1 / 18

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

meris
Download Presentation

Beam Modulation due to Longitudinal Space Charge

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related