Nonlinear Simulation Of Interaction Between Energetic Particles And Waves In Fusion Plasmas

Alfvenic instability driven by energetic particles is one of the important topics in burn-ing plasmas. Alfven wave is also one of the most fundamental waves in plasmas and has a variety of forms in a toroidal device due to different physical effects. In a non-uniform magnetized plasma, the shear Alfven wave has a continuous spectrum. The continuum can be broken up by toroidicity in a toroidal plasma and a new discrete toroidicity-induced shear Alfven eigenmodes (TAEs) can exist with its frequency inside the toroidicity-induced continuum gaps. In burning plasmas, energetic particles generated by nuclear fusion or in-jected by auxiliary heating method can destabilize TAE modes which can undermine plasma confinement and destroy fusion devices. With the increase of mode amplitudes driven by energetic particles, the phenomena of the TAE mode frequency chirping are often observed in experiments. It should be noted that the results of this work, although for laboratory fusion plasmas, are also of general interest for understanding wave-particle interactions and nonlin-ear processes in many other complex systems, such as the energetic electron-driven whistler chorus observed in the Earth’s magnetosphere. We develop kinetic code EAC (Energetic particle and toroidal Alfven wave interaction Code) based on a reduced model. EAC code is a drift-kinetic, perturbative, nonlinear, Sf-PIC code. For zero background damping, it is found that the wave amplitude in nonlinear phase can either saturate for weak energetic particle drives or slowly increase for strong drives. This slow nonlinear growth in the strong drive cases is found to be associated with broadening and overlapping of resonance regions. Besides resonance overlapping effects in a single mode, the resonance regions for different toroidal waves can also overlap with each other and lead to wave amplitude nonlinear growth (associated with trapped particle resonances) or enhance saturation level (associated with passing particle resonances). For the near-marginal-stability case (γL-γd《γL) with a large background damping, the mode nonlinear evolution exhibits three types of chirping phenomena:the up-down chirping; mainly downward chirping; and mainly upward chirping. For up-down split chirpings, a hole/clump formation is observed clearly in the correspond-ing evolution of energetic particle distribution The downward/upward chirping of the mode frequency is associated with the negative drift of the phase island in the KAM surfaces or the resonance δf structures in the radial direction. It is found that the frequency chirping is resulted from the phase-or resonance-locking, which acts to maintain maximum power exchange between energetic particles and waves. The phase space dynamics provides a key mechanism for understanding the chirping direction of the waves and the transport process of the particles. EAC code is including rich physical effects (full wave-particle interaction, three dimensional geometry of mode structure, full particle orbit) and powerful diagnostic method to analyze phase space dynamics (exactly numerical resonant condition, KAM sur-faces/poincare plot, fine structure in the three dimensional particle distribution). The code provide a very effective numerical tool to investigate nonlinear physics of waves driven by energetic particles.