A digital filtering scheme for particle codes in curvilinear coordinates

Abstract

Summary form only given. Statistical noise has long been a significant limitation for particle-in-cell (PIC) calculations at high densities. This noise is manifested in the charge and current density source terms to the field equations, which results in fluctuations in fields. Such fluctuations in fields can cause non-physical net heating of particles. The noise and consequent fluctuations are inversely proportional to the square root of the number of particles, so the brute force reduction of noise by increasing the number of particles is computationally inefficient. The problem is significantly more severe in curvilinear coordinates, where the inter-particle distance is proportional to the radius r/sup -1/ in cylindrical coordinates, and to r/sup -1/ in spherical coordinates, resulting in most severe noise on axis. A common remedy for this problem is the use of spectral filters or digital filters. Spectral filters operate in k-space, most appropriate when a spectral field solution is performed. Digital filters are more amenable to finite difference field solutions in real space, which is generally the case for bounded PIC codes in curvilinear coordinates. In this work, we extend a digital filtering scheme to curvilinear coordinates. The filtering scheme is applied to charge density for the electrostatic case in a one-dimensional radial model, and filtering of current density for the electromagnetic case in an axisymmetric model. The impact on particle shape and spectral content is measured to gauge the impact of the filter. An optimization is described and implemented to improve the performance of the filter, which can require many passes for best results.