Explosive evolution of near-threshold kinetic instabilities

In the past, studies of waves close to marginal stability have revealed a rich variety of behavior in different physical contexts. One of the possible outcomes is an explosive growth of the mode amplitude, which forms the core of this thesis. This outcome has been predicted in both the fluid mechanics and the plasma literature. While we make some comments regarding the fluids context, in this work we focus on the near-threshold waves that are excited in kinetic systems (such as plasmas). With a few exceptions, the explosive behavior is found to asymptote to an attractor that depends on a system parameter that we shall discuss. When the mode amplitude is sufficiently large, the explosive growth loses physical meaning, and here we explore the transition between the weakly-nonlinear regime where the explosive description holds, and the strongly-nonlinear phase where the mode amplitude saturates. By investigating the phase space dynamics associated with the kinetic response, we find a link between a local flattening, or folding, of the particle distribution function and the breakdown of the explosive description. Since the explosive growth sets the stage for long-term frequency chirping modes, it is hoped that the present work can be of relevance for the prediction of the variety of chirping modes that have been observed in many experimental situations. These modes are expected to have a very significant effect on the confinement properties of fusion plasmas.