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Multi-pass Beam Breakup (BBU) in energy recovery linacs (ERL)

Multi-pass Beam Breakup (BBU) in energy recovery linacs (ERL). Eduard Pozdeyev, BNL. Instability mechanism and threshold. B. E. x. Beam establishes a feedback that can become unstable. The threshold is approximately. 1 accel.-1 decel., 2D. N accel.-N decel., 1D.

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Multi-pass Beam Breakup (BBU) in energy recovery linacs (ERL)

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  1. Multi-pass Beam Breakup (BBU) in energy recovery linacs (ERL) Eduard Pozdeyev, BNL

  2. Instability mechanism and threshold B E x Beam establishes a feedback that can become unstable. The threshold is approximately 1 accel.-1 decel., 2D N accel.-N decel., 1D E. Pozdeyev, BNL

  3. Experimental observation of BBU at JLab FEL IR wiggler  E. Pozdeyev, BNL

  4. Beam behavior below the threshold: Q(I) Also valid for Ith<0!  F=2106.0 MHz, m12sin(Tr)<0 F=2116.584 MHz, m12sin(Tr)>0 E. Pozdeyev, BNL

  5. Formula, BBU codes benchmarking: Comparison to experiments E. Pozdeyev, BNL

  6. Multi-pass BBU codes Multi-pass BBU code can be separated in two groups according to their algorithm: TRACKING or EIGENVALUE E. Pozdeyev, BNL

  7. Mitigation techniques: development of low-QHOM, high-gradient cavities • Design of multi-cell cavities with low-Q (~104), low-R/Q HOMs seems to be the most reliable way to increase the BBU threshold • The work is under way at BNL, JLAB, Cornell U… BNL JLAB E. Pozdeyev, BNL

  8. Mitigation techniques: HOM frequency spread (large-scale machines) Cornell ERL Q=2.1E4, Ncav=320 (Hoffstaetter, Bazarov, Song) 6-GeV JAERI ERL Cav./HOM parameters - ? (M. Sawamura, R. Hajima) E. Pozdeyev, BNL

  9. Optical BBU suppression methods: n-phase advance, rotation • Adjustment of m12 and/or m34 was effectively used at JLAb FEL (D. Douglas). Effective for small machines. Provides a suppression factor of a few. • Strong coupling (rotation or reflection) promises to suppress BBU significantly in a two-pass machine if x-y modes are degenerate and well –separated (R. Rand, T. Smith). Effective for small, two-pass machines. Easily provides suppression by a factor of a few. Its effectiveness reduces for a large number of cavities. Its effect on multi-pass machines has not been properly studied. E. Pozdeyev, BNL

  10. Enhancement of rotation: double elliptical cavities ba b a S21 f Larger mode degeneracy can be achieved via axially asymmetric design of accelerating cavities. 70 MHz S21 f For a square cavity a/b ≈1.05-1.07 ±d is the variation of the transverse cavitysize E. Pozdeyev, BNL

  11. Narrow (limited) band feedback, broad band feedback BPF • Narrow (limited) band feedback can be used to mitigate effect of a few modes in a small machine • Broad band (Bunch-by-Bunch) feedback can be used in large scale machines. Complexity: Bunch passes through a machine only once or a few times. Instability growth rates can be of the order of a few tens of microseconds. V e i V E. Pozdeyev, BNL

  12. Prediction of BBU threshold at eRHIC Linac based on CEBAF experience CEBAF: QHOM=3.2e4, R/Q=50, R/Q·Q=1.6e6, Ncav=320, Npass=5 eRHIC(LR): QHOM=892, R/Q=57, R/Q·Q=4.2e4, Ncav=200, Npass=3 • Ith, CEBAF=20 mA • Scaling: • Ith 1/sqrt(Q) (J. Bisognano). • Ith 1/N2pass • Ith 1/Ncav • All numbers plugged in, the projection is Ith,eRHIC=530 mA E. Pozdeyev, BNL

  13. Simulation of BBU threshold at eRHIC linac (very preliminary) • eRHIC Linac Parameters: • 200 16MeV/pass cavities, measured Cu-model HOMspectrum • 50 foc. and 50 defoc. quadrupoles, G=1.262 T/m • 3 acel.-decel. passes, each is 1.3 km long • 28 MHz bunch rep.rate E. Pozdeyev, BNL

  14. Other effects that require accurate consideration • Cumulative (single-pass) BBU • Short-range transverse wakes (“banana-effect”). 1cm-long bunch can be long enough to be affected by short range wakes. It can be of important for applications requiring “good emittance”. • CSR • Fast ion instability • … E. Pozdeyev, BNL

  15. Acknowledgements • BNL: V. Ptitsyn, V. Litvinenko, R. Calaga • JLab: L. Merminga, G. Krafft, B. Yunn, C. Tennant, S. Benson , D. Douglas, K. Jordan, G. Neil, H. Wang, C. Hovater, R. Rimmer • Stanford: Todd Smith • Cornell: I. Bazarov, G. Hoffstaetter • DESY: Stefan Simrock • JAERI:M. Sawamura, R. Hajima E. Pozdeyev, BNL

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