Self-organization in foliated phase space: Construction of a scale hierarchy by adiabatic invariants of magnetized particles

TL;DR

This paper explores how adiabatic invariants in magnetized plasma phase space create hierarchical structures, leading to self-organization and density gradients near magnetic dipoles, with implications for plasma confinement.

Contribution

It introduces a novel framework linking adiabatic invariants to phase space foliation and plasma self-organization near magnetic dipoles.

Findings

Plasma self-organizes into steep density gradients.

Adiabatic invariants act as Casimir invariants in phase space.

Density structures respond to energy level inhomogeneity.

Abstract

Adiabatic invariants foliate phase space, and impart a macro-scale hierarchy by separating microscopic variables. On a macroscopic leaf, long-scale ordered structures are created while maximizing entropy. A plasma confined in a magnetosphere is invoked for unveiling the organizing principle ---in the vicinity of a magnetic dipole, the plasma self-organizes to a state with a steep density gradient. The resulting nontrivial structure has maximum entropy in an appropriate, constrained phase space. One could view such a phase space as a leaf foliated in terms of Casimir invariants ---adiabatic invariants measuring the number of quasi-particles (macroscopic representation of periodic motions) are identified as the relevant Casimir invariants. The density clump is created in response to the inhomogeneity of the energy level (frequency) of quasi-particles.