Manuel Kirchen

A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm

Abstract We propose a spectral Particle-In-Cell (PIC) algorithm that is based on the combination of a Hankel transform and a Fourier transform. For physical problems that have close-to-cylindrical symmetry, this algorithm can be much faster than full 3D PIC algorithms. In addition, unlike standard finite-difference PIC codes, the proposed algorithm is free of spurious numerical dispersion, in vacuum. This algorithm is benchmarked in several situations that are of interest for laser–plasma interactions. These benchmarks show that it avoids a number of numerical artifacts, that would otherwise affect the physics in a standard PIC algorithm — including the zero-order numerical Cherenkov effect.

Stable discrete representation of relativistically drifting plasmas

Representing the electrodynamics of relativistically drifting particle ensembles in discrete, co-propagating Galilean coordinates enables the derivation of a Particle-In-Cell algorithm that is intrinsically free of the numerical Cherenkov instability for plasmas flowing at a uniform velocity. Application of the method is shown by modeling plasma accelerators in a Lorentz-transformed optimal frame of reference.

Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates.

Particle-in-cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including, e.g., laser-wakefield acceleration, when viewed in a Lorentz-boosted frame) but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination of the NCI is verified empirically and confirmed by a theoretical analysis of the instability. Moreover, it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.

Accurate modeling of plasma acceleration with arbitrary order pseudo-spectral particle-in-cell methods

Particle in Cell (PIC) simulations are a widely used tool for the investigation of both laser- and beam-driven plasma acceleration. It is a known issue that the beam quality can be artificially degraded by numerical Cherenkov radiation (NCR) resulting primarily from an incorrectly modeled dispersion relation. Pseudo-spectral solvers featuring infinite order stencils can strongly reduce NCR—or even suppress it—and are therefore well suited to correctly model the beam properties. For efficient parallelization of the PIC algorithm, however, localized solvers are inevitable. Arbitrary order pseudo-spectral methods provide this needed locality. Yet, these methods can again be prone to NCR. Here, we show that acceptably low solver orders are sufficient to correctly model the physics of interest, while allowing for parallel computation by domain decomposition.

Novel approaches to suppress the numerical Cherenkov instability in Pseudo-Spectral Particle-in-Cell plasma simulation codes

Summary form only given. Typically, the most serious numerical instability in particle-in-cell simulations of relativistic particle beams is the numerical Cherenkov instability, arising from coupling between electromagnetic and nonphysical beam modes.1 Over the past few years, we have developed a variety of approaches for ameliorating this instability in Pseudo-Spectral Time-Domain algorithms, quantitatively assessed their stability analytically, and verified results using the WARP simulation code2-4. Currently, we are developing novel approaches that promise to be even more effective at suppressing numerical instabilities in relativistic beam simulations.5 In this presentation, we describe briefly the new algorithms, present numerical dispersion relations quantifying their stability, and again substantiate results with WARP simulations. Finally, we compare these new algorithms with earlier ones from the perspectives of both effectiveness and efficiency.