Apar-T: code, validation, and physical interpretation of particle-in-cell results

TL;DR

This paper introduces the Apar-T particle-in-cell code, validates it through multiple tests, and explores how PIC models relate to real plasmas, emphasizing the effects of coarse-graining and finite superparticle size on plasma behavior and fluctuations.

Contribution

The paper presents a new PIC code, Apar-T, with validation, a novel method for initializing relativistic particle distributions, and a detailed analysis of how PIC models approximate real plasma physics.

Findings

Validation tests confirm Apar-T's accuracy in simulating plasma phenomena.

A new method improves initial particle distribution setup for relativistic plasmas.

PIC models' fluctuation levels and thermalization times depend on superparticle count, differing from real plasmas.

Abstract

We present the parallel particle-in-cell (PIC) code Apar-T and, more importantly, address the fundamental question of the relations between the PIC model, the Vlasov-Maxwell theory, and real plasmas. First, we present four validation tests: spectra from simulations of thermal plasmas, linear growth rates of the relativistic tearing instability and of the filamentation instability, and non-linear filamentation merging phase. For the filamentation instability we show that the effective growth rates measured on the total energy can differ by more than 50% from the linear cold predictions and from the fastest modes of the simulation. Second, we detail a new method for initial loading of Maxwell-J\"uttner particle distributions with relativistic bulk velocity and relativistic temperature, and explain why the traditional method with individual particle boosting fails. Third, we scrutinize the question of what description of physical plasmas is obtained by PIC models. These models rely on two building blocks: coarse-graining, i.e., grouping of the order of p~10^10 real particles into a single computer superparticle, and field storage on a grid with its subsequent finite superparticle size. We introduce the notion of coarse-graining dependent quantities, i.e., quantities depending on p. They derive from the PIC plasma parameter Lambda^{PIC}, which we show to scale as 1/p. We explore two implications. One is that PIC collision- and fluctuation-induced thermalization times are expected to scale with the number of superparticles per grid cell, and thus to be a factor p~10^10 smaller than in real plasmas. The other is that the level of electric field fluctuations scales as 1/Lambda^{PIC} ~ p. We provide a corresponding exact expression. Fourth, we compare the Vlasov-Maxwell theory, which describes a phase-space fluid with infinite Lambda, to the PIC model and its relatively small Lambda.