Axisymmetric Electromagnetic Wave Propagation Computation Using the Constrained Interpolation Profile Scheme With Large Time Steps

Abstract

Conventional explicit time-domain methods used to solve Maxwell's equations are reliable and robust but are conditionally stable and often require the fulfillment of the condition Courant-Friedrichs-Lewy (CFL) ≤ 1. While this is acceptable for many applications, in some instances, where Maxwell's equations are solved alongside systems with slower propagation velocities, explicit methods prove costly. This is the case for nonrelativistic electromagnetic Particle-In-Cell methods that are required to study plasma thrusters. Several algorithms have been proposed to retain a nearly explicit formulation using large time steps to achieve higher CFL values. Among these is the semi-Lagrangian constrained interpolation profile (CIP) method. While the ability of this method to handle CFL > 1 has been demonstrated for planar 2-D-3-D cases, this has not been done for 2-D cases with cylindrical symmetry. In this article, a procedure is presented to compute the electromagnetic wave propagation in 2-D domains with cylindrical symmetry using the CIP method. The CIP scheme is extended for CFL ≥ 1 cases, and a ghost node method is proposed to deal with the axis singularity and with the wall boundary condition. The results are compared with the fields of a Hertzian dipole and with a coaxial cable, and they show a good agreement.