The burning plasmas of the next generation tokamak fusion experiment ITER
will contain signicant populations of highly energetic ions. Both fusion gener-
ated alpha particles and fast ions accelerated by auxiliary heating schemes are
capable of exciting instabilities in the Alfven frequency range, which may in
turn cause redistribution of energetic particles and lead to deleterious events
such as e.g. monster sawtooth crashes. On present day machines, many aspects
of fast ion collective eects are observed and well understood, including e.g. ex-
citation of toroidal Alfven eigenmodes (TAEs) and frequency sweeping Alfven
cascades. However, a currently hot topic is the role of kinetic and nonlinear
Alfvenic instabilities, including explanations for rapid frequency sweeping and
unambiguous identication of energetic particle modes.
This thesis presents theoretical research carried out on the linear and non-
linear dynamics of fast particle driven instabilities, with a major focus on such
events in tokamaks. In the linear regime, we investigate particle behavior in
the presence of a given electromagnetic perturbation. In particular, we formu-
late a condition on the prescribed wave amplitude to cause stochastic particle
motion and we calculate the rate coecients for the associated diusive ran-
dom walks. We also derive analytic expressions for the damping rate of even
and odd TAEs, which arises as a result of non-ideal coupling to radially prop-
agating waves. The damping is found to be weak for the odd mode, which
raises concern for the connement of energetic particles on ITER, where an-
tiballooning instabilities are likely to be resonantly driven by passing, fusion
born alpha particles.
Nonlinearly, we develop a simple one-dimensional model to investigate the
impact of signicant frequency shifts on the dynamics of frequency sweeping,
weakly driven modes. We include a number of previously neglected long range
eects that are all capable of signicantly altering the temporal frequency
sweeping patterns. In the case when the fast particle collision operator con-
tains both a drag-like slowing-down term, due to binary, small-angle Coulomb
collisions, and velocity space diusion, the model predicts transiently hooked
and steady state frequency sweeping patterns. The latter scenario turns out
to be analytically tractable
