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

Abstract

Trapped electron mode (TEM) turbulence exhibits a rich variety of collisional and zonal flow physics. This work explores the parametric variation of zonal flows and underlying mechanisms through a series of linear and nonlinear gyrokinetic simulations, using both particle-in-cell and continuum methods. A new stability diagram for electron modes is presented, identifying a critical boundary at ηe = 1, separating long and short wavelength TEMs. A novel parity test is used to separate TEMs from electron temperature gradient driven modes. A nonlinear scan of ηe reveals fine scale structure for ηe 1, consistent with linear expectation. For ηe < 1, zonal flows are the dominant saturation mechanism, and TEM transport is insensitive to ηe. For ηe > 1, zonal flows are weak, and TEM transport falls inversely with a power law in ηe. The role of zonal flows appears to be connected to linear stability properties. Particle and continuum methods are compared in detail over a range of ηe = d ln Te/d ln ne values from zero to five. Linear growth rate spectra, transport fluxes, fluctuation wavelength spectra, zonal flow shearing spectra, and correlation lengths and times are in close agreement. In addition to identifying the critical parameter ηe for TEM zonal flows, this paper takes a challenging step in code verification, directly comparing very different methods of simulating simultaneous kinetic electron and ion dynamics in TEM turbulence.

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

“…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. 22 So far, there are very few theoretical works 23 on ZFs in CTEM turbulence driven by the trapped electron precession drift resonance.…”

“…[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.…”

“…However, relatively short scale ZFs, i.e., q r ρ θi ∼ 1, have been found in recent nonlinear gyrokinetic simulations of CTEM turbulence. 17,20,21 The goal of this work is hence to extend the ZF growth calculation to this short wavelength regime.…”

Extreme Heat Fluxes in Gyrokinetic Simulations: A New Criticalβ

“…As a consequence of its zonal flow dynamics, TEM turbulence is likely not prone to an NZT. While for certain parameter regimes, zonal flows play some role in TEM saturation [21], the mode should be able to fall back on non-zonal saturation at similar or slightly larger transport values if the zonal flows are critically weakened.…”

Transport properties of finite-β microturbulence

“…Recently, advances have been made in explaining the saturation mechanisms of TEM turbulence [23][24][25]. In this section, the effects of finite β on both linear and nonlinear TEMs are to be examined.…”