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  • Open Access

Longitudinal modes of bunched beams with weak space charge

Alexey Burov*

  • Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

  • *burov@fnal.gov
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Phys. Rev. Accel. Beams 24, 064401 – Published 7 June, 2021

DOI: https://doi.org/10.1103/PhysRevAccelBeams.24.064401

Abstract

Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation to a parameterless integral equation. For any multipolarity, the discrete part of the spectrum is found to consist of infinite number of modes with real tunes, which limit point is the incoherent zero-amplitude frequency. In other words, notwithstanding the rf bucket nonlinearity and potential well distortion, the Landau damping is lost. Hence, even a tiny coupled-bunch interaction makes the beam unstable; such growth rates for all the modes are analytically obtained for arbitrary multipolarity. In practice, however, the finite threshold of this loss of Landau damping is set either by the high-frequency impedance roll-off or intrabeam scattering. Above the threshold, growth of the leading collective mode should result in persistent nonlinear oscillations.

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Phys. Rev. Accel. Beams 24, 064401– Published 7 June, 2021
  • Received 22 March 2021
  • Accepted 18 May 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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