<i>N</i>-body plasma simulation of classical and Bohm diffusion employing Kepler's analytical solutions

A numerical approach to the simulation of two- and three-dimensional self-consistent N-body charged-particle dynamics is developed employing analytical solutions, with Kepler's laws of planetary motion being applied to close encounters of two particles. In the presence of a uniform magnetic field, in a quiet homogeneous plasma without microscopic instabilities, the diffusion process of electrons induced by Coulomb collisions is investigated. With an accurate treatment of binary collisions, it is found that the numerically computed electron diffusion rates match quantitatively with the results of an analytical approach that incorporates individual scattering angles into the random step size. In two dimensions, it is found that the diffusion coefficient Dei,class is inversely proportional to the square of the magnetic field strength B0: Dei,class∝1/B02. When the collision frequency becomes comparable to the electron cyclotron frequency, Bohm diffusion Dei,Bohm∝1/B0 is obtained. The diffusion rate according to the N-body simulation is consistently higher than that expected when only electron–ion collisions are considered, which suggests that electron–electron collisions play roles in enhancing electron transport. Relaxation of electron distribution function is demonstrated by preliminary three-dimensional N-body simulations.