# Magneto-HydroDynamic activity and Energetic Particles - Application to Beta Alfven Eigenmodes

## TL;DR

This paper investigates Beta Alfven Eigenmodes (BAEs) in fusion plasmas, deriving their properties, analyzing their stability with energetic particles, and exploring the potential for metastable modes through linear and nonlinear analyses.

## Contribution

It provides an analytical derivation of BAE characteristics, a linear stability criterion, and introduces a nonlinear scenario for metastable mode existence, validated analytically and numerically.

## Key findings

- Derived BAE dispersion relation and structure.
- Established a linear destabilization criterion matching experiments.
- Proposed and verified a nonlinear scenario for metastable modes.

## Abstract

The goal of magnetic fusion research is to extract the power released by fusion reactions and carried by the product of these reactions, liberated at energies of the order of a few MeV. The feasibility of fusion energy production relies on our ability to confine these energetic particles, while keeping the thermonuclear plasma in safe operating conditions. For that purpose, it is necessary to understand and find ways to control the interaction between energetic particles and the thermonuclear plasma. Reaching these two goals is the general motivation for the work conducted during the PhD. More specifically, our focus is on one type of instability, the Beta Alfven Eigenmode (BAE), which can be driven by energetic particles and impact on the confinement of both energetic and thermal particles. In this work, we study the characteristics of BAEs analytically and derive its dispersion relation and structure. Next, we analyze the linear stability of the mode in the presence of energetic particles. First, a purely linear description is used, which makes possible to get an analytical linear criterion for BAE destabilization in the presence of energetic particles. This criterion is compared with experiments conducted in the Tore-Supra tokamak during the PhD. Secondly, because the linear analysis reveals some features of the BAE stability which are subject to a strong nonlinear modification, the question is raised of the possibility of a sub-critical activity of the mode. We propose a simple scenario which makes possible the existence of meta-stable modes, verified analytically and numerically. Such a scenario is found to be relevant to the physics and scales characterizing BAEs.