Space-charge limited current for 1-d cylindrical diodes

By introducing a physics approximation method into analyzing the nonlinear Poisson's equation, an analytical expression for the space-charge-limited current density for a one-dimensional (1-D) cylindrical diode has been investigated and developed. This expression is different from Child-Langmuir law for the planar diode and is simpler than Langmuir-Blodgett law for the cylindrical diode. This expression builds an explicit connection between the current density and the physical parameters, which is helpful in optimizing the design of the cylindrical vacuum diode. In addition, a comparison between our analytical result and Langmuir-Blodgett law shows that the physics approximation method is valid in nonlinear differential equation analysis and can be used in other similar cases. Applying the approximation method, we get the relativistic theory corrected current for 1-D cylindrical diodes.