Three dimensional axisymmetric space charge simulation via boundary elements and emitted particles

The boundary element (i.e., charge density) method can often be used to reliably and efficiently compute field strengths and field emission currents where space charge is not a factor. In order to approximate space charge effects, launching and tracking of simulated particles are added to a basic boundary element scheme. Quantities of most interest include the emitted current and gate current once the startup transients die out. Simplistic initial attempts at such a simulation reveal difficulties in the following areas: (1) choosing a single time step suitable for all emitted particles; (2) computing the effect of newly emitted particles on the tip field controlling the next emission step; and (3) stabilizing the computed result. Methods for combating these problems are implemented and tested in the case of concentric spheres where one dimensional potentials can be reliably numerically approximated by use of an ordinary differential equation solver. Finally, the resulting code is applied to laboratory geo...