标题： 超越童-兰缪尔极限 显示英文标题

标题： Beyond the Child-Langmuir Limit

摘要： 本文描述了一种用于二极管中电子束的完全非线性和非定常平面流动的新求解公式。 使用特征变量——即跟随粒子轨迹的变量——求解通过一个精确的解析但隐式的公式表达，适用于任意选择的入射速度$v_0$、电场$E_0$和电流$J_0$。 对于稳态解，这种方法阐明了最大电流$J_max$的来源，该电流由 Child 和 Langmuir 对$v_0=0$的推导以及 Jaffe 对$v_0>0$的推导所得。 隐式格式用于找到（1）具有恒定输入通量$J_0>J_max$的非稳态解，这会导致虚拟阴极的形成，以及（2）平均通量超过$J_max$绝热平均值的时间周期解。 显示英文摘要

摘要： This paper describes a new solution formulation for fully nonlinear and unsteady planar flow of an electron beam in a diode. Using characteristic variables - i.e., variables that follow particle paths - the solution is expressed through an exact analytic, but implicit, formula for any choice of incoming velocity $v_0$, electric field $E_0$ and current $J_0$. For steady solutions, this approach clarifies the origin of the maximal current $J_max$, derived by Child and Langmuir for $v_0=0$ and by Jaffe for $v_0>0$. The implicit formulation is used to find (1) unsteady solutions having constant incoming flux $J_0>J_max$, which leads formation of a virtual cathode, and (2) time-periodic solutions whose average flux exceeds the adiabatic average of $J_max$.