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Beam-induced instabilities of Josephson plasma waves in a cylindrical beam-waveguide system with a layered superconducting shell

Yu. O. Averkov1,*, O. Yu. Averkov1, Yu. V. Prokopenko1,2, N. Williams3,4, and V. A. Yampol'skii1

  • *Contact author: yuriyaverkov@gmail.com
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Phys. Rev. B 114, 154508 – Published 14 September, 2026

DOI: https://doi.org/10.1103/fwlr-sthl

Abstract

We theoretically investigate the eigenspectrum and excitation of terahertz (THz) electromagnetic waves in a cylindrical beam-waveguide system containing a layered superconducting shell. The system is driven by a nonrelativistic tubular electron beam, which is assumed to be charge-neutralized by a stationary ion background. This charge compensation enables rectilinear beam propagation in the absence of an external focusing magnetic field and allows the superconductor to remain in the Meissner state. Starting from a hybrid electrodynamic boundary-value formulation, we derive the general dispersion relation for coupled beam-Josephson plasma waves (JPWs). The eigenmode spectrum and beam-induced instabilities are then analyzed in detail in the quasielectrostatic slow-wave approximation. It is shown that bulk-surface JPWs can exhibit negative dispersion, which enables the development of absolute instability during their interaction with the electron beam. For surface JPWs, the propagating branch has positive dispersion, so its beam-induced excitation is associated with convective amplification rather than absolute instability. An analytical expression for the instability growth rate is derived for the absolute-instability regime. At large longitudinal wave numbers, the frequencies of the bulk-surface waves asymptotically approach the Josephson plasma frequency ωJ. The anisotropy coefficient γ is found to play a crucial role in the surface-JPW spectrum: the azimuthally symmetric surface mode (n=0) preserves its traveling-wave character even at high anisotropy, whereas azimuthally asymmetric modes (n≥1) degenerate into localized oscillations with frequencies close to ωJ due to the shunting effect caused by the high in-plane conductivity. Numerical analysis of the absolute instability of bulk-surface JPWs shows that, among the modes considered, the maximum growth rate is attained for the n=1 mode. A crossover is revealed in the dependence of the growth rate on the thickness of the superconducting shell. For low-azimuthal-index modes, thinner shells enhance the instability by reducing the modal energy stored in the superconducting material and increasing the effective coupling impedance, whereas for higher-order modes (n≥9), the instability is enhanced when the shell thickness increases because thicker shells support whispering-gallery-like field distributions. These properties indicate that the proposed structure can serve as a flexible platform for tunable THz radiation sources.

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Phys. Rev. B 114, 154508– Published 14 September, 2026
  • Received 4 June 2026
  • Revised 19 August 2026
  • Accepted 24 August 2026
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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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