Nonlinear wave-particle resonance in deterministic and stochastic kinetic plasmas

In kinetic plasma physics, BGK modes are ubiquitous solutions to the Vlasov equation, with particles travelling along orbits where the single particle energy is conserved. Approximate extensions of these exact solutions have been successfully used in the past to understand the formation and evolution of ‘holes’ and ‘clumps’, coherent structures on the particle distribution function which under certain conditions form in the nonlinear phase of the evolution of kinetic plasmas. In this thesis, analytical results are shown which consider perturbations and deformations to BGK orbits, allowing one to robustly construct more exotic orbits that allow for mode growth and frequency chirping. Computational results produced using the DARK code are presented, examining stochastic and deterministic populations in a 1D electrostatic plasma, and how they affect electrostatic waves exhibiting Landau resonance, based on Berk-Breizman models. A model is presented for parametric mode-mode destabilisation via holes and clumps interacting via the background distribution. Finally, work using the machine learning framework ERICSON is presented, analysing frequency spectrograms of magnetic perturbations in Alfvénic and sub-Alfvénic frequency ranges.