Abstract

The effect of nonlinear stabilization of the instability of a tubular electron beam when it moves along the surface of a solid dielectric cylinder is investigated theoretically. It is assumed that the beam is nonrelativistic, infinitely thin in the radial direction, and moves along the surface of the cylinder parallel to the lines of force of an external constant magnetic field, which prevents the transverse motion of the beam electrons. The mechanism of nonlinear stabilization of azimuthally symmetric E-type electromagnetic waves with different values of radial mode indices is studied by the method of slowly varying amplitudes and phases. The physical cause of excitation of such waves is the Vavilov–Cherenkov resonance, and the nonlinear stabilization mechanism is based on the trapping of beam particles by the field of the excited wave. It is shown that, as the radial mode index of the excited wave increases, the saturation time of instability and the maxima and the “period” of amplitude oscillations at the nonlinear stage of instability saturation decrease. It is shown that, at the nonlinear stage of instability, the waves excited by the beam have elliptical polarization. Moreover, in the vacuum region, the directions of rotation of the electric field vectors of E₀₁ and E₀₂ waves turn out to be opposite.

中文翻译：

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管状带电粒子束与介电圆柱体相互作用的数值分析

摘要

理论上研究了管状电子束沿固体电介质圆柱体表面移动时的非线性稳定性对不稳定性的影响。假设电子束是非相对论的，在径向方向上无限薄，并且沿着圆柱体的表面平行于外部恒定磁场的力线移动，这阻止了电子束的横向运动。方位对称E的非线性稳定机制通过缓慢改变振幅和相位的方法研究了具有不同径向模式指数值的新型电磁波。激发此类波的物理原因是Vavilov–Cherenkov共振，非线性稳定机制是基于被激发波的场捕获束状粒子。结果表明，随着激发波径向模指数的增加，不稳定的饱和时间以及在不稳定的非线性阶段的振幅振荡的最大值和“周期”减小。结果表明，在不稳定的非线性阶段，被光束激发的波具有椭圆偏振。此外，在真空区域中，电场矢量E ₀₁和E的旋转方向原来₀₂波相反。