Child's Law Benchmark

Application ID: 17329

Space charge limited emission is a phenomenon that restricts the current of charged particles that can be released from a surface. As the electron current released by a cathode increases, so does the magnitude of the charge density in the immediate vicinity of the cathode. This distribution of charge density exerts an electric force on the emitted electrons, directed toward the cathode. The space charge limited current is the maximum current that can be released such that the emitted particles are not repelled back toward the cathode.

In this example, the space charge limited current in a plane-parallel vacuum diode is computed using the Space Charge Limited Emission node. The resulting electric potential distribution and current are compared with the analytical solution given by Child's Law. The current density is computed using a study that establishes a bidirectional coupling between the particle trajectories and the electric potential.

This model example illustrates applications of this type that would nominally be built using the following products: