Calculation of inductive electric fields in pulsed coaxial devices using electric vector potentials

In many high-voltage pulsed power systems the electric fields are predominantly inductive rather than electrostatic. That is, in the usual expression for generalized electric field, E = -/spl nabla//spl Phi/-/spl part/A//spl part/t, /spl Phi/ is the scalar potential that gives rise to the electrostatic field, and A is the magnetic vector potential, from which the inductive field is derived. In problems where there are regions without charge separation or steady state currents flowing, the electrostatic component does not exist, and the usual technique of solving the scalar Laplace´s equation for the potential is inappropriate for determining the electric fields. Calculation of the magnetic vector potential is plagued by choice of gauge condition and specification of correct boundary conditions. Especially for coaxial (axisymmetric) systems typical of many pulsed power components and systems, where the current flow is in the r, z plane, there are two components of the vector potential that must be solved-each with its own boundary conditions. Specification of all the correct boundary conditions is nontrivial. In this paper, we present a convenient technique for the calculation of inductive electric fields in coaxial systems. The technique is based on the introduction of a vector electric potential that is derived from Poisson´s equation, in combination with Faraday´s Law and the E, D constitutive relation. In coaxial geometry, the electric vector potential is only azimuthal and, therefore, quasi-scalar. It is conveniently calculated with any two-dimensional Poisson equation solver, and the resultant inductive field distribution easily calculated. We have used the technique in several pulsed power system designs with success. Specific examples of the application of the technique are given.