Generalized algorithm for control of numerical dispersion in explicit time-domain electromagnetic simulations

Abstract

We describe a modification to the finite-difference time-domain algorithm for electromagnetics on a Cartesian grid which eliminates numerical dispersion error in vacuum for waves propagating along a grid axis. We provide details of the algorithm, which generalizes previous work by allowing 3D operation with a wide choice of aspect ratio, and give conditions to eliminate dispersive errors along one or more of the coordinate axes. We discuss the algorithm in the context of laser-plasma acceleration simulation, showing significant reduction—up to a factor of 280, at a plasma density of 1023m−3 —of the dispersion error of a linear laser pulse in a plasma channel. We then compare the new algorithm with the standard electromagnetic update for laser-plasma accelerator stage simulations, demonstrating that by controlling numerical dispersion, the new algorithm allows more accurate simulation than is otherwise obtained. We also show that the algorithm can be used to overcome the critical but difficult challenge of consistent initialization of a relativistic particle beam and its fields in an accelerator simulation.