Fast ion effects on the threshold conditions of ion temperature gradient mode and electron temperature gradient mode

We investigate the fast ion effects on the threshold conditions of ion temperature gradient (ITG) mode and electron temperature gradient (ETG) mode, both analytically and numerically, using the gyrokinetic equation. The onset condition for ITG mode shows a strong and monotonic favorable dependence on the fraction of fast ions, and mostly favorable but non-monotonic dependence on the fast ions' normalized temperature Tf/Ti (Tf is the effective temperature of fast ions, Ti is the temperature of thermal ions). Overall, favorable parametric trends are consistent with those for the linear growth rate reported in previous papers, as they are largely determined by kinetic wave-particle resonance effects. While general analytic expressions for the critical normalized thermal ion temperature gradient scale length (R/LTi)c are quite complicated, an explicit compact expression (RLTi)c=(43+32π2|ŝ|q…