Z Pinch Kinetics II -- A Continuum Perspective: Betatron Heating and Self-Generation of Sheared Flows

TL;DR

This paper develops a continuum kinetic model for Z pinch dynamics, analyzing betatron heating and flow self-generation, validated by simulations, revealing how anisotropy and shear interact in magnetized plasma flows.

Contribution

It introduces a hybrid CGL model based on local orbit densities and explores flow-anisotropy relations through kinetic equilibrium analysis.

Findings

Betatron heating produces agyrotropic anisotropy balancing gyrophase mixing.

A hybrid CGL model effectively describes Z pinch behavior.

Self-generated sheared flows resist flux changes via betatron heating.

Abstract

Adiabatic compression of a self-magnetizing current filament (a Z pinch) is analyzed via the adiabatic invariants of its constituent cyclotron and betatron motions. Chew-Goldberger-Low (CGL) models are recovered for both trajectories but with distinct anisotropy axes, about the magnetic field for cyclotron fluid and about the electric current for betatron fluid. In particular, betatron heating produces agyrotropic anisotropy which balances with gyrophase mixing. A hybrid CGL model is proposed based on the local densities of cyclotron and betatron orbits, then validated by numerical experiments. The relation between anisotropy and shear is explored by constructing the kinetic equilibrium of a flow expanded in the flux function. Flow as a linear flux function is simply bi-Maxwellian, while higher powers display higher-moment deviations. Next, weakly collisional gyroviscosity (magnetized pressure-strain) is considered in a forward process (forced flow) and an inverse process (forced anisotropy). The forward process phase-mixes flow into a simple flux function, freezing flow into flux and inducing anisotropy. In the inverse process, betatron heating-induced anisotropy self-generates a sheared flow to resist changes in flux. This flow, arising from momentum diffusion, is concentrated in the betatron region.