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CSR Microbunching including Linac Wakefields Z. Huang, M. Borland, P. Emma, K.-J. Kim

CSR Microbunching including Linac Wakefields Z. Huang, M. Borland, P. Emma, K.-J. Kim SLAC and Argonne Berlin S2E Workshop 8/19/2003. energy profile. long. space. temporal profile. micro-bunching. s d  3  10 - 6. 230 fsec. s d  3  10 - 5. CSR Microbunching in LCLS.

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CSR Microbunching including Linac Wakefields Z. Huang, M. Borland, P. Emma, K.-J. Kim

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  1. CSR Microbunching including Linac Wakefields Z. Huang, M. Borland, P. Emma, K.-J. Kim SLAC and Argonne Berlin S2E Workshop 8/19/2003

  2. energy profile long. space temporal profile micro-bunching sd 310-6 230 fsec sd 310-5 CSR Microbunching in LCLS SC-wiggler damps bunching

  3. chirped beam path length difference compressed beam d d z z Dipole 2 Dipole 3 Dipole 1 Dz=R56 Dd • Radiation from bunch tail • catch up the head, may increase • energy spread and emittance z’ z s Compressor and CSR Formation length (overtaken length) lf~ (24 r2l)1/3 , r is the bend radius

  4. CSR Impedance • Ignore transverse effects • Ignore shielding • source size ~ << b (pipe radius) • Ignore transient effect Lf << Lb • (not the usual case, but included in1D codes) •  Steady-state, free-spaceCSR longitudinal impedance (Derbenev et al., Murphy et al.) k =2p/l = w/c

  5. density modulation at l CSR impedance R56 energy modulation at l CSR Microbunching • CSR emitted from sub-bunch structures for wavelengths l << sz interacts back to the bunch, leading to a microbunching instability • (similar to microwave instability in a ring) • This process can be initiated by either density or energy modulation

  6. f(s) DE/E0 gex CSR Microbunching Simulation

  7. before chicane A = 1% l = 15 mm after chicane A 11% l 1.5 mm gex = 0 sE/E0 = 210-6 G  11 energy modulation

  8. Linear evolution of b(k;s) can be described by an integral equation (Heifets et al.; Huang&Kim) Theory • Define a bunching parameter b at modulation wavelength l = 2p/k (fourier decomposes the current) • For arbitrary initial condition (density and/or energy modulation), this determines the final microbunching

  9. Staged Amplification • Typical chicane • dipole separation DL >> dipole length Lb 2 1 3 • Ignore the induced bunching from energy modulation in the same dipole (Saldin et al.) • Consider staged amplification from dipole to dipole by • setting K(s’,s)=O(Lb/DL)=0 if s-s’< DL

  10. dominant in low-gain dominant in high-gain Iterative Solution • Integral equation can be solved by two iterations • Calculate gain=|bfinal/binitial| as a function of l, and compare with simulation results

  11. Berlin CSR Benchmark Chicane • Elegant and CSR_calc (matlab based) codes used • a few million particles are loaded with 6D quiet start • CSR algorithm based on analytical wake models

  12. 250 MeV z  0.83 mm   110-5 4.54 GeV z  0.19 mm   310-5 14.35 GeV z  0.022 mm   110-4 150 MeV z  0.83 mm  210-5 BC-1 L 6 m R56-36 mm BC-2 L 22 m R56-22 mm DL-1 L 12 m R560 DL-2 L 66 m R56=0 To damp the instability, a SC wiggler can be placed right before BC2 To increase the incoherent energy spread (still small for FEL instab.) LCLS Acceleration and Compression Systems 7 MeV z  0.83 mm   510-4 rf gun Linac-1 L  9 m rf  -38° Linac-2 L  330 m rf  -43° Linac-3 L  550 m rf  -10° new Linac-0 L 6 m undulator L 120 m X ...existing linac SLAC linac tunnel undulator hall

  13. CSR also induced energy modulation in BC1 BC1 • BC1 gain in density modulation is low (so is BC2) sd=1.2×10-5, en=1 mm after BC1

  14. BC1+BC2 • BC2 not only amplifies density modulation gained in BC1, but turns BC1 energy modulation into gain in density modulation • Total gain of BC1+BC2 > BC1 gain X BC2 gain Wiggler off Wiggler on

  15. LCLS CSR Microbunching Gain • LCLS has four bend systems: BC1, BC2, and two beam transport dog legs (DL1, DL2) • DLs have very small R56  ignore induced density modulation but keep track of induced energy modulation

  16. Effect of Linac Wake • For a density-modulated beam, linac wake or impedance induces energy modulation, which turns into additional density modulation at bunch compressors through R56 • Longitudinal high-frequency impedance of a periodic accelerator structure (to the leading order) is BC1 BC2 DL1 Linac 1 Linac 2 L = 330 m (capacitive) • (k) / Z(k) I(k) L, where L ~ 300 m, comparable to energy modulation induced in BCs through CSR impedance

  17. Effect of Linac Wake (continued) • Linac wakefields increase the gain by about a factor of 2 • Reasonable agreement with Elegant S2E gain simulation (nonlinear lattice + wake, transient CSR and l compresses less than s)

  18. Summary • CSR microbunching instability is governed by an integral equation which is solved by two iterations for a typical chicane • Initialized by density and/or energy modulation, cascading through multiple chicanes and bends • Two similar but independent CSR codes shows reasonable agreement with each other and with theory • Geometric wakefields in the LCLS linac enhance the energy modulation and the total gain • Further enhancement in gain when LSC is taken into account…

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