Potential and field computations by an optimized Monte Carlo technique

The Monte Carlo method is applied to diverging field problems. The computational effort, expressed by the number of steps in random walks, is related to the relative space potential, the prespecified walk termination distance, and the degree of field nonuniformity in the gap. To obtain potential and field distributions in a given system, equations for these quantities are developed at neighboring space points using Green's function. The accuracy of the algorithm is markedly enhanced by seeking the optimal spacing of the neighboring points. The technique compares satisfactorily with the charge-simulation method in a case study on a hemispherically capped rod-plane gap.<>