A FREQUENCY-DEPENDENT FINITE-DIFFERENCE TIME-DOMAIN FORMULATION FOR TRANSIENT PROPAGATION IN PLASMA

Computation of transient electromagnetic propagation through plasma has been a difficult problem. Frequency domain solutions are available for one or two dimensions and stratified plasma geometries. Transient solutions have been obtained via transformations to the time domain, or by microscopic solution of the equations of motion of the charged particles. The finite-difference time-domain (FDTD) method is capable of explicitly computing macroscopic transient electromagnetic interactions with general three-dimensional geometries. However, previous FDTD formulations were not capable of analyzing plasmas for two reasons. First, FDTD requires that at each time step the permittivity and conductivity be specified as constants that do not depend on frequency, while even for the simplest plasmas these parameters vary with frequency. Second, the permittivity of a plasma can be negative, which can cause terms in FDTD expressions to become singular. A new FDTD formulation for frequency dependent materials ((FD)2TD) has been developed, which removes the above limitations. In a previous paper, (FD)2TD was applied to computation of transient propagation through a polar dielectric. In this paper we show that (FD)2TD may also be applied to compute transient propagation in plasma when the plasma can be characterized by a complex frequency-dependent permittivity. While the computational example presented in this paper is for a pulse normally incident on an isotropic plasma slab, the (FD)2TD formulation is fully three-dimensional. It can accommodate arbitrary transient excitation, with the one limitation that the excitation pulse must have no zero frequency energy component. Time-varying electron densities and/or collision frequencies could also be included. The formulation presented here is for an isotropic plasma, but extension to anisotropic plasma should be fairly straightforward.