Some remarks on the finite-difference time-domain modeling of rotating charges

The finite-difference time-domain (FDTD) modeling of a charge executing uniform circular motion is presented. It is demonstrated that the successful realization of this task requires initializing the FDTD time-stepping with the static electric field that the charge creates, which is computed by solving the associated Poisson problem. Next, the motion of the charge is described using the charge conservation Current Density Decomposition scheme which effectively describes the time varying charge distribution via equivalent currents. The numerically predicted electric field created by the charge motion is compared against the analytically expected solution as provided by the Liénard-Wiechert potentials.