The derivation of space-charge-limited current between concentric sphere

In high-power microwave diode design, the space-charge-limited current is important because of its relation to the diode impedance, and the formation of the virtual cathode. Although the Langmuir-Blodgett law, as a numerical solution, is helpful, a simple functional expression would be more convenient for practical research and the divergence of the series for large Rc/Ra would be avoided. First principle has been applied to derivate two-dimensional space-charge-limited current for planar plane capacitor and coaxial cylinders and its reliability has been examined adequately. This paper obtained the functional expression of space-charge-limited current for concentric sphere, the space-charge factor in this expression is got by comparison with classical Langmuir flow between concentric sphere.