A bunch compressor design and several Xband FELs

A bunch compressor design and several X-band FELs Yipeng Sun, ARD/SLAC 2011 -04 -13, LCLS-II meeting

Design of two bunch compressors Presentation Title Page 2

Magnetic bunch compression Bunch L phase space e- source 3 -Dip. Chicane RF Energy modulation (correlation): RF structure, laser, wake field etc. Bunch compression Page 3 Dispersive region: chicane, wiggler arc, dogleg etc.

Different bunch compressors 3(4) dipole chicane, R 56 <0, T 566 >0 achromatic to any order Wiggler, R 56 <0, T 566 >0 achromatic to any order? Arc, R 56 >0, T 566 >0 2 -Dip. Dogleg w/ quad+sextupole, R 56 >0, T 566 tunable Chicane w/ quadrupole+sextupole, R 56 tunable, T 566 tunable NLCTA chicane shape

Dispersion relations Bunch compression Page 5

Bunch compressor with dipoles and drifts Bunch compression Page 6

General chicane (1) Bunch compression Page 7

General chicane (1) Bunch compression Page 8

General chicane (2) Bunch compression Page 9

General chicane (2) Bunch compression Page 10

An FEL with LCLS injector (S-band+X-band harmonic) Plus X-band Linac 2 and Linac 3 Presentation Title Page 11

Scaling 250 -10 p. C Total length of accelerator Assume 70% RF in linac Final bunch length versus bunch charge Presentation Title Page 12

Longitudinal wake potential 'long' range Presentation Title Page 13

Linac 3 length needed for de-chirp after BC 2 Presentation Title Page 14

Accelerator shape (LCLS injector + X-band) Presentation Title Page 15

Li. Track, LCLS, 250 p. C, 3 k. A Presentation Title Page 16

Li. Track, LCLS injector+X-band, 250 p. C, 3 k. A Presentation Title Page 17

Optics LCLS-Injector + X-band Presentation Title Page 18

Elegant simulation, 250 p. C, 3 k. A (w/ and w/o CSR) LCLS w/o CSR Presentation Title Page 19

Elegant simulation, 250 p. C, 3 k. A LCLS-Injector + X-band (½ R 56 in BC 2, 0. 7 bending angle Presentation Title Page 20

Elegant simulation, 250 p. C, 5 k. A LCLS (L 3, 30 degree) LCLS-Injector + X-band (½ R 56 in BC 2, 0. 7 bending angle) Presentation Title Page 21

Elegant simulation, 250 p. C, 5 k. A, Projected emittance LCLS (L 3, 30 degree) LCLS-Injector + X-band (½ R 56 in BC 2, 0. 7 bending angle) Presentation Title Page 22

Elegant simulation, 250 p. C, 5 k. A, Trajectory LCLS (L 3, 30 degree) LCLS-Injector + X-band (½ R 56 in BC 2, 0. 7 bending angle) Presentation Title Page 23

LCLS-Injector + X-band (0. 5 R 56 in BC 2, 0. 7 bending angle), 250 p. C, 5 k. A BC 1 end BC 2 entrance BC 2 end Presentation Title Page 24 Linac 3 end

Potential X-band advantage over S-band • Maintain a flat energy profile when pushing for shorter bunch length and higher peak current (i. e. 6 k. A at 250 p. C), due to stronger X-band longitudinal wake in Linac 3, to remove energy correlation (chirp); plus possible cancellation of nonlinear chirp between RF, wake and CSR effects. • Similar or smaller CSR emittance growth in BC 2, benefiting from a weaker dipole and a larger energy correlation generated in Linac 2 (previous argument) • Compact (300 m vs 1000 m, at 14 Ge. V) • For LCLS, increasing current from 3 k. A to 6 k. A requires a smaller L 1 phase to generate a longer bunch in ~400 m Linac 2, so that the L wake chirp is much smaller, and the bunch is compressed more in BC 2 with same L 2 phase; if keeping similar L 1 phase and increasing L 2 phase (i. e. from 36 d to 37. 5), the final energy profile will be very nonlinear. Presentation Title Page 25

Elegant simulation, 250 p. C, 5 k. A LCLS (L 1, 19 degree; L 2, 36 degree; L 3, 30 degree) LCLS (L 1, 22 degree; L 2, 37. 5 degree; L 3, 0 degree) Presentation Title Page 26

An X-band RF based FEL with optics linearization 250 p. C Presentation Title Page 27

Bunch length after compression Final coordinate (square) Minimum length Neglect small initial un-correlated energy spread 1 st order optimal compression: 2 nd order optimal compression: 3 rd order optimal compression: Bunch compression Page 28

Full compression using optics linearization 1 st order dispersion 2 nd order dispersion 3 rd order dispersion Bunch compression Page 29

Minimize CSR (1) short interaction time Bunch compression Page 30

New design BC 1 (1) first order B 1 0. 2 m 7 degree B 2 0. 2 m 3 degree QF QD R 56 = 17 mm B 3 0. 2 m -3 degree B 4 0. 2 m -7 degree

New design BC 1 (2) second order SF 1&2 SD 1&2 T 166 = T 266 = 0; symmetric K 3(SF 1) = -K 3(SD 2) K 3(SF 2) = -K 3(SD 1) T 566 = 170 mm

Minimize CSR (2) phase space matching general Large β X’ X’ CSR x Small β X’ specific CSR x Optimal β and α x Optimized to minimize CSR impact on emittance Bunch compression Page 33

X-band based 2 stage FEL (1) 250 pc, 300 micron Bunch compression Page 34

Final profile at 7 Ge. V (collimation in middle of BC 1) Presentation Title Page 35

Slice emittance evolution, 250 p. C, 6 k. A BC 1 entrance BC 1 end BC 2 entrance Presentation Title Page 36 Linac 3 end

An X-band RF based FEL with normal chicane BC 10 p. C Presentation Title Page 37

Max bunch length w/o harmonic RF Bunch compression Page 38

Bunch compressor and linac design BC 1 BC 2 Bunch compression Page 39 Linac cell

X-band based 2 stage FEL (3) 10 pc, 40 micron 54 Me. V (C. Limborg) 6 Ge. V

FEL simulation Setup • FEL at 2 ke. V , 6 Å (FEL at 8 ke. V, 1. 5 Å) • Electron Charge 10 p. C, Centroid Energy 6 Ge. V, peak current 3 k. A with profile as shown in previous slides – S 2 E file down to undulator entrance • LCLS Undulator with larger gap lw = 3 cm (1. 5 cm); beta-function ~ 15 m Juhao Wu

FEL performance 1. 5 angstrom 6 angstrom Juhao Wu Presentation Title Page 42

BC parameters summary Bunch compression Page 43

Possible test at NLCTA Presentation Title Page 44

Motivation and simulation condition Motivation o. Demonstrate effective bunch compression (5 to 10 times) with x-band RF §Scheme 1: use normal chicane + positive RF chirp (current NLCTA) §Scheme 2: use optics w/ higher order dispersion + positive/negative RF chirp (need to install 4/6 sextupoles in the big chicane) o. Investigate tolerances on timing jitter, misalignment etc. ; emittance growth Simulation condition: üIn Elegant, including transverse and longitudinal wake, coherent synchrotron radiation (CSR), longitudinal space charge (LSC) and velocity bunching ü 0. 5 million macro-particles üFor scheme 1, current operating optics üFor scheme 2, new optics ü 20 p. C beam at 5 Me. V, 0. 5 ps RMS bunch length, 5 e-3 RMS energy spread, 1 m. mrad transverse emittance üBeam energy: 60 Me. V at BC 1, 120 Me. V at BC 2 Bunch compression Page 45

NLCTA optics (current operation) R 56 =-73 mm T 566 = 111 mm R 56 =-10 mm T 566 = 15 mm Bunch compression Page 46

Scheme 1 (1) L phase, current and bunch length Initial Linac 1 BC 1 Linac 2 Bunch compression Page 47 BC 2

Scheme 1 (2) no compression, on crest Initial Linac 1 BC 1 Linac 2 Bunch compression Page 48 BC 2

Scheme 1 (3) 2 stage compress 20 times, end Bunch compression Page 49

Scheme 1 (4) effect of timing jitter, near full compression Timing jitter between laser and RF (assumed same for two RF sections) On phase + 115 fs (0. 5 degree) Bunch compression Page 50 - 115 fs

Scheme 1 (5) effect of timing jitter, under compression Timing jitter between laser and RF (assumed same for two RF sections) On phase + 115 fs (0. 5 degree) Bunch compression Page 51 - 115 fs

Scheme 2 (1) optics Install 4/6 sextupoles in the big chicane 6 meters long Chicane w/ quadrupole+sextupole, R 56 tunable, T 566 tunable Bunch compression Page 52

Scheme 2 (2) L phase and current Bunch compression Page 53

Scheme 2 (3) 1 stage compress 10 times, end Bunch compression Page 54

Scheme 2 (4) Sensitivity to timing jitter Deviation between analytical formulae and simulation due to: v. Small difference of beam(RF) parameters being employed v. Collective effects in simulation Bunch compression Page 55

Thank you for your patience! I would like to thank the following people for their great help and useful discussions: C. Adolphsen , K. Bane, A. Chao, Y. Cai, Y. Ding, J. England, P. Emma, Z. Huang, C. Limborg, Y. Jiao, Y. Nosochkov, T. Raubenheimer, M. Woodley, W. Wan, J. Wu Bunch compression Page 56

Current less sensitive to RF phase jitter 20 p. C, 80 micron Bunch compression Page 57

LCLS 150 Me. V z 0. 83 mm 0. 10 % 6 Me. V z 0. 83 mm 0. 1 % rf gun Lh L =0. 6 m rf=-160 L 0 L =6 m 250 Me. V z 0. 19 mm 1. 8 % L 1 DL-1 L =12 m R 56 0 13. 6 Ge. V z 0. 022 mm 0. 01 % Paul Emma L =9 m rf = -25° . . . existing linac 4. 3 Ge. V z 0. 022 mm 0. 76 % L =330 m X L =550 m rf = -41° rf = -10° L 2 L 3 BC-1 L =6 m R 56= -36 mm BC-2 L =22 m R 56= -25 mm undulator L =120 m DL-2 L =66 m R 56 = 0 TESLA-XFEL 6 Me. V 120 Me. V z 2. 0 mm z 0. 5 mm 0. 1 % Lh 2. 0 % L =1. 4 m rf= -191 L=8 m rf -22° rf gun L 0 C L = 16 m rf = -40° L 1 375 Me. V z 0. 1 mm 1. 4 % 1. 64 Ge. V z 0. 020 mm 0. 5 % 20. 5 Ge. V z 0. 020 mm 0. 01 % L = 72 m rf = -40° L 850 m rf = 0° L 2 L 3 BC-1 BC-2 L 4 m L 14 m R 56= -76 mm R 56= -36 mm BC-3 L 18 m R 56= -11 mm undulator L =? m (2003 parameters)

Energy change + optics (dispersion) (2) Emittance & trajectory (slice) For sufficiently large slice number, one can assume same energy change in one slice Change slice trajectory Other terms Change slice emittance

CSR energy change + phase rotation (smear) Emittance & trajectory (slice) For over-compress, CSR-process can be treated as an integral process, with continuing bunch compression (lengthening). Change slice trajectory & emittance Negligible