Numerical study of the transverse diffusion coefficient for a one component model of plasma

In this paper, we discuss the results of some molecular dynamics simulations of a magnetized one component plasma, targeted to estimate the diffusion coefficient D⊥ in the plane orthogonal to the magnetic field lines. We find that there exists a threshold with respect to the magnetic field strength |B⃗ |: for weak magnetic field, the diffusion coefficients scale as 1/|B⃗ |2 , while a slower decay appears at high field strength. The relation of this transition with the different mixing properties of the microscopic dynamics is investigated by looking at the behavior of the velocity autocorrelation. The diffusion process is well understood for stochastic motions,1 which are supposed to mimic the behavior of a chaotic dynamical system. Many questions are instead left open in the study of the diffusive properties of a system, which is in a partially ordered state.2 A central issue, as regards magnetized plasma confinement, is the diffusion of charged particles in the direction perpendicular to the magnetic field lines. A widely accepted law, predicting that the transversal diffusion D⊥ coefficient is proportional to the inverse of the square of the magnetic field strength |B⃗ |, was proposed more than 50 years ago.3 Being based on kinetic theory, this law is expected to hold whenever the microscopic dynamics is chaotic. However, as the magnetic field |B⃗ | is increased, a partially ordered state seems to set in Refs. 4 and 5, at least for a pure electron plasma. Our purpose was to investigate the consequences (if any) of this transition on the diffusion process. Therefore, we have performed molecular dynamics simulations of a magnetized one component plasma, that is, a set of mutually interacting electrons subject to a constant external magnetic field. We estimate the diffusion coefficient D⊥ in the plane orthogonal to the field for different values of the magnetic field strength |B⃗ |. We find that the kinetic law holds for low |B⃗ | when the microscopic dynamics is chaotic. However, as the magnetic field grows, the diffusion coefficient seems to saturate to a plateau, while the microscopic state turns to a partially ordered one.