Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. I. Effective mode number profile and resonant frequency tracking

Abstract

The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in a JT-60U tokamak scenario with realistic geometry, large magnetic drifts, and strong beam drive. For this purpose, the recently developed orbit-based resonance analysis (ORA) method for circulating particles is extended, so that it can be applied to the nonlinear regime, where the spectrum of orbit-based poloidal mode numbers morb varies in time as the fast ions undergo wave-particle trapping and radial transport. In particular, the extended ORA method captures the effect of nonlinear overlaps between resonances associated with neighboring harmonics (morb,n) and (morb+1,n) that cause long-distance ballistic transport. Two cases with low toroidal mode numbers n≳1 are studied: an n = 1 mode without resonance overlap and a strongly driven n = 3 mode with resonance overlap. For both cases, an effective radial profile of the resonant poloidal mode number mres=Meff(r) is computed and used to track the effective resonant frequency ωres(t) of individual particles during their radial motion r(t). In Paper II, this frequency tracking technique will be applied to study the nonlinear frequency chirping and convective amplification of the modes.