Nonlinear evolution of beam driven waves on MAST

Paper in proceeding, 2010

Experiments on Alfvénic instabilities driven by super-Alfvénic beams in the spherical tokamak MAST have exhibited a variety of modes excited in a broad range of frequencies from Alfvén Cascade eigenmodes, Toroidal Alfvén Eigenmodes, and chirping modes in the frequency range 50 - 150 kHz, to compressional Alfvén eigenmodes in the frequency range 0.4 - 3.8 MHz, which is approaching the cyclotron frequency of plasma ions, ω ≈(0.1 ÷ 1)ωBi. For energetic ions produced via neutral beam injection, the unstable distribution function is formed by Coulomb collisions, with dynamical friction (drag) and velocity space diffusion dominating in different regions of phase space (separated by the critical velocity Vcrit). The aim of the present work is to demonstrate that the nonlinear evolution of these modes is determined by the type and strength of relaxation processes. In particular, we validate the recent theoretical finding that drag encourages the beam-driven waves near marginal stability to follow an explosive scenario. An effcient numerical tool has now been created for this task, the results of which show similarities with features that are observed in recent and past experiments, indicating the central role that the drag might play in the evolution of beam or alpha particle driven waves in tokamaks. This has galvanised the current ongoing effort to perform quantitative modelling of Alfvénic instabilities in the presence of drag using the HAGIS code. The universal feature of these strongly nonlinear scenarios that incorporate drag is the asymmetry of the mode evolution with respect to the wave-particle resonance. As a result we observe a transition from a steady state non-linear wave to one with a hooked frequency chirp. To connect the bump-on-tail model to the experiments we characterise the relative importance of the drag and the velocity space diffusion by considering the wave particle resonance condition, Ω = k|| V||res - ω + pωBb - kVDb = 0, and calculate the width of the resonance due to diffusion ∆Ωdiff and drag ∆Ωdrag from the the Fokker-Planck operator for different types of modes. The importance of the parameter V||res/Vcrit is assessed.