Energetic Particle Instabilities Simulated in GYRO

The Eulerian gyrokinetic code GYRO [1] has been used to study instabilities driven by a sparse, hot species (such as fusion-produced $\alpha$-particles) superimposed on the equilibrium profile in different geometries. The energetic particles are distributed according to a high temperature Maxwellian. Unstable Toroidal Alfv\'en Eigenmodes (TAEs) have been identified in gaps in the Alfv\'en continuum at the degenerate frequency of two toroidally-coupled modes with the same toroidal mode number $n$ and adjacent poloidal mode numbers $m$. Frequency and growth rate have been mapped out as functions of $n$, background plasma pressure gradients (starting from zero), safety factor, magnetic shear, and density gradient of the hot species in flux-tube geometry. Global geometry simulations using measured profiles from DIII-D are compared to TAEs and other Alfv\'en modes observed in that machine [2]. To monitor the gap Alfv\'en modes (and possibly subdominant modes outside the gap) in the presence of background plasma density gradients (and possibly dominant ITG/TEM modes), GYRO will be modified to find frequency and growth rate of sub-dominant modes.\par \vskip6pt \noindent [1]~J.~Candy and R.E.\ Waltz, J.~Comput.\ Phys.\ {\bf 186}, 545 (2003).\hfil\break [2]~M.A.\ Van Zeeland, et al., Nucl.\ Fusion {\bf 46}, S880 (2006).\par