Suppression of numerical errors in the charge conservation law for finite-difference time-domain method with higher-order accuracy

A new fourth-order Finite-Difference Time-Domain (FDTD) method, incorporating a correction for numerical errors in the charge conservation law, is presented. This FDTD method was designed to reduce numerical dispersion errors and relax the Courant condition. A crucial feature is the correction of the current density to numerically satisfy the charge conservation law. Such a correction for the current density is necessary in plasma kinetic simulations to prevent the generation of non-physical electric fields, which could adversely affect the results. Furthermore, the dispersion relation is tailored to meet the requirements of plasma kinetic simulations by ensuring that the numerical frequency increases monotonically. The results of plasma kinetic simulations using a Particle-In-Cell (PIC) code with the new method are compared with those of the conventional method. The new method, featuring the correction for current density and a monotonically increasing numerical frequency, reduces the rate of increase in energy densities in plasma kinetic simulations.