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.Comment: 24 pages, 14 figures, accepted in Astronomy & Astrophysic
