FOXTAIL: Modeling the nonlinear interaction between Alfv\'en eigenmodes   and energetic particles in tokamaks
  FOXTAIL is a new hybrid magnetohydrodynamic-kinetic code used to describe interactions between energetic particles and Alfv\'en eigenmodes in tokamaks with realistic geometries. The code simulates the nonlinear dynamics of the amplitudes of individual eigenmodes and of a set of discrete markers in five-dimensional phase space representing the energetic particle distribution. Action-angle coordinates of the equilibrium system are used for efficient tracing of energetic particles, and the particle acceleration by the wave fields of the eigenmodes is Fourier decomposed in the same angles. The eigenmodes are described using temporally constant eigenfunctions with dynamic complex amplitudes. Possible applications of the code are presented, e.g., making a quantitative validity evaluation of the one-dimensional bump-on-tail approximation of the system. Expected effects of the fulfillment of the Chirikov criterion in two-mode scenarios have also been verified. 
Emmi Tholerus, Thomas Johnson, Torbj\"orn Hellsten
physics.plasm-ph