  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.

Plasma Physics