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

Presentation Title Page 2 Design of two bunch compressors

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

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

Bunch compression Page 5 Dispersion relations

Bunch compression Page 6 Bunch compressor with dipoles and drifts

Bunch compression Page 7 General chicane (1)

Bunch compression Page 8 General chicane (1)

Bunch compression Page 9 General chicane (2)

Bunch compression Page 10 General chicane (2)

Presentation Title Page 11 An FEL with LCLS injector (S-band+X-band harmonic) Plus X-band Linac2 and Linac3

Presentation Title Page 12 Scaling Total length of accelerator Assume 70% RF in linac pC Final bunch length versus bunch charge

Presentation Title Page 13 Longitudinal wake potential 'long' range 'short' range

Presentation Title Page 14 Linac3 length needed for de-chirp after BC2

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

Presentation Title Page 16 LiTrack, LCLS, 250pC, 3kA

Presentation Title Page 17 LiTrack, LCLS injector+X-band, 250pC, 3kA

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

Presentation Title Page 19 Elegant simulation, 250 pC, 3 kA (w/ and w/o CSR) LCLS LCLS w/o CSR

Presentation Title Page 20 Elegant simulation, 250 pC, 3 kA LCLS LCLS-Injector + X-band (½ R56 in BC2, 0.7 bending angle)

Presentation Title Page 21 Elegant simulation, 250 pC, 5 kA LCLS (L3, 30degree) LCLS-Injector + X-band (½ R56 in BC2, 0.7 bending angle)

Presentation Title Page 22 Elegant simulation, 250 pC, 5 kA, Projected emittance LCLS (L3, 30degree) LCLS-Injector + X-band (½ R56 in BC2, 0.7 bending angle)

Presentation Title Page 23 Elegant simulation, 250 pC, 5 kA, Trajectory LCLS (L3, 30degree) LCLS-Injector + X-band (½ R56 in BC2, 0.7 bending angle)

Presentation Title Page 24 LCLS-Injector + X-band (0.5 R56 in BC2, 0.7 bending angle), 250 pC, 5 kA BC1 end BC2 end Linac3 end BC2 entrance

Presentation Title Page 25 Potential X-band advantage over S-band Maintain a flat energy profile when pushing for shorter bunch length and higher peak current (i.e. 6kA at 250pC), due to stronger X-band longitudinal wake in Linac3, to remove energy correlation (chirp); plus possible cancellation of nonlinear chirp between RF, wake and CSR effects. Similar or smaller CSR emittance growth in BC2, benefiting from a weaker dipole and a larger energy correlation generated in Linac2 (previous argument) Compact (300m vs 1000m, at 14GeV) For LCLS, increasing current from 3kA to 6kA requires a smaller L1 phase to generate a longer bunch in ~400m Linac2, so that the L wake chirp is much smaller, and the bunch is compressed more in BC2 with same L2 phase; if keeping similar L1 phase and increasing L2 phase (i.e. from 36d to 37.5), the final energy profile will be very nonlinear.

Presentation Title Page 26 Elegant simulation, 250 pC, 5 kA LCLS (L1, 19degree; L2, 36degree; L3, 30degree) LCLS (L1, 22degree; L2, 37.5degree; L3, 0degree)

Presentation Title Page 27 An X-band RF based FEL with optics linearization 250 pC

Bunch compression Page 28 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 29 Full compression using optics linearization 1 st order dispersion 2 nd order dispersion 3 rd order dispersion

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

New design BC1 (1) first order B1 0.2m 7 degree B2 0.2m 3 degree B3 0.2m -3 degree B4 0.2m -7 degree QD QF R56 = 17 mm

New design BC1 (2) second order SF1&2 SD1&2 symmetric K3(SF1) = -K3(SD2) K3(SF2) = -K3(SD1) T166 = T266 = 0; T566 = 170 mm

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

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

Presentation Title Page 35 Final profile at 7GeV (collimation in middle of BC1)

Presentation Title Page 36 Slice emittance evolution, 250 pC, 6 kA BC1 entrance BC2 entrance Linac3 end BC1 end

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

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

Bunch compression Page 39 Bunch compressor and linac design BC1 BC2Linac cell

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

FEL simulation Setup FEL at 2 keV, 6 Å (FEL at 8 keV, 1.5 Å) Electron Charge 10 pC, Centroid Energy 6 GeV, peak current 3 kA with profile as shown in previous slides –S2E file down to undulator entrance LCLS Undulator with larger gap w = 3 cm (1.5 cm); beta-function ~ 15 m Juhao Wu

Presentation Title Page 42 FEL performance Juhao Wu 1.5 angstrom 6 angstrom

Bunch compression Page 43 BC parameters summary

Presentation Title Page 44 Possible test at NLCTA

Bunch compression Page 45 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: In Elegant, including transverse and longitudinal wake, coherent synchrotron radiation (CSR), longitudinal space charge (LSC) and velocity bunching 0.5 million macro-particles For scheme 1, current operating optics For scheme 2, new optics 20 pC beam at 5MeV, 0.5ps RMS bunch length, 5e-3 RMS energy spread, 1 m.mrad transverse emittance Beam energy: 60 MeV at BC1, 120 MeV at BC2

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

Bunch compression Page 47 Scheme 1 (1) L phase, current and bunch length InitialLinac1BC1Linac2BC2

Bunch compression Page 48 Scheme 1 (2) no compression, on crest InitialLinac1BC1Linac2BC2

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

Bunch compression Page 50 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)- 115 fs

Bunch compression Page 51 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)- 115 fs

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

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

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

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

Bunch compression Page 56 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 57 Current less sensitive to RF phase jitter 20pC, 80 micron

L =6 m L =9 m  rf =  25° L =330 m  rf =  41° L =550 m  rf =  10° BC-1 L =6 m R 56 =  36 mm BC-2 L =22 m R 56 =  25 mm DL-2 L =66 m R 56 = 0 DL-1 L =12 m R 56  0 undulator L =120 m 6 MeV  z  0.83 mm    0.1 % 150 MeV  z  0.83 mm    0.10 % 250 MeV  z  0.19 mm    1.8 % 4.3 GeV  z  mm    0.76 % 13.6 GeV  z  mm    0.01 %...existing linac L0 rf gun L3L1 X Lh L =0.6 m  rf =  L2 LCLS L = 16 m  rf =  40° L = 72 m  rf =  40° L  850 m  rf = 0° BC-2 L  14 m R 56 =  36 mm BC-3 L  18 m R 56 =  11 mm undulator L =? m 6 MeV  z  2.0 mm    0.1 % 120 MeV  z  0.5 mm    2.0 % 375 MeV  z  0.1 mm    1.4 % 1.64 GeV  z  mm    0.5 % 20.5 GeV  z  mm    0.01 % L3L0 Lh L =1.4 m  rf =  rf gun CL1 BC-1 L  4 m R 56 =  76 mm L = 8 m  rf   22° L2TESLA-XFEL (2003 parameters) Paul Emma

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

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