Slow relaxation in the two dimensional electron plasma under the strong magnetic field

TL;DR

This paper investigates slow relaxation phenomena in a two-dimensional electron plasma model under strong magnetic fields, revealing superdiffusive Levy flight behavior and a linear relationship between relaxation time and electron number.

Contribution

It introduces a detailed numerical analysis of slow relaxation and superdiffusive Levy flight dynamics in 2D electron plasma, highlighting the importance of trajectory correlations.

Findings

Slow relaxation time scales linearly with electron number.

Electrons exhibit superdiffusive Levy flight motion.

Correlation among trajectories influences slow relaxation.

Abstract

We study slow relaxation processes in the point vortex model for the two-dimensional pure electron plasma under the strong magnetic field. By numerical simulations, it is shown that, from an initial state, the system undergoes the fast relaxation to a quasi-stationary state, and then goes through the slow relaxation to reach a final state. From analysis of simulation data, we find (i) the time scale of the slow relaxation increases linearly to the number of electrons if it is measured by the unit of the bulk rotation time, (ii) during the slow relaxation process, each electron undergoes an superdiffusive motion, and (iii) the superdiffusive motion can be regarded as the Levy flight, whose step size distribution is of the power law. The time scale that each electron diffuses over the system size turns out to be much shorter than that of the slow relaxation, which suggests that the correlation among the superdiffusive trajectories is important in the slow relaxation process.