Density limit in a first principles model of a magnetized plasma in the Debye--H\"uckel approximation

TL;DR

This paper proposes a first principles statistical mechanics model using Debye--H"uckel approximation to explain the density limit in magnetized plasmas, linking it to a transition from ordered to chaotic motion.

Contribution

It introduces a novel theoretical approach connecting plasma density limits to a chaos transition, aligning with empirical data in fusion devices.

Findings

Density threshold corresponds to order-chaos transition in plasma dynamics.

The density limit scales with the square of the magnetic field.

Model predictions fit empirical plasma collapse data reasonably well.

Abstract

A crucial problem concerning a large variety of fusion devices is that the confinement due to an external magnetic field is lost above a critical density, while a widely accepted first principles explanation of such a fact is apparently lacking. In the present paper, making use of standard methods of statistical mechanics in the Debye--H\"uckel approximation, we give indications that for a plasma there exists a density threshold corresponding to a transition from order to chaos, the ordered motions being those in which the confining Lorentz force on a single electron prevails over the diffusive effect of the Coulomb forces. The density limit, which is proportional to the square of the magnetic field, turns out to fit not too badly the empirical data for plasma collapses in a large set of fusion devices.