Rokhlenko A, Lebowitz J L
Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019, USA.
Phys Rev Lett. 2003 Aug 22;91(8):085002. doi: 10.1103/PhysRevLett.91.085002. Epub 2003 Aug 19.
An approximate analytic solution is constructed for the 2D space-charge-limited emission by a cathode surrounded by nonemitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.
针对由宽度为Λ的非发射导电壁架包围的阴极的二维空间电荷限制发射，构建了一个近似解析解。真空中静电问题的一个基本精确解（通过保角映射）与空间电荷区域中线性化问题的解相匹配，该区域的边界由于强磁场的存在而变得尖锐。阴极边缘附近狭窄区间内的电流密度增长强烈依赖于Λ。我们得到了一个关于总电流与Λ的函数关系的经验公式，该公式可推广到更一般的阴极几何形状。
