Differences between real and particle-in-cell plasmas: effects of coarse-graining

Abstract

The PIC model relies on two building blocks. The first stems from the capability of computers to handle only up to $\sim10^{10}$ particles, while real plasmas contain from $10^4$ to $10^{20}$ particles per Debye sphere: a coarse-graining step must be used, whereby of the order of $p\sim10^{10}$ real particles are represented by a single computer superparticle. The second is field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e. physical quantities depending on the number $p$. They all derive from the plasma parameter $\Lambda$, which we show to be proportional to $1/p$. We explore three examples: the rapid collision- and fluctuation-induced thermalization of plasmas with different temperatures, that scale with the number of superparticles per grid cell and are a factor $p\sim10^{10}$ faster than in real plasmas; the high level of electrostatic fluctuations in a thermal plasma, with corrections due to the finite superparticle sizes; and the blurring of the linear spectrum of the filamentation instability, where the fastest growing modes do not dominate the total energy because of a high level of fluctuations. We stress that the enhanced collisions and correlations of PIC plasmas must be kept negligible toward kinetic physics.