To optimize thrust performance, the expression of space‐charge‐limited current for vacuum arc thruster is derived from Poisson's equation. The commonly used ring‐type and coaxial‐type vacuum arc thrusters are simplified to the equivalent current sheet in planar geometry and cylindrical capacitor, respectively, for this calculation. Both the spatial distribution and peak magnitude of space‐charge‐limited current are given explicitly, together with their dependences on gap distance, applied voltage, charge number, and ion mass. For typical experimental parameters of the vacuum arc thruster, it is shown that the maximum current density drops significantly when the gap distance becomes large and grows when the applied voltage increases; moreover, a cathode material of lower atomic weight yields a higher current density. The expressions of total current for these two types of vacuum arc thruster are also presented. This work, to our best knowledge, is the first application of space‐charge‐limited current to the vacuum arc thruster and practically very interesting for engineering design.

中文翻译：

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真空电弧推进器的空间限制电流

为了优化推力性能，真空泊松推力器的空间电荷限制电流表达式是根据泊松方程推导出来的。对于此计算，常用的环形和同轴真空推力器分别简化为平面几何形状和圆柱电容器中的等效电流表。明确给出了空间电荷限制电流的空间分布和峰值幅度，以及它们对间隙距离，施加电压，电荷数和离子质量的依赖性。对于真空电弧推进器的典型实验参数，显示出当间隙距离变大时，最大电流密度显着下降，而当施加电压增加时，最大电流密度增加；此外，较低原子量的阴极材料产生较高的电流密度。还介绍了这两种真空电弧推力器的总电流表达式。据我们所知，这项工作是在真空电弧推力器中首次应用空间电荷限制电流，这实际上对工程设计非常有趣。