Nonlinear Hybrid Simulations of Energetic Particle Modes in Realistic Tokamak Flux Surface Geometry

Abstract

First results from nonlinear simulations of energetic particle modes and the resulting transport of energetic ions using realistic tokamak geometry are presented and compared with results obtained with a shifted-circle model equilibrium and otherwise equivalent parameters. The modes excited in both cases have similar frequencies and mode structures and cause a similar amount of energetic ion transport during the first few hundred Alfvén times of the nonlinear evolution. The similarity in transport is interesting since it stands in contrast to the reduced linear growth rate and saturation level in the non-circular case: for the parameters chosen, both are reduced by a factor of 2 compared to the circular case. These results motivate further studies, including a verification of our results with other codes, a clarification of the mechanisms underlying the linear stabilization, and a detailed analysis of the mode activity and particle redistribution during the nonlinear evolution.

Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas

“…Thus, consistent with EP radial redistributions as they are transported nonlinearly, SAW wave-packets readily respond to instantaneous local forcing and maximize wave-particle power exchange. This is consistent with observations from numerical simulation results, reporting that SAW continuous spectrum is crucial in the nonlinear mode dynamics and frequency chirping [73,94,96,97,100,101,102,103,104] (cf. also Appendix A.3).…”

Nonlinear Simulation of Energetic Particle Modes in High-Beta Tokamak Plasma

“…Taking also into account the results of Ref. [10], where the effect of realistic non-circular magnetic flux surface geometry was studied, one may summarize the results obtained so far as follows: magnetic geometry and bulk pressure effects affect the linear stability and nonlinear evolution of EPM, but little effect on the overall energetic particle transport was seen with the diagnostics currently implemented in MEGA. In particular, the reduction of the energetic ion density in the central region of the plasma (r/a 0.5) is similar in all cases studied.…”

“…This work is the continuation of a series of simulations with increasing physical detail, starting with circular magnetic geometry and zero pressure [14], considering realistic geometry [10] and now adding realistic bulk pressure in the fluid limit.…”

“…The simulation setup is the same as the "shaped" case studied in Ref. [10]; except that the bulk density ρ m = m i n i and bulk pressure P are now evolved in time. The profiles of the safety factor q(r) and toroidal bulk beta β bulk (r) = 2μ 0 P(r)/v 2 A0 are plotted in Fig.…”

“…The division by the reference field n H (R, Z, t 1 ) (not done in Ref. [10]) amplifies fluctuations near the boundary, where n H is small. The change in the density field found after the major peak in n = 1 mode activity is shown in Fig.…”