A MHD invariant and the confinement regimes in Tokamak

TL;DR

This paper explores a generalized invariant in tokamaks that links plasma vorticity, safety factor, and density, providing insights into confinement regimes and phenomena like pellet-induced rotation and edge localized modes.

Contribution

It introduces an extension of Ertel's theorem as a frozen-in invariant applicable to tokamak plasma dynamics, connecting large-scale vorticity with current and density profiles.

Findings

Reversed-q profile is required for pellet-induced rotation.

In H-mode, current density accumulates at the edge, forming a vorticity-current sheet.

Invariant explains filamentation and magnetic perturbation penetration.

Abstract

Fundamental Lagrangian, frozen-in and topological invariants can be useful to explain systematic connections between plasma parameters. At high plasma temperature the dissipation is small and the robust invariances are manifested. We invoke a frozen-in invariant which is an extension of the Ertel's theorem and connects the vorticity of the large scale motions with the profile of the safety factor and of particle density. Assuming ergodicity of the small scale turbulence we consider the approximative preservation of the invariant for changes of the vorticity in an annular region of finite radial extension (i.e. poloidal rotation). We find that the ionization-induced rotation triggered by a pellet requires a reversed-$q$ profile in an off-axis region of the core. In the $H$-mode, the invariance requires the accumulation of the current density in the rotation layer at the edge. Then this becomes a vorticity-current sheet which may explain experimental observations related to the penetration of the Resonant Magnetic Perturbation and the filamentation during the Edge Localized Modes.