Beam Optimization with Fast Particle Tracking (FPT) LCLSII Physics Meting, 1/7/215 Lanfa Wang Motivation Physics Model of FPT Benchmark with ELEGANT Results for new injector beam
Motivation Complexity of LCLS-II beam dynamics (compared with LCLS) Strong space charge at injector (CW gun, low beam energy) Strong CSR effect (more bending magnets in transportation line) Strong LSC in linac (long by-pass beamline, low beam energy) Low beam energy For design/optimization purpose, we need a fast program, which should includes wakefield, CSR and space charge. ELEGANT provide detail tracking and including all the collective effects above, but it is not fast enough LiTrack is fast, but CSR and LSC is not included 2
Strong Impact of CSR and space charge without CSR and space charge with CSR +space charge Ji Qiang, et.al. WEP7, FEL15 3
Introduction to FPT Original for collective effects, Longitudinal space charge is added recently, it includes Geometric wake and resistive wall wake; 1D CSR in free space (and 2D CSR with shielding) 1D/2D LSC (uniform beam, Gaussian beam, or arbitrary beam) 4
CSR 1D free space CSR [Saldin, E.L. et al. Nucl.Instrum.Meth. A398 (1997) 373] Pro: Fast computation con: no shielding, no 2D effect 2D CSR with shielding Pro: shielding effect, resistive wall effect; 2D effect ; con: slow computation for very short bunch 4 35 3 25 Z ( ) 2 15 Real, Zhou Imaginary,Zhou Real, Wang Imaginary,Wang 1 5-5 2 4 6 8 1 k (1/mm) 5
2D CSR Apply to arbitrary pipe cross-section Fast CER computation; =6μm (5THz), σ r =.1mm Ante-chamber CSR Field at end of the LCLSII BC2 magnet Integrated field after the magnet 6
Shielding and CSR energy loss long wavelength dominant; frequency up to 5 THz is need beam of 1pC at Undulator Begin, sigz= 29.896(fs) 1.5 beam of 3pC at Undulator Begin, sigz= 113.57(fs) I (ka) 1.5 1.5 1pC I (ka) 1.5 3pC 5-5 5 1 z (fs) Beam Spectrum -2-1 1 2 3 4 5 z (fs) 4 Beam Spectrum Magnitude I(f) 4 3 2 1 Magnitude I(f) 3 2 1-1 -5 5 1 Frequency (THz) -2-1 1 2 Frequency (THz) LCLS-II Beam spectrum 7
Micro-bunch instability driven by CSR (KEK DR) No Saw-tooth instability observed with long wavelength CSR Short wavelength (High frequency) CSR is important for micro-bunch instability μm CSR is needed for LCLS-II f up to.5thz N=5.5e1 f up to 1.5THz KEK DR: beam energy 1.1GeV; Circumference 135.5m Bunch length 6.53 mm; bunch density.3.2.1-2 -1 1 2 3 q N=8.5E1 (L. Wang, H. Ikeda, K. Oide K. Ohmi and D. Zhou, TUPME17, IPAC13) 8 3 2 1
Longitudinal Space charge (LSC) 1D free space for round Gaussian and uniform beam Pro: Fast computation; good for long wavelength con: 2D effect (energy spread, damping) is not included 2D LSC with arbitrary beam and chamber [L. Wang, Y. Li, PRSTAB, 18, 2421 (215)] Pro: 2D effect and shielding effect; good for all wavelength Field spread converts to slice energy spread; Large slice energy spread for short wavelength; 1.2 1 Round uniform beam Z (arb. uints).8.6.4.2 1 2 3 4 5 6 7 8 /(ka) 9
LCLS 6/19/214 data, 1kA, 4GeV, 18pC, BC2 R56 = 24.7mm (Yuantao, Ding) LCLS 4GeV, 18pC, 1kA, LH off 4 LH =2.2uJ,Initial E =1.3keV 4 LH =3.7uJ,Initial E =11.4keV 4 E (MeV) 2-2 E (MeV) 2-2 E (MeV) 2-2 -4-1 1 t (fs) LH =5uJ,Initial E =12.3keV 4-4 -1 1 t (fs) LH =7.2uJ,Initial E =13.8keV 4-4 -1 1 t (fs) LH =9.9uJ,Initial E =15.6keV 4 E (MeV) 2-2 E (MeV) 2-2 E (MeV) 2-2 -4-1 1 t (fs) -4-1 1 t (fs) -4-1 1 t (fs) 1
ELEGANT Space Charge Model 1D LSC Elegant uses round uniform beam model with a = 3σ; good approximation at long wavelength. 3D space charge To be released 11
Benchmark FPT with ELEGANT Initial beam at 1MeV x-px plane: sigma_x =.1227mm, sigma_x' =.1411e-4, alphax=-.524, emittance_normalized =.3 mm-mrad y-py plane: same as x-px plane z-pz plane: sigma_z =.979mm, sigma_de = 1keV, alphaz =.368e-3 12
Without collective effects Initial Ideal Gaussian beam from 1MeV of LCLS linac Without wake, CSR and space charge compare Beam at BC2 END Red: ELEGANT Blue: FPT Beam energy 1.6GeV Beam energy 1.644GeV 13
With wake (RF structure, beam pipe) Peak current is lower due to the effect of wake 14
Wake+CSR Peak current increases with CSR 15
Wake+CSR+LSC The LSC kicker is compared with ELEGNAT and analysis For design, we can consider the long wavelength effect only (NOT instability); which includes the de-chirp effect and also a small number of macro-particle can be used; For instability, the main issue is how to handle noise. some ideas to reduce the noise and improve the resolution; under going.1.5 E (MeV) -.5 -.1-2 -1 1 2 t(fs) N sim FPT play trick at L1: Ez N real For frequency f >.25f c ~ c 4 s Micro-bunching at 2~3um; ubi starts from very beginning Bunching.14.12.1.8.6.4.2 5 1 15 ( m) FPT: 8 Millions particles ELEGANT: 5 Millions particles 16
Micro-bunch instability by ELEGANT and IMPACT (FEL15, TUP66) Wake+CSR+Spacecharge 5MP, 124bins, ELEGANT ~3μm Amp=.15% 624MP, 248 bins, IMPACT ~2.3μm Amp=.15% At undulator begin 17
LSC for emittance.45um 35 3 25 x y Z LSC ( ) 1.5 1.5 2 x 15 Long-by-pass contributed largest LSC at L1 (blue) and L2 (black) also important The wavelength at peak is close ( m) 2 15 1 5 5 1 15 2 25 3 35 4 s(m) BC1BEG BC2BEG DL1BEG DL2BEG DL1END DL2END bc1beg=12m bc2beg=335m dl1beg=928m dl1end=13m dl2beg=277m dl2end=31m.5 1 1.5 2 2.5 3 ( m) Bunching factor 6.7 and 1 are used 18
Optimization with FPT 19
3pC beam at 1MeV (Feng Zhou).7 Bunch emittance=4.3463e-7/4.356e-7 (m-rad).6 emittance ( m-rad).5.4.3.2 X-emittance Y-emittance.1-2 -15-1 -5 5 1 15 t (ps) Head 2
Optimization with FPT, LSC off, example for New 3pC Zero chirp High peak current >1kA Smooth current profile L1 phase= 2.8 degree Linearizer phase= 155 degree L2 Phase= 29.6 degree BC1 = 8mrad (R56~-33mm) BC2 = 43.8mrad (R56~-4mm) Confirmed with ELEGANT with CSR, (LSC off) Need to check LSC effect, the impact on the current profile is likely small. This is just one example, it can be further improved with more study Head ELEGNAT 21
1pC beam 1MeV (Feng Zhou) Peak current: 12A Emittance:.25um emittance ( m-rad).35.3.25.2.15.1.5 X-emittance Y-emittance -15-1 -5 5 1 t (ps) 4GeV at Undulator Begin Peak current: >1.1kA Small chirp Linearizer = 163 o R56BC2= -34 mm Continue study, matching... 22
Summary FPT provide fast computation with good agreements with ELEGANT; it provides flexibilities for different models (2D LSC, CSR shield effect, transverse SC also straight forward, etc.) Preliminary study shows optimization with FPT works well (>1kA, flat current profile) We demonstrated that the collective effects can be minimized 23
Next Optimization with (wake+csr)+lsc - Optimization with long wavelength effect (not instability), therefore a small number of particles is required - Micro-bunch instability (LSC) resolution is limited ~ > 2 s, improve the resolution - Noise reduction schemes integrated S2E optimization (MOGA/People) with GPT (injector)+fpt (linac), especially for low charge.. Ultimate goal: online optimization. Lots of works to be done and can be done to improve the beam quality (we already have very good emittance)! 24
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