Application of N-body gravitational algorithm to collective charged particle dynamics

Conventionally, N-body simulation employs softening parameters to smooth out the singularity of the central force. In this work, the Kepler problem is solved analytically when the distance between two charged particles becomes at an order of Landau length. On top of evaluating charged particle diffusion in the presence of background magnetic field (D. Bohm, The characteristics of electrical discharges in magnetic fields, McGraw-Hill, p.65, 1949), the study is extended to investigate collective motion of plasmas. Having alike charges in the system and Debye shielding, plasma N-body simulation is expected to be less laborious in constructing hierarchies (J. Barnes and P. Hut, Nature 324, 446, 1986).