Statistical equilibrium model for stellarators

TL;DR

This paper introduces a statistical equilibrium model for stellarators that accounts for plasma fluctuations, enabling smooth solutions where traditional models face singularities, thus improving magnetic confinement analysis.

Contribution

It develops a novel variational equilibrium principle based on plasma fluctuations, supporting smooth solutions in three-dimensional toroidal domains.

Findings

Supports smooth solutions for specific fluctuation statistics.

Models smoothing of singular current sheets via magnetic field fluctuations.

Provides a new approach to equilibrium modeling in stellarators.

Abstract

In three dimensional toroidal domains without symmetry, the standard magnetohydrodynamic (MHD) equilibrium model used for magnetic confinement fusion does not generally support smooth solutions. Instead, solutions have singular plasma currents on resonant magnetic surfaces that violate the MHD assumption of length-scale separation, further leading to the non- or slow convergence of numerical approximations under refinement. In this work, we present an improved equilibrium principle derived from a statistical model for plasma fluctuations. Instead of being static, we assume that the plasma magnetic field is ergodically and rapidly fluctuating relative to the MHD time scale. By averaging the resulting force, we derive a variational equilibrium problem for the statistical mean magnetic field which depends on fluctuation variance. Then, through asymptotics, numerical simulations, and a Grad-Shafranov type argument, we show that the variational principle supports smooth solutions for specific fluctuation statistics chosen to minimally modify the standard equilibrium modeling paradigm. Physically, this model smooths singular current sheets with a length scale determined by the magnetic field fluctuations.