Effects of trapped alpha particles on ballooning modes in tokamaks

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Abstract
The effects of a trapped, precessing alpha particle population on ballooning modes are examined for a large aspect ratio, shifted circular flux surface tokamak equilibrium. The alphas are modeled in the deeply trapped limit and with a Maxwellian distribution in energy. The resulting kinetic ballooning equation is solved numerically, and the dependence of the eigenvalues and stability boundaries on shear, background pressure gradient, and ratio of hot‐to‐background tempera‐ tures (and densities) is investigated. In the low‐frequency regime (ω ≪ ωdH =alpha precessional drift frequency), the alpha component has a stabilizing influence, while in the intermediate frequency range (ω≲ωdH) the alphas destabilize ballooning modes through interaction with the trapped particle precessional drift resonance. Parameter ranges which should be typical of alpha production in near term tokamak devices such as the Tokamak Fusion Test Reactor (TFTR) [Phys. Rev. Lett. 5 2, 1492 (1984)] are considered.