Resonance broadened quasi-linear (RBQ) model for fast ion distribution relaxation due to Alfvénic eigenmodes

Abstract

The burning plasma performance is limited by the confinement of the super-alfvénic fusion products such as alpha particles and the auxiliary heating ions capable of exciting the Alfvénic eigenmodes (AEs) (Gorelenkov et al 2014 Nucl. Fusion 54 125001). In this work the effect of AEs on fast ions is formulated within the quasi-linear (QL) theory generalized for this problem recently (Duarte 2017 PhD Thesis University of São Paulo, Brazil). The generalization involves the resonance line broadened interaction of energetic particles (EP) with AEs supplemented by the diffusion coefficients depending on EP position in the velocity space. A new resonance broadened QL code (or RBQ1D) based on this formulation allowing for EP diffusion in radial direction is built and presented in details. In RBQ1D applications we reduce the wave particle interaction (WPI) dynamics to 1D case when the particle kinetic energy is nearly constant. The diffusion equation for EP distribution evolution is then solved simultaneously for all particles along the angular momentum direction.We make initial applications of the RBQ1D to a DIII-D plasma with elevated q-profile where the beam ions show stiff transport properties (Collins et al (The DIII-D Team) 2016 Phys. Rev. Lett. 116 095001). AE driven fast ion profile relaxation is studied for validations of the QL approach in realistic conditions of beam ion driven instabilities in DIII-D.