Transition to chaos in magnetized, weakly coupled plasmas

TL;DR

This paper uses numerical simulations to identify the transition from order to chaos in a magnetized plasma, occurring when plasma and cyclotron frequencies are comparable, confirming theoretical predictions.

Contribution

It provides numerical evidence for the chaos transition in weakly coupled plasmas based on the ratio of plasma to cyclotron frequencies, aligning with theoretical estimates.

Findings

Chaos occurs when \\omega_p/\\omega_c \\sim 1

Simulation results agree with theoretical predictions

Threshold differs from kinetic theory estimates

Abstract

We report the results of numerical simulations for a model of a one component plasma (a system of N point electrons with mutual Coulomb interactions) in a uniform stationary magnetic field. We take N up to 512, with periodic boundary conditions, and macroscopic parameters corresponding to the weak coupling regime, with a coupling parameter \Gamma=1/64. We find that a transition from order to chaos takes place when the density is increased or the field decreased so that the ratio \omega_p/\omega_c between plasma and cyclotron frequencies becomes of order 1 (or equivalently the ratio r_L/\lambda_D between Larmor radius and Debye length becomes of order 1). The result is in agreement with the theoretical prediction obtained in [1], on the basis of an old estimate of Iglesias, Lebowitz and MacGowan [2] for the intensity of the electric field acting on one electron and due to all the other ones. A comparison can be made with the threshold obtained from kinetic theory arguments, which corresponds to the condition \nu_{ee}/\omega_c=1, where \nu_{ee} is the electron collision frequency. The latter threshold has a completely different dependence on the physical parameters and, for \Gamma=1/64, gives a critical value of \omega_p about 80 times larger.