Transition from order to chaos, and density limit, in magnetized plasmas

TL;DR

This paper estimates the threshold at which plasma motion becomes chaotic under magnetic confinement, predicting a density limit that aligns with empirical data from fusion devices.

Contribution

It introduces a theoretical estimate of the plasma density limit based on microfield fluctuations, linking chaos onset to confinement breakdown.

Findings

Density limit increases with the square of magnetic field strength.

The theoretical density limit aligns well with experimental data from fusion machines.

Chaos in electron motion leads to loss of plasma confinement.

Abstract

It is known that a plasma in a magnetic field, conceived microscopically as a system of point charges, can exist in a magnetized state, and thus remain confined, inasmuch as it is in an ordered state of motion, with the charged particles performing gyrational motions transverse to the field. Here we give an estimate of a threshold, beyond which transverse motion become chaotic, the electrons being unable to perform even one gyration, so that a breakdown should occur, with complete loss of confinement. The estimate is obtained by the methods of perturbation theory, taking as perturbing force acting on each electron that due to the so--called microfield, i.e., the electric field produced by all the other charges. We first obtain a general relation for the threshold, which involves the fluctuations of the microfield. Then, taking for such fluctuations the fomula given by Iglesias, Lebowitz and MacGowan for the model of a one component plasma with neutralizing background, we obtain a definite formula for the threshold, which corresponds to a density limit increasing as the square of the imposed magnetic field. Such a theoretical density limit is found to fit pretty well the empirical data for collapses of fusion machines.