电子束空间极限电流的非线性理论研究

从电子束一维稳态传输的电势非线性Poisson方程出发，推导了圆柱波导内实心束和环形束空间极限电流与电子入射电势的依赖关系，给出了数值求解方法和解的特征，分析比较了数值计算与现有解析公式及粒子模拟的结果.考虑电子的横向运动，对数值方法进行了二维修正，计算结果与粒子模拟结果具有很好的一致性.说明利用数值方法计算电子电势非线性微分方程能够得到更精确的电子束在圆柱波导内的空间极限电流；另外，对其他形状的波导，尤其是难以得到解析式的情况，根据实际几何结构设置边界条件，数值方法可以方便地给出束流传输特性，对设计新型结构的高功率微波器件提供理论指导. 关键词： 相对论电子束 圆柱波导 空间极限电流 束流传输

Nonlinear analysis on electron beam current in cylindrical waveguide

The space-charge-limited currents of both solid electron beam and annular electron beam in cylindrical waveguide are derived from the nonlinear Poisson equation for potential in the region of electron beams.Corrections for the transverse motion of electrons are made to the solution,which bring more consistent with the results from PIC simulations.Though numerical computation,it is showed that electrons located along the axis and by outer radius of solid and annular electron beams respectively and electrons standing near to the outside of the beam has larger axial velocity than these inside.This approach is available for analyzing the characteristics of electron beam transporting in high power microwave generator with other configuration waveguide.