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Beam Modulation due to Longitudinal Space Charge

Beam Modulation due to Longitudinal Space Charge. Zhirong Huang, SLAC Berlin S2E Workshop 8/18/2003. Introduction. SDL microbunching observations through rf zero-phasing LSC driven microbunching instability (TESLA-FEL-2003-02) Injector modulation studies

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Beam Modulation due to Longitudinal Space Charge

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  1. Beam Modulation due to Longitudinal Space Charge Zhirong Huang, SLAC Berlin S2E Workshop 8/18/2003

  2. Introduction • SDL microbunching observations through rf zero-phasing • LSC driven microbunching instability (TESLA-FEL-2003-02) • Injector modulation studies • Important to know beam modulation induced by LSC • Discuss methods to evaluate current and energy modulation in the linac • Discuss its impact on rf zero-phasing measurements • Do not discuss gain in bunch compressors (until Thursday)

  3. LSC Impedance • For a round, parallel electron beams with a uniform transverse cross section of radius rb, the longitudinal space charge impedance on axis is (cgs units) • Off-axis LSC is smaller and can increase the energy spread • Free space approximation is good when • /(2) << beam pipe radius

  4. Space Charge Oscillation • If there is a density modulation, space charge pushes particles from high density to low density, creating energy modulation in the process I E • Energy modulation converts back to density modulation to complete space charge oscillation with frequency

  5. Space Charge Oscillation II • Density and energy modulation in a drift at distance s • At a very large g, plasma phase advance (Ws/c) << 1, • beam is “frozen,” energy modulation gets accumulated • (Saldin/Schneidmiller/Yurkov, TESLA-FEL-2003-02) • LSC acts like a normal impedance at high energies

  6. Non-rigid beam • At lower energies (in the injector…), beam is not rigid • Space charge simulations may be time-consuming and noisy at high frequencies • Linear evolution of high-frequency beam modulations can be described by the same integral equation for CSR microbunching • (Heifets et al., PRSTAB-064401; Huang/Kim, PRSTAB-074401) In a drift LSC ignore in the linac

  7. Including Acceleration • beam energy r(s) increases in the linac. Generalize the momentum compaction R56’(! s) as the path length change at s due to a small change in  (not ) at : • The integral equation for LSC microbunching in the linac is • In a drift,  Space charge oscillation • For very large g, R56’=0, b(k,s)=b0(k,s), beam is “frozen”

  8. Comparison with Parmela • Energy Modulation • Parmela simulations (C. Limborg) of a 3-m drift at 6 and 12 MeV (beam size changes due to optics and transverse SC) • Theory-1D: integral equation using average LSC impedance • Theory-3D takes into account transverse variations of LSC (J.H. Wu)

  9. (courtesy of J.H. Wu) LSC 3-D Model • LSC impedance is r-dependant, which leads to decoherence • We have • Impedance at arbitrary radial coordinate r from a -ring with unit charge and radial coordinate a is • Convolution with a Parabolic distribution,

  10. Comparison with Elegant • Borland implemented 1-D LSC impedance in elegant • Current modulation at different accelerating gradients Elegant tracking (M. Borland) Analytical calculation

  11. Injector Modulation Studies • Assume 10% initial density modulation at gun exit at 5.7 MeV • After 67 cm drift + 2 accelerating structures (150 MeV in 7 m), LSC induced energy modulation Parmela simulations (C. Limborg) • LSC induced energy modulation in the LCLS injector is small at shorter wavelengths (<250 m), where the downstream gain is the highest • Density modulation at these wavelengths is also reduced

  12. SDL microbunching experiment (W. Graves, T. Shaftan et al.) 65 MeV Energy spectrometer X (E) profile E E E E z z z z z

  13. Long. Phase Space Distortion • rf zero phasing energy spectrum is sensitive to beam energy • modulation • Small modulation gets projected to large modulation • Energy modulation can be induced by LSC in the zero-phasing section if c/» L (length of the section, ~15 m)

  14. Enhancement of horizontal modulation Energy deviation = chirp + sinusoidal modulation Total charge Energy profile or magnification

  15. Define “gain” = x modulation amplitude/current modulation I0=300 A, =130, rb=600 m  Gm >> l (Z. Huang, T. Shaftan, SLAC-PUB-9788, 2003) • zero-phasing images are dominated by effects of • energy modulation instead of current modulation

  16. Beam size and It’s Effect on the modulation Beam size in the zero-phasing linac is varied (courtesy of T. Shaftan)

  17. IR measurements Bolometer signal, uVs (T. Shaftan) Filters: >40 um >100 um >160 um Wavelength, um

  18. Summary • LSC induced modulation in the linac can be described by a modified integral equation that includes acceleration • Comparable energy modulation with Parmela simulations • Initial studies suggest that accumulated energy modulation at the end of the injector is small at the most dangerous modulation wavelengths for LCLS • Density modulation is reduced in the injector, but can be amplified by downstream bunch compressors… • Energy spectrum of a chirped beam is sensitive to beam energy modulation, which could be induced by LSC in the SDL linac ( means to measure energy modulation)

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