Thermal equilibrium of non-neutral plasma in dipole magnetic field

TL;DR

This paper investigates how non-neutral plasmas self-organize into equilibrium states within inhomogeneous dipole magnetic fields, revealing that adiabatic invariants govern the relaxed configurations, which resemble rigidly rotating clumps.

Contribution

It extends the understanding of plasma self-organization from homogeneous to dipole magnetic fields, highlighting the role of adiabatic invariants in determining equilibrium states.

Findings

The relaxed state is a rigidly rotating plasma clump.

Density distribution becomes inhomogeneous in dipole fields.

Adiabatic invariants dictate the plasma's equilibrium configuration.

Abstract

Self-organization of a long-lived structure is one of the remarkable characteristics of macroscopic systems governed by long-range interactions. In a homogeneous magnetic field, a non-neutral plasma creates a "thermal equilibrium" which is a Boltzmann distribution on a rigidly rotating frame. Here, we study how a non-neutral plasma self-organizes in inhomogeneous magnetic field; as a typical system we consider a dipole magnetic field. In this generalized setting, the plasma exhibits its fundamental mechanism that determines the relaxed state. The scale hierarchy of adiabatic invariants is the determinant; the Boltzmann distribution under the topological constraint by the robust adiabatic invariants (hence, the homogeneous distribution with respect to the fragile invariant) is the relevant relaxed state, which turns out to be a rigidly rotating clump of particles (just same as in a homogeneous magnetic field), while the density is no longer homogeneous.