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  • Open Access

Single bunch stability to monopole excitation

Sam Heifets and Boris Podobedov

  • Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309

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Phys. Rev. ST Accel. Beams 2, 044402 – Published 14 April, 1999

DOI: https://doi.org/10.1103/PhysRevSTAB.2.044402

Abstract

We study single bunch stability with respect to monopole longitudinal oscillations in electron storage rings. Our analysis is different from the standard approach based on the linearized Vlasov equation. Rather, we reduce the full nonlinear Fokker-Planck equation to a Schrödinger-like equation which is subsequently analyzed by perturbation theory. We show that the Haissinski solution [Nuovo Cimento Soc. Ital. Fis. 18B, 72 (1973)] may become unstable with respect to monopole oscillations and derive a stability criterion in terms of the ring impedance. We then discuss this criterion and apply it to a broadband resonator impedance model.

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References (9)

  1. J. Haissinski, Nuovo Cimento Soc. Ital. Fis. 18B, 72, (1973).
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  3. H. Bruck, in Accelerateurs Circulaires des Particles (Presses Universitaires de France, Paris, 1966).
  4. J. Schonfeld, Ann. Phys. (N.Y.) 160, 149 (1985).
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  8. A. Nadji et al., Proceedings of the European Particle Accelerator Conference, Barcelona, Spain, 1996 (Institute of Physics, Bristol, UK, 1996), p. 676.
  9. S. X. Fong et al., KEK Report No. 94-190, 1994.

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Phys. Rev. ST Accel. Beams 2, 044402– Published 14 April, 1999
  • Received 18 January 1999
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