Numerical thermalization of two-dimensional plasmas in the presence of binary collisions with the particle-in-cell method

Summary form only given. Numerical self-heating and thermalization are two unphysical artifacts in particle-in-cell (PIC) simulations due to the implicit assumptions used in the numerical method. Numerical self-heating in plasma simulations can typically be suppressed by using higher order finite-difference methods, field smoothing and particle weighting schemes. On the other hand, numerical thermalization is associated with the granularity of the particles that introduces relaxation in the velocity distribution functions (i.e. the particle velocity distribution approaches Maxwellian). In 2D collisionless plasma simulations, the rate of relaxation has been shown to be proportional to 1/ND, where ND is the number of particles per Debye length1. This scaling has been illustrated to be true in several previous works using electrostatic PIC codes. Here we will focus on the study of numerical thermalization for 2D collisional plasma using an in-house electromagnetic PIC (IPIC or Ihpc Particle-In-Cell) code. The binary collision model in IPIC is implemented based on the Fokker-Planck Collision operator to mimic Coulomb collisions in real plasmas2. Our numerical results confirm that without collisions, the 1/N
_D
scaling remains intact as expected. However, in the presence of binary collisions, the relaxation rate is also scaled with 1/N
_D
at small N
_D
, but the scaling parameter varies distinctly as ND increases. The implications of this previously unidentified observation will be discussed.