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本文对电子回旋脉塞不稳定性的自洽非线性理论进行了研究。所用模型是在圆柱波导内沿轴向均匀磁場旋转并漂移的相对论电子注。由于相对论效应在波导中激起横电模式,我们在轴向波数和轴向电子速度为零的坐标系中导出了非线性耦合方程。从理论上描述了单一受激波的場幅值和频率偏移的非线性变化。联立求解考虑相对论效应的运动方程和非齐次波动方程,从而描述了电子与波的自洽特性。波的饱和有两种饱和机理,即自由能耗尽和相位捕获。两种饱和机理的逐漸过渡导致能量转換效率与电子注能量的关系曲线有一个峰值。数值计算结果表明,电子到波的能量转换效率在电子注坐标系中可以超过60%。
In this paper, we study the self-consistent nonlinear theory of the electron malalignment instability. The model used is a relativistic electron note that rotates and drifts along an axially uniform magnetic field within a cylindrical waveguide. Due to the relativistic effect of stimulating the transverse mode in the waveguide, we derive the nonlinear coupling equation in a coordinate system where the axial wavenumber and axial electron velocity are zero. The nonlinear variation of field amplitude and frequency offset of a single shock wave is theoretically described. Solving the equations of motion and non-homogeneous wave equations considering relativistic effects, the self-consistent properties of electrons and waves are described. Saturation of waves There are two kinds of saturation mechanisms, namely, free energy depletion and phase capture. The gradual transition of the two saturation mechanisms leads to a peak in the energy conversion efficiency versus electron energy. The numerical results show that the electron-to-wave energy conversion efficiency can exceed 60% in the electron-injection coordinate system.