Tailoring steep density profile with unstable points

TL;DR

This paper explores how unstable fixed points in the Hamiltonian dynamics of plasma particles can be used to create steep density profiles, enhancing plasma confinement by applying a maximum entropy principle.

Contribution

It demonstrates how unstable fixed points influence plasma density profiles and introduces a method to tailor these profiles for better confinement.

Findings

Unstable fixed points can induce steep density profiles.

Maximum entropy principle guides equilibrium state selection.

Steep profiles improve plasma confinement.

Abstract

The mesoscopic properties of a plasma in a cylindrical magnetic field are investigated from the view point of test-particle dynamics. When the system has enough time and spatial symmetries, a Hamiltonian of a test particle is completely integrable and can be reduced to a single degree of freedom Hamiltonian for each initial state. The reduced Hamiltonian sometimes has unstable fixed points (saddle points) and associated separatrices. To choose among available dynamically compatible equilibrium states of the one particle density function of these systems we use a maximum entropy principle and discuss how the unstable fixed points affect the density profile or a local pressure gradient, and are able to create a steep profile that improves plasma confinement.