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 ND2 due to discrete particle effects by collisionless particle-in-cell (PIC) simulations, where ND is the particle number in a Debye length. The ND2 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 ND 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.