Relaxation of Magnetically Confined Tokamak-Plasmas to Mechanical Equilibria

TL;DR

This paper analyzes how magnetically confined tokamak plasmas relax towards mechanical equilibrium, revealing the dynamics of the process and providing geometric insights crucial for developing nonlinear transport theories.

Contribution

It introduces a geometric framework for plasma relaxation, deriving the affine connection near equilibrium and linking it to the evolution of generalized frictions and thermodynamic modes.

Findings

Plasmas relax towards mechanical equilibrium following specific geometric paths.

The evolution equations for generalized frictions align with shortest paths in the Hermitian moments space.

An expression for the affine connection near equilibrium is derived, aiding nonlinear transport modeling.

Abstract

The relaxation of magnetically confined plasmas in a toroidal geometry is analyzed. From the equations for the Hermitian moments, we show how the system relaxes towards the mechanical equilibrium. In the space of the parallel generalized frictions, after fast transients, the evolution of collisional magnetically confined plasmas is such that the projections of the evolution equations for the parallel generalized frictions and the shortest path on the Hermitian moments coincide. For spatially-extended systems, a similar result is valid for the evolution of the {\it thermodynamic mode} (i.e., the mode with wave-number k = 0). The expression for the affine connection of the space covered by the generalized frictions, close to mechanical equilibria, is also obtained. The knowledge of the components of the affine connection is a fundamental prerequisite for the construction of the (nonlinear) closure theory on transport processes.