Noise and error minimization in particle-based plasma simulation methods

We describe a novel noise-error minimizing method applicable to particle-based plasma simulation algorithms; e.g., PIC, (variational) energy-conserving, delta-f, hybrid, etc.

The method uses spatial ensemble averaging to describe the error in these methods. At its heart is a bias-variance optimization: Particle size too large leads to too much smoothing of the density and to (statistical) biased estimate. Particle size too small leads to each particle contributing to only one cell and to higher level of noise.

An important property is provided by the covariance matrix for density fluctuations. That matrix has negative correlations due to Brownian Bridge rather than Poisson: the total number of particles is fixed rather than the expected number of particles fixed.

By applying optimal particles instead of the standard (usually linear, quadratic, or cubic splines), noise-error levels may be reduced a few times, which equivalently implies using a few times fewer simulation particles.

Numerical simulations confirm the theoretical conclusions and reveal additional challenges: using optimal size particles as a sole guideline for selecting grid spacing may lead to under-resolved physics. Guidelines to that effect will be presented.