Progress on gyrokinetic simulation of high-n energetic particle driven instabilities

A hybrid model, in which ions are described by the gyrokinetic equations and electrons are treated as a massless fluid, has been developed for arbitrary shape flux surfaces and equilibrium profiles, based on the GEM turbulence simulation code ( Y.~Chen and S.~E.~Parker, J. Comp. Phys. 189 (2003). The perturbed magnetic field is given by $\delta {\bf B}_\perp=\nabla A_\parallel\times{\bf b}$, with $A_\parallel$ given by the parallel Ampere's law. The electric field is given by ${\bf E}=-\nabla \phi-(\partial A_\parallel/\partial t) {\bf b}$, with $\phi$ obtained from the quasi-neutrality condition. The primary coupling of the hot particles to the bulk plasma comes from the hot particle term in the quasi-neutrality condition. This hybrid model can be shown to reduce to the MHD equations for the shear Alfv\'en modes under the assumption $E_\parallel=0$. Linear simulation shows the existence of global modes with TAE features in terms of mode location and frequency. However, small variation in the equilibrium profiles (such as q-profile and temperature profile) often leads to strongly unstable unphysical mode peaking at the inner mid-plane. We will attemp to resolve this difficulty, either by improving the electron model or by improving numerical algorithms to avoid the unphysical modes.