Nonlinear Stabilization of Resistive Instability of a Tubular Charged Particle Beam Moving above a Solid-State Plasma Cy
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S IN PLASMA
Nonlinear Stabilization of Resistive Instability of a Tubular Charged Particle Beam Moving above a Solid-State Plasma Cylinder Yu. O. Averkova, b, *, Yu. V. Prokopenkoa, c, **, and V. M. Yakovenkoa, *** a Usikov
Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, Kharkiv, 61085 Ukraine b Karazin Kharkiv National University, Kharkiv, 61022 Ukraine c Kharkiv National University of Radio Electronics, Kharkiv, 61166 Ukraine *e-mail: [email protected] **e-mail: [email protected] ***e-mail: [email protected] Received November 9, 2018; revised December 12, 2018; accepted December 20, 2018
Abstract—Nonlinear stabilization of instability of an infinitely thin tubular electron beam moving along the surface of a solid-state plasma cylinder is analyzed. It is assumed that the electron collision frequency in the plasma cylinder is much higher than the frequency of plasma eigenmodes (oscillations). The beam is assumed to be nonrelativistic, and, thus, the problem is solved in the electrostatic approximation. It is shown that the growth of the wave amplitude is stabilized nonlinearly due to the self-trapping of the beam electrons by the field of the electrostatic wave excited in the beam itself. It is found that the saturation time of instability and the maximum amplitude of the excited wave depend on the radius of the plasma cylinder. It is established that the larger the radius of the plasma cylinder, the later the nonlinear stage of instability begins and the larger the maximum amplitude of the excited wave. DOI: 10.1134/S1063780X19060011
1. INTRODUCTION Search for new mechanisms of generation of electromagnetic waves by charged particle beams propagating in various electrodynamic systems is an important problem of modern radiophysics and electronics. The motion of charged particle beams in such systems is accompanied by the development of instabilities, including electrostatic ones, which leads to the generation of various types of oscillations. A stationary mode is established as a result of nonlinear interaction of charged particles with the eigenwaves of the electrodynamic system. We note that, until now, nonlinear stabilization of beam instabilities has been considered only for cases of collisionless and weakly collisional plasmas. Nonlinear waves in plasma without allowance for thermal effects were first studied by A.I. Akhiezer, G.Ya. Lyubarskii, and R.V. Polovin more than half a century ago [1–3]. In particular, they showed that the frequency of nonlinear plasma oscillations is independent of the amplitude only in the nonrelativistic limit. It was shown in [3] that, in the relativistic case, the period of an intense plasma wave increases with increasing amplitude. Among the first studies on the nonlinear theory of beam–plasma instabilities where
nonlinear stabilization of these instabilities due to the trapping of the beam electrons by a plasma wave was considered, it is worth mentioning works [4–18]. In those works, modulated and unmodulated relativistic bea
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