Theory and modeling of electron fishbones

Abstract

Internal kink instabilities exhibiting fishbone like behavior have been observed in a variety of experiments where a high energy electron population, generated by strong auxiliary heating and/or current drive systems, was present. After briefly reviewing the experimental evidences of energetic electrons driven fishbones, and the main results of linear and nonlinear theory of electron fishbones, the results of global, self-consistent, nonlinear hybrid MHD-Gyrokinetic simulations will be presented. To this purpose, the extended/hybrid MHD-Gyrokinetic code XHMGC will be used. Linear dynamics analysis will enlighten the effect of considering kinetic thermal ion compressibility and diamagnetic response, and kinetic thermal electrons compressibility, in addition to the energetic electron contribution. Nonlinear saturation and energetic electron transport will also be addressed, making extensive use of Hamiltonian mapping techniques, discussing both centrally peaked and offaxis peaked energetic electron profiles. It will be shown that centrally peaked energetic electron profiles are characterized by resonant excitation and nonlinear response of deeply trapped energetic electrons. On the other side, off-axis peaked energetic electron profiles are characterized by resonant excitation and nonlinear response of barely circulating energetic electrons which experience toroidal precession reversal of their motion.

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

“…This nonlinear EP dynamics has been studied extensively in the last decades. Due to the focus on the EP dynamics, most of these studies have been carried out with global simulations neglecting the nonlinear kinetic dynamics of both the thermal ions and thermal electrons (Berk & Breizman 1990;Briguglio, Zonca & Vlad 1998;Todo, Berk & Breizman 2003;Schneller et al 2012;Vlad et al 2013Vlad et al , 2016Wang et al 2016;Biancalani et al 2017;Cole et al 2017), with some of them including the nonlinear kinetic dynamics of the thermal ions Todo et al 2019). Note that, in particular, following the electron dynamics is numerically very challenging, due to the larger thermal velocity with respect to ions.…”

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 .…”

Single-n versus multiple-n simulations of Alfvénic modes

“…This behaviour suggests that saturation occurs because of a "net" outward radial displacement of the resonant EP fraction, as discussed, e.g., in Refs. [8,54,55]. Here, it is worthwhile noting that the qualitative behavior of frequency chirping in Fig.…”

“…A detailed analysis of the driving resonances, which is, nevertheless, outside the scope of the present paper, can be obtained, e.g., using the Hamiltonian mapping techniques in order to generate kinetic Poincaré plots (see, e.g., Refs. [59,60,55]). Note that the frame corresponding to the n = 1 (stable) simulation is dominated by regions in the (µ, u) plane which exhibit a negative transfer of energy from the particles to the waves, i.e., a net damping contribution (blue pattern colors).…”