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 10 23 m À3 -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.

Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime

“…First, using the Cartesian code vorpal with a newly developed perfect dispersion algorithm (Cowan et al 2012), vorpal-pd, made it possible to use large grid spacings (∼15 grid points per wavelength in the direction of propagation) and proportionally larger time steps. This approach reproduces the correct group velocity of a broad-bandwidth laser pulse.…”

“…The coefficients α i , β i , and γ ij are chosen to guarantee that waves propagating along the x axis (the laser propagation direction in our simulations) in vacuum experience no numerical dispersion, as described in (Cowan et al 2012). The only constraint is that the longitudinal grid spacing ∆x must satisfy ∆x ≤ ∆y, ∆z for the transverse grid spacings ∆y and ∆z.…”

“…In this section we give a brief overview of the perfect dispersion method we use; a more complete description together with detailed benchmarks will be presented in (Cowan et al 2012). Our method is based on that in (Pukhov 1999;Kärkkäinen et al 2006), in which the FDTD algorithm is modified by smoothing the fields in the curl operator in one of Maxwell's equations.…”

“…We use a newly-developed perfect-dispersion algorithm (Cowan et al 2012) implemented in the fully explicit 3D Cartesian vorpal simulation framework , subsequently referred to as vorpal-pd. The algorithm, briefly described in Sec.…”

Convergence in nonlinear laser wakefield accelerators modeling in a Lorentz-boosted frame

“…The latter is one of the configurations that is being considered as the first stage in the EuPRAXIA project [22]. These simulations are run using both the CK (using Cowan's parameter settings [7]) and the PSATD solvers, and with a 4-pass bilinear filter plus compensation [23]. The laser group velocities evaluated for the given parameters using the linear plasma fluid theory are γ g ≈ 13.2, and 41.8 for 10 19 cm −3 and 10 18 cm −3 respectively.…”