Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfvén eigenmodes

Abstract

A “stiff transport” critical gradient model of energetic particle (EP) transport by EP-driven Alfvén eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the local AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or the trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEM peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from local equilibrium E × B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in the study by Waltz et al. [Nucl. Fusion 55, 123012 (2015)]: the EP-driven AE growth rate should be determined with rather than without an added thermal plasma drive.