Effects of Alpha Populations on Tokamak Ballooning Stability

Abstract

Fusion product alpha populations can significantly influence tokamak stability due to coupling between the trapped alpha precessional drift and the kinetic ballooning mode frequency. This effect is of particular importance in parameter regimes where the alpha pressure gradient begins to constitute a sizeable fraction of the thermal plasma pressure gradient. Careful, quantitative evaluations of these effects are necessary in burning plasma devices such as the Tokamak Fusion Test Reactor and the Joint European Torus, and we have continued systematic development of such a kinetic stability model. In this model we have considered a range of different forms of the alpha distribution function and the tokamak equilibrium. Both Maxwellian and slowing-down models have been used for the alpha energy dependence while deeply trapped and, more recently, isotropic pitch angle dependences have been examined. In the latter case the drift reversal of the not so deeply trapped alphas is an important new feature not included in the deeply trapped model. The tokamak equilibrium was initially described using the nearly concentric circular flux surface model as well as more realistic analytic and numerical calculations that include the higher order poloidal harmonics of the equilibrium. An improved analytic model gives especially close agreement with the finite β numerical equilibrium. Detailed comparisons of these various models are presented. Our results indicate that alpha populations can significantly deteriorate the first stability window for ballooning modes as the alpha pressure gradient is increased and as the background electron temperature is raised (for the slowing-down model) or, equivalently, the ratio of alpha to background temperature is lowered (for the Maxwellian model). A related effect is the observed destabiliation with increased aspect ratio (ϵp-1 = R0/rp where rp is the local pressure gradient scale length). These scalings are consistent with an interaction between the ballooning mode frequency and the alpha precessional drift at energies involving increasingly larger fractions of the alpha distribution. Such regimes will characterize the central regions of burning tokamak devices and should be observable for the projected ranges alpha pressure and background temperature.