Kinetic properties of the particle-in-cell simulation of a Lorentz plasma

The phenomenon of numerical thermalization in the standard particle-in-cell (PIC) simulation of Vlasov plasmas has been extensively studied at the early stage of its development [1] and was considered well understood. However, it was recently reported [2] that the well-established scaling law for the thermalization time could be compromised by the presence of an additional stochastic force acting on the particles, which is used to simulate collisional processes in a weakly ionized gas. In the present work, we are interested in the problem of electron-ion collisions in a fully ionized plasma. We investigate the thermal relaxation phenomenon in the PIC simulation of a Lorentz plasma in one dimension [3]. The pitch-angle scattering of the electrons by the stationary ion background is modeled by a Monte-Carlo algorithm. The numerical results obtained indicate that the thermal relaxation time is proportional to $N_{D}$ (the number of particles per Debye length), and not $N_{D}^{2}$ as in the standard PIC simulations. Our results appear to complement those found by the previous study [2]. \\[4pt] [1] C. K. Birdsall and A. B. Langdon, \textit{Plasma Physics via Computer Simulation} (McGraw-Hill, New York, 1985). \\[0pt] [2] M. M. Turner, Phys. of Plasmas \underline {13}, 033506 (2006). \\[0pt] [3] R. Shanny, J. M. Dawson, and J. M. Greene, Phys. of Fluids \underline {10}, 1281 (1967).