为了对径向线内电子束的空间极限电流及相关物理参量进行分析,在径向方向无穷长与束流密度轴向均匀的假设条件下,对电势满足的线性泊松方程进行了解析求解,得到了空间极限电流的解析表达式,接下来对束流密度轴向非均匀分析条件下电势满足的非线性方程进行了数值求解,并与解析结果进行了对比。研究表明径向电子束具有较高的空间极限电流且当束流接近于极限电流传输时,束密度的非均匀性明显增加,相关结论可以为径向高功率微波器件的设计提供指导。

In order to study the space charge limited current and its related physical quantities, considering the infinitely long radial direction and the current density being constant in axial direction, the Poisson equation for electrical potential is solved theoretically and the expression of the space charge limited current of the beam is obtained. Then the non-linear Poisson equation which takes into consideration the non-uniform distribution of the charge density in axial direction is solved numerically. The numerical results and analytical results are compared. The results show that the radial beam has a higher space charge limited current in radial transmission line. When the beam value approaches to the space charge limited current, the non-uniform distribution of the charge density increases significantly. The relevant conclusion can provide guidance on the design of radial high power microwave devices.