Single-n versus multiple-n simulations of Alfvénic modes

Abstract

The results of a set of simulations of Alfvén modes driven by an energetic particle population are presented, with the specific aim of comparing single-n and multiple-n simulations (n being the toroidal mode number). The hybrid reduced O(3 0) MHD gyrokinetic code HMGC is used (0 ≡ a/R 0 being the inverse aspect ratio of the torus, with a and R 0 the minor and major radius, respectively), retaining both fluid (wave-wave) and energetic particles nonlinearities. The code HMGC retains selfconsistently, in the time evolution, the wave spatial structures as modified by the energetic particle (EP) term. Simulations with toroidal mode numbers 1 n 15 have been considered. For the specific energetic particle drive considered, single-n simulations are either stable (n=1), or weakly unstable (n = 2, 3, 13, 14, 15), or strongly unstable (4 n 12), with 4 n 12 modes exhibiting similar growth-rates, while n = 4 the largest saturated amplitude. A variety of modes are observed (TAEs, upper and lower KTAEs, EPMs). Nevertheless, no appreciable global modification of the EP density profile is observed at saturation. On the contrary, multi-n, fully nonlinear simulation exhibits an appreciable broadening of the EP radial density profile at saturation, thus showing an enhanced radial transport w.r.t. the single-n simulations. Moreover, the subdominant modes are strongly modified by the nonlinear coupling which results both from the MHD and from the Energetic Particle terms.

Physics of Alfvén waves and energetic particles in burning plasmas

“…In the following, we show that important qualitative and quantitative changes take place in the wave-particle nonlinear dynamics when the effect of "phase locked" particles in non-perturbative. When fluctuations maintain wave-particle resonance condition via "phase locking" through the nonlinear evolution, the chirping rate is proportional to mode amplitude, as observed experimentally, e.g., by (Heidbrink, 2008;Podestà et al, 2011), and in numerical simulations of nonlinear EPM evolutions Vlad et al, 2004Vlad et al, , 1999Zonca et al, 2002) as well as nonlinear fishbone dynamics Vlad et al, 2012Vlad et al, , 2013. This behavior is also demonstrated analytically for nonlinear EPM dynamics .…”

“…Hybrid MHD gyrokinetic simulations have confirmed the fact that rapid EP transport is expected when the system is significantly above marginal stability and that fast radial particle redistributions lead to fishbone mode saturation and downward frequency chirping Vlad et al, 2012). Simulation results also indicate that fluid nonlinearities do not qualitatively alter the dynamics of the fishbone burst cycle and EP transport .…”

“…Sec. II) are more recent Vlad et al, 2012Vlad et al, , 2013. Fishbone linear stability analyses based on the same approach are reported by (Park et al, 1999).…”

Nonlinear dynamics of shear Alfvén fluctuations in divertor tokamak test facility plasmas

“…1, in this work, we investigate a single toroidal mode number n in each simulation case, while multi-n simulations will be part of future work (see Ref. 39 for a recent publication on this subject). Thus, MHD nonlinear mode-mode coupling is neglected, but EP nonlinearities are self-consistently retained.…”

Shear Alfvén fluctuation spectrum in divertor tokamak test facility plasmas

“…Numerical simulation results, presented here, assume a typical DTT reference scenario and a model "slowing-down" EP distribution function, making use of the hybrid magnetohydrodynamic(MHD)gyrokinetic simulation code (HMGC) 20,21 . HMGC has been extensively applied to study the resonant interactions between SAW and EPs as well as the corresponding nonlinear behaviors and ensuing EP confinement issues [22][23][24][25][26][27] . HMGC has also been used to investigate plasma scenarios of practical interest, such as ITER 28 , Japan Atomic Energy Research Institute Tokamak-60 Upgrade (JT-60U) [29][30][31] , Doublet III-D (DIII-D) 32,33 and Fusion Advanced Studies Torus (FAST) 8,34,35 .…”