Magnetic axis safety factor of finite $\beta$ spheromaks and transition from spheromaks to toroidal magnetic bubbles

TL;DR

This paper investigates the safety factor in finite-beta spheromaks, revealing its dependence on beta, and extends equilibrium models to include toroidal magnetic bubbles with potential applications to interplanetary magnetic clouds.

Contribution

It demonstrates the beta dependence of the safety factor on the magnetic axis and introduces a method to model toroidal magnetic bubbles with inverted pressure profiles.

Findings

Safety factor on the axis depends on beta, reducing its gradient.

Extended equilibrium models to include magnetic bubbles with lower interior pressure.

Relevance to interplanetary magnetic clouds with inverted pressure profiles.

Abstract

The value of the safety factor on the magnetic axis of a finite-beta spheromak is shown to be a function of beta in contrast to what was used in P. M. Bellan, Phys. Plasmas 9, 3050 (2002); this dependence on beta substantially reduces the gradient of the safety factor compared to the previous calculation. The method for generating finite-beta spheromak equilibria is extended to generate equilibria describing toroidal magnetic "bubbles" where the hydrodynamic pressure on the magnetic axis is less than on the toroid surface. This "anti-confinement" configuration can be considered an equilibrium with an inverted beta profile and is relevant to interplanetary magnetic clouds as these clouds have lower hydrodynamic pressure in their interior than on their surface.