Direct Integration 3-D FDTD Method for Single-Species Cold Magnetized Plasma
Finite-difference equations for 3-D single-species cold magnetized plasma EM propagation are systematically generated using a new, algorithmic approach for generating finite-difference time-domain (FDTD) updates. This new approach is then generalized to handle systems with complex dispersion of arbitrarily high-order. It is shown how this results in the second-order accurate algorithms with numerical dispersion relations that can always be cast in the form of continuum dispersion counterparts via simple substitutions, avoiding laborious analysis. This allowed here the first reporting of a numerical Appleton–Hartree equation. The problem of field collocation is handled by the repetition of the Yee algorithm so that all field variables are defined at the corners of a new cubic computational cell. This cell offers new properties, such as full-vector control of the solution at each node. A new technique for deriving the stability condition is introduced to FDTD and shows that the new method has retained the same stability criterion of free-space propagation. Several simulation results are presented, one of which reveals a previously unreported problem, common to some gyrotropic methods—the tendency for spurious fields to arise at source locations. It is shown how this spuriousness, which has contaminated the results of a previous report, may be removed.