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CSR Impedance From a Wiggler and the Impact on the Beam Instability in Damping Rings

KEK-SLAC ISG9 Meeting. CSR Impedance From a Wiggler and the Impact on the Beam Instability in Damping Rings. Tor Raubenheimer, and Juhao Wu, Gennady Stupakov December 10 - 13, 2002.

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CSR Impedance From a Wiggler and the Impact on the Beam Instability in Damping Rings

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  1. KEK-SLAC ISG9 Meeting CSR Impedance From a Wigglerand the Impact on the Beam Instability in Damping Rings Tor Raubenheimer, and Juhao Wu, Gennady Stupakov December 10 - 13, 2002 Presented at the 9th KEK-SLACInternational Linear Collider Study Group(ISG) Meeting , KEK, Japan, December 10 - 13, 2002

  2. KEK-SLAC ISG9 Meeting Motivation • Damping rings for future Linear Colliders, e.g., NLC, requires very fast damping  long wigglers; • Extracted beam must be very stable sensitive to bursting instabilities; • Microwave instabilities from vacuum system are real concerns; • Recent CSR studies indicate additional potential problem.

  3. KEK-SLAC ISG9 Meeting Damping RingNominal Parameters NLC TESLA

  4. KEK-SLAC ISG9 Meeting CSR instability • Stupakov-Heifets theory [PRST-AB, 5(2002)054402] indicates a potential instability due to the CSR in dipoles; • Experimental observations [John Byrd, et al. , PRL 89(2002)224801; NSLS/BNL; BESSY-II] Model predictions ---- Courtesy of J. Byrd

  5. KEK-SLAC ISG9 Meeting CSR Impedance • Theory is developed (known,[Stupakov-Heifets, 2002]) • We need impedance • Dipoles ( > 0) (known, [Murphy, et al., 1995]) • Scaling • longest wavelength determines threshold • Wigglers ( < 0) (We need to solve) • Could we approximate the wiggler as a sequence of dipoles with an effective radius?

  6. KEK-SLAC ISG9 Meeting CSR Wiggler Wake • Early studies [Yong-Ho Chin, LBL-29981 (1990); Saldin et al., NIMA 417 (1998) 158] • We introduce Wake as therefore, the wake Green function • Our results are universal by expressing G with only one parameter , as long as K is large.

  7. KEK-SLAC ISG9 Meeting Numerical G-function Start over from retarded potential Wake has the correct dependences: Zeros and peaks at nlFEL/2 and scalingas s-1/3 for small s and s-1 for large s

  8. KEK-SLAC ISG9 Meeting Simple Physics Model(ala Derbenev) • Dipole: • Wiggler: W||~ s - 1/3 s-1/3 comes from retarded position • W|| = 0, for s = n lFEL ; • W|| = max, for s = lFEL/2; • W||~ s - 1/3 , for s  0; • W||~ s - 1 , for s >> lFEL.

  9. KEK-SLAC ISG9 Meeting Real Part of the Impedance Real part of the impedance with peaks at nlFEL which continues to increase towards lc. Check with the wiggler radiation spectrum[Alferov, et al. , 1974; Krinsky, et al. , 1983], perfect agreement.

  10. KEK-SLAC ISG9 Meeting Imaginary Part of the Impedance

  11. KEK-SLAC ISG9 Meeting Complete Numerical ResultsNLC damping ring Why dips not peaks??? • Growth rate Dipoles and wigglers Wigglers Dipoles

  12. KEK-SLAC ISG9 Meeting Inside Wiggler Yeah, right peaks!!! NLC TESLA

  13. KEK-SLAC ISG9 Meeting Estimate at FEL frequency • At FEL and harmonics, Z = R – i L, with L>>1, R>0, but R<<L. • Gaussian in energy spread • Dispersion relation is • 3D FEL theory give instability growth length about 50 m for the NLC wiggler.

  14. KEK-SLAC ISG9 Meeting ATF Damping RingThreshold vs. wavelength • We hope to get experimental verification! Wiggler on Wiggler off Pipe cut-off wavelength (Assuming 3 cm height ) Nominal current

  15. KEK-SLAC ISG9 Meeting Discussion • The fact that the impedance of the dipole and that of the wiggler have different scaling at low-frequency, supports a wigger ring design together with other study results. • For practical CSR purpose, (< 0.1 fFEL), the wiggler impedance is • What about waveguide cut-off and resonances? • How to compare with experiment?

  16. KEK-SLAC ISG9 Meeting References: • G. Stupakov & S. Heifets, PRST-AB 5(2002) 054402; • J. Byrd, et al. , PRL 89(2002) 224801; • G. Carr, et al. , NIMA 463(2001)387; B. Podobedov, et al. , PAC2001, P. 1921; S. Kramer, et al. , EPAC2002, P. 1523; • M. Abo-Bakr, et al. , PRL 88(2002) 254801; • Yong-Ho Chin, LBL-29981 (1990); E.L. Saldin, et al. , NIMA 417(1998)158; • J.B. Murphy, et al. ,PAC95, P. 2980;Part. Accel. 57(1997)9; • J.B. Murphy, et al. ,NIMA 346(1994)571;J.B. Murphy, et al. ,PAC95, P. 284; • Derbenev, et al. , DESY-TESLA-FEL95-05; R.L. Warnock & P. Morton, Part. Accel. 25(1990)113;A. Faltens, L.J. Laslett, Part. Accel. 4(1973)151;BNL-20550(1975); • D.F. Alferov, et al. , Sov. Phys. Tech. Phys. 18(1974)1336;S. Krinsky, et al. , Handbook on Syn. Rad. Vol. 1(1983) 65.

  17. KEK-SLAC ISG9 Meeting Calculation details • The rate of energy loss where and  is determined by and

  18. KEK-SLAC ISG9 Meeting Analytical check • Estimate of the extreme points They are plotted as “+”s in the plot for G.

  19. KEK-SLAC ISG9 Meeting Analytical check • Short-range limit [perturbative approach] • Simple approach Dipoles Effective radius

  20. KEK-SLAC ISG9 Meeting Undulator (X-ray FEL) Yeah, right peaks!!! LCLS TESLA XFEL

  21. KEK-SLAC ISG9 Meeting How to treat wiggler (An estimate) • Treat the wiggler as 2N pieces of Dipoles • Impedance • Threshold in NLC Damping Ring drops from 1.75×1010 with dipoles only to 7.25 ×109. average It is serious!!! Recall the design value is 7.5 ×109; But is bending magnet approach for wiggler valid?

  22. KEK-SLAC ISG9 Meeting Acknowledgements • Thank A.W. Chao, S.A. Heifets, Z. Huang of SLAC; • Thank J.B. Murphy, J.-M. Wang , S. Krinsky, B. Podobedov, S. Kramer of NSLS / BNL. • Work supported by contract DE-AC03-76SF00515 with US DOE.

  23. KEK-SLAC ISG9 Meeting An estimate on the FEL instability • 1-D theory predicts very short-gain length • However, minimal beam-radiation overlap • 3-D TDA simulation gives, for NLC wigglers, but the wiggler is only about 50 m. Single pass isn’t dangerous, but how about multi-turn? Need numerical simulations with momentum compaction for ring.

  24. KEK-SLAC ISG9 Meeting Complete Numerical ResultsNLC damping ring threshold Wigglers Why peaks not dips??? Dipoles Dipoles and wigglers

  25. KEK-SLAC ISG9 Meeting Analytical Asymptotic Expression Real part of the impedance is linear in k; Imaginary part is k Log[k]. • Low-frequency (up to ) with the FEL wavenumber. • High-frequency ( ) Effective dipole radius Average over one period

  26. KEK-SLAC ISG9 Meeting Length Scales • Cooperative/formation length for a radiation wavelength lf • Dipole: • Wiggler: Periodicity leads to interference • Pipe cut-off wavelength: 1 mm; • Long-range wake applicable for: For l < FEL“may” approximate as 2N dipoles ; but for longer, has to include interference; need look at FEL frequency and harmonics

  27. KEK-SLAC ISG9 Meeting Low-frequency ImpedanceAnalytical • Wiggler impedance: • Total impedance: We may use the low-frequency impedance for practical purpose!

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