Topic/Type: 1. Plasma Simulation, Invited

### PIC-MCC (Particle In Cell with Monte Carlo Collisions) simulations of low temperature plasmas

M. M. Turner

School of Physical Sciences and National Centre for Plasma Science and Technology, Dublin City University, Ireland

The particle-in-cell method is a classical approach to plasma simulation. Al-
though this technique ﬁrst appeared more than forty years ago, it remains the
preferred approach for many problems where a kinetic treatment is desired.
This is especially true in low-temperature plasma physics, where violently
non-Maxwellian electron energy distributions are common, often featuring
bumps, holes and other curious structures. Such complicated distribution
functions are typically formed by a subtle interplay between collisional effects
and non-local interactions with electric and magnetic ﬁelds. It is important to
get this right in a simulation, because the electron energy distribution func-
tion affects the ionization rate, transport processes, radiative processes, etc.
These parameters are of great importance in low-temperature plasma appli-
cations, which motivate much work in this ﬁeld. Consequently, one wants to
have a simulation method that in principle captures these effects accurately.
As a direct solution of the coupled system of the Boltzmann equation and
Maxwell?s equations, particle-in-cell simulation combined with Monte Carlo
collisions is such a method. This approach should capture the physics ac-
curately, provided that the numerical parameters are properly chosen. The
numerical parameters in question are three: the time step $\small \Delta t$, the cell size
$\small \Delta x$ and the number of super-particles per cell, $\small N_C$. The literature contains
various heuristics for choosing these parameters, and it is usually assumed
that these heuristics apply whether or not Monte Carlo collisions are em-
ployed. We will show here that this is not always so?Monte Carlo collisions
in fact change the kinetic properties of a particle-in-cell simulation, such that
the rate of numerical thermalisation may increase by orders of magnitude.
This is in turn means that numerical effects may distort the electron energy
distribution function (in particular) to a much greater extent than is often
realised. These effects means that new heuristics are needed, especially for
choosing the number of particles. We will discuss the implications of these
results.