Gyrokinetic δf particle simulation of trapped electron mode driven turbulence

Abstract

The linear instabilities and nonlinear transport driven by collisionless trapped electron modes (CTEM) are systematically investigated using three-dimensional gyrokinetic δf particle-in-cell simulations. Scalings with local plasma parameters are presented. Simulation results are compared with previous simulations and theoretical predictions. The magnetic shear is found to be linearly stabilizing, but nonlinearly the transport level increases with increasing magnetic shear. This is explained by the changes in radial eddy correlation lengths caused by toroidal coupling. The effect of zonal flows in suppressing the nonlinear CTEM transport is demonstrated to depend on electron temperature gradient and electron to ion temperature ratio. The suppression effect is consistent with the rate of shearing on turbulent eddies due to zonal flows and the radial sprectra broadening. Strong geodesic acoustic modes (GAM) are generated along with zonal flows.

Theory of fine-scale zonal flow generation from trapped electron mode turbulence

“…16 These different behaviors are not necessarily in conflict due to parametric dependencies. 18,19 The geodesic acoustic modes' contribution to the shearing effects of ZFs is found to be insignificant in Ref. 20, which is consistent with previous predictions.…”

“…[6][7][8][9][10][11][12] The TEM driven turbulence and transport have also been studied experimentally in some tokamaks, such as ASDEX upgrade, 13 Alcator C-Mod, 14 and DIII-D. 15 Recently, some gyrokinetic simulation works have paid more attention to ZF effects on the CTEM turbulence. 14,[16][17][18][19][20][21] The nonlinear upshift of the critical density gradient for CTEMs due to suppression by turbulence-generated ZFs was reported, 14 which is analogous to the case for ITG modes. 4 On the other hand, weak influence of ZFs on the transport level was claimed for different parameter regimes.…”

Role of zonal flows in trapped electron mode turbulence through nonlinear gyrokinetic particle and continuum simulation

“…In contrast, zonal flows were shown to have little effect on the TEM saturation level in cases with strong electron temperature gradients and T e = 3T i [7]. This apparent contradiction was addressed by work that bridged the two regimes [8,9]. The importance of zonal flows in TEM turbulence was found to vary with ∇T e , T e /T i , and magnetic shear [8,10].…”

“…This apparent contradiction was addressed by work that bridged the two regimes [8,9]. The importance of zonal flows in TEM turbulence was found to vary with ∇T e , T e /T i , and magnetic shear [8,10]. A simplified and qualitative fluid linear and wave-kinetic nonlinear model [11] of the TEM zonal flow growth rate, neglecting ion dynamics and density gradient driven TEMs, finds a weaker zonal flow growth rate at larger η e .…”

Fully electromagnetic nonlinear gyrokinetic equations for tokamak edge turbulence

“…Sometimes, nonlinearity associated with the magnetically trapped electrons is important. [86][87][88][89] In Eq. (26), the last term represents the sloshing energy.…”