Multi-phase hybrid simulation of energetic particle driven magnetohydrodynamic instabilities in tokamak plasmas

Magnetohydrodynamic (MHD) instabilities driven by energetic particles in tokamak plasmas and the energetic particle distribution formed with the instabilities, neutral beam injection, and collisions are investigated with hybrid simulations for energetic particles and an MHD fluid. The multi-phase simulation, which is a combination of classical simulation and hybrid simulation, is applied to examine the distribution formation process in the collisional slowing-down time scale of energetic ions for various beam deposition power ( P NBI ) and slowing-down time ( τ s ). The physical parameters other than P NBI and τ s are similar to those of a Tokamak Fusion Test Reactor (TFTR) experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874). For P NBI = 10 MW and τ s = 100 ms, which is similar to the TFTR experiment, the bursts of toroidal Alfvén eigenmodes take place with a time interval 2 ms, which is close to that observed in the experiment. The maximum radial velocity amplitude (vr) of the dominant TAE at the bursts in the simulation is v r / v A ∼ 3 × 10 − 3 where vA is the Alfvén velocity at the plasma center. For P NBI = 5 MW and τ s = 20 ms, the amplitude of the dominant TAE is kept at a constant level v r / v A ∼ 4 × 10 − 4 . The intermittency of TAE rises with increasing P NBI and increasing τ s (= decreasing collision frequency). With increasing volume-averaged classical energetic ion pressure, which is well proportional to P NBI τ s , the energetic ion confinement degrades monotonically due to the transport by the instabilities. The volume-averaged energetic ion pressure depends only on the volume-averaged classical energetic ion pressure, not independently on P NBI or τ s . The energetic ion pressure profile resiliency, where the increase in energetic ion pressure profile is saturated, is found for the cases with the highest P NBI τ s where the TAE bursts take place.