Study of discrete-particle effects in a one-dimensional plasma simulation with the Krook type collision model

The thermal relaxation time of a one-dimensional plasma has been demonstrated to scale with N_D² due to discrete particle effects by collisionless particle-in-cell (PIC) simulations, where N_D is the particle number in a Debye length. The N_D² scaling is consistent with the theoretical analysis based on the Balescu-Lenard-Landau kinetic equation. However, it was found that the thermal relaxation time is anomalously shortened to scale with N_D while externally introducing the Krook type collision model in the one-dimensional electrostatic PIC simulation. In order to understand the discrete particle effects enhanced by the Krook type collision model, the superposition principle of dressed test particles was applied to derive the modified Balescu-Lenard-Landau kinetic equation. The theoretical results are shown to be in good agreement with the simulation results when the collisional effects dominate the plasma system.