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  • Open Access

Head-tail modes for strong space charge

A. Burov

  • FNAL, Batavia, Illinois 60510, USA

Phys. Rev. ST Accel. Beams 12, 044202 – Published 30 April, 2009Erratum Phys. Rev. ST Accel. Beams 12, 109901 (2009)

DOI: https://doi.org/10.1103/PhysRevSTAB.12.044202

Abstract

The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are explored. The Landau damping rates are also found. The suppression of the transverse mode coupling instability by the space charge is explained.

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References (10)

  1. C. Pellegrini, Nuovo Cimento A64, 447 (1969).
  2. M. Sands, SLAC Reports No. TN-69-8, TN-69-10, 1969.
  3. F. Sacherer, CERN Report No. SI-BR/72-5, 1972; in Proceedings of the 9th International Conference on High Energy Accelerators, SLAC, 1974, p. 374.
  4. A. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators (J. Wiley & Sons, Inc., New York, 1993).
  5. Handbook of Accelerator Physics and Engineering, edited by A. W. Chao and M. Tigner (World Scientific, Singapore, 1998), p. 136, Eq. (22). Our Eq. (26) for the round beam follows after a substitution a=1, 1/(1+u)=z. It has to be taken into account though that Eq. (22) of the “Handbook” contains a typo, confirmed by A. W. Chao in private communication: parameters αx,y in that equation must be substituted by αx,y/4.
  6. M. Blaskiewicz, Phys. Rev. ST Accel. Beams 1, 044201 (1998).
  7. M. Blaskiewicz, Phys. Rev. ST Accel. Beams 6, 014203 (2003).
  8. A. Burov and V. Lebedev, Phys. Rev. ST Accel. Beams 12, 034201 (2009).
  9. A. Burov and V. Danilov, Phys. Rev. Lett. 82, 2286 (1999).
  10. E. Kamke, “Handbook of Ordinary Differential Equations” [in German (Akademische Verlagsgesellschaft, Leipzig, 1959) or Russian (Nauka, Moscow, 1976) translation].

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