Kinetic effects of energetic particles on a 2/1 resistive MHD instability in a DIII-D discharge

The kinetic effects energetic particles have on the stability of the m/n=2/1 tearing mode in a DIII-D discharge are investigated as a function of q$_{min}$, $\beta $, S=$\tau _{R}$/$\tau _{A}$ and $\beta _{frac}=\beta _{h}$/$\beta $ ($\beta _{h}$ is energetic particle $\beta )$.~ Using experimental equilibrium reconstructions as a basis we generate a series of equilibria varying q$_{min}$ and $\beta $. The non-ideal MHD stability of the n=1 mode is then calculated including the $\delta $f kinetic-MHD model in the 3-D extended MHD code NIMROD. The particle distribution models the slowing-down distribution from neutral beams in experiment. The interaction between the particles and the mode drives a real frequency and changes the linear stability. For the range of ideal unstable, resistive unstable and MHD stable modes, this drive is~analyzed in phase space with particle diagnostics. In the ideal unstable regime at low q$_{min}$, the particles damp the mode. However, it is observed that in the MHD-only stable regime, the interaction is strong near the axis, and can cause destabilization of the n=1 mode. These results are compared with experimental data, which includes low amplitude n=1 and 2 in a nonlinearly saturated state.