 0=2 e 16 cm-3 Final Focus

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 1 cm mask inserted at above location witness beam ramped drive beam

Temporal Bunch Shaping: Diagnostic Deflecting Mode Cavity Courtesy of D. Alesini Lowest dipole mode is TM 110 Zero electric field on-axis (in pillbox approx. ) Deflection is purely magnetic Polarization selection requires asymmetry J. D. Fuerst, et. al. , DESY Report CDR 98, 1998 Pillbox Fields on axis kr = 0

Deflecting Cavity: Power & Resolution screen deflection: n=1 45 fs n=7 50 k. W n=5 n=3 n=9 9 cells; 50 k. W; 50 fs resolution

ELEGANT Simulations ELEGANT Simulation Results • Using RFDF element with 9 cells • 10, 000 macroparticles • Shunt Impedance: RT = 6. 12 MΩ • Power: P = V 02/RT Initial Current Profile V 0 = 0 ; P = 0 V 0 = 272 k. V ; P = 12 k. W V 0 = 545 k. V ; P = 48 k. W V 0 = 609 k. V ; P = 61 k. W

Deflecting Cavity: HFSS Design d t b 3 b b 2 b b 1 HFSS Geometry of 1/2 structure DIMENSION VALUE [mm] a 5 b 18. 21 b 1 18. 44 b 2 18. 306 b 3 18. 21 t 3. 0 d 15. 62 Resonance of the π-Mode out of phase by 90˚ E-field H-field • X-Band, 9 -cell design. • Collaboration with INFL Frascatti. • Will be built at UCLA; diffusion bonded at SLAC. • Powered by a VA-24 G X-Band klystron @ 50 k. W. • Frequency: 9. 59616 GHz

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 +1358 MHz Desired +53 MHz Undesired -7 MHz Desired -2 MHz

Prototype Cavity

Constraints on Brightness & Emittance blowout regime transformer ratio betatron matching Q=300 p. C ; L=2 mm; sz = 0. 5 mm ~110 µm ~50 mm mrad ~250 m. A/µm 2 n 0 min ~ 2. 8 x 1013 cm-3

Permanent Magnet Quad Focusing standard iron quads Power. Trace 1. 08 Simulation PMQs (110 T/m) ELEGANT Simulation Result • Hybrid Permanent Magnet and Iron • Grey cubes are Alnico; M=1. 175 T g=25. 7; E=13. 13 Me. V; Q = 300 p. C • Field gradient: sx. B’=110 =130 µm; x=41 mm mrad T/m; B’’=-0. 002 T/m 2 sy=57 diameter: µm; y=15 mm mrad • Bore 8 mm sz =0. 51 mm; sd =1. 84% • Benefits: cheaper, better field profile • Downsides: small bore; in-vacuum

Scaling to Higher Charge: 4 n. C Q=4 n. C ; L=4 mm; sz = 1 mm ~500 µm ~420 mm mrad n 0 min ~ 0. 8 x 1013 cm-3 ~12 m. A/µm 2

Scaling to Higher Charge: 4 n. C scaling applied to laser at cathode: Q = 4 n. C; 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 sextupoles Final Focus

Scaling to Higher Charge: 4 n. C scaling applied to laser at cathode: dispersion killed to 1 st 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) 2 nd order longitudinal dispersion T 566 killed GUN PWT Pre-Focus tail is 3 rd order (U 5666) octupoles needed? sextupoles Final Focus

Scaling to Higher Charge: 4 n. C scaling applied to laser at cathode: dispersion killed to 2 nd Order longitudinal ph. space and profile at end ELEGANT, 1000 particles simulation of sbahn and final focus horizontal dispersion killed to second order 2 nd order longitudinal dispersion not killed GUN PWT Pre-Focus tail is 2 nd and 3 rd order (T 566, U 5666) sextupoles Final Focus

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 m. A/µm 2 @ 300 p. C) • High Charge: - scaling to high charge (~4 n. C) 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