Secondary instability of electromagnetic ion-temperature-gradient modes for zonal flow generation

Abstract

An analytical model for zonal flow generation by toroidal ion-temperature-gradient (ITG) modes, including finite β electromagnetic effects, is derived. The derivation is based on a fluid model for ions and electrons and takes into account both linear and nonlinear β effects. The influence of finite plasma β on the zonal flow growth rate (γ ZF ) scaling is investigated for typical tokamak plasma parameters. The results show the importance of the zonal flows close to marginal stability where γ ZF /γ IT G >> 1 is obtained. In this region the parameter γ ZF /γ IT G increases with β, indicating that the ITG turbulence and associated transport would decrease with β at a faster rate than expected from a purely linear or quasi-linear analysis.

Gyrokinetic nonlinear isotope effects in tokamak plasmas

“…Therefore, the Gyro-Bohm scaling, present at short scale length in any plasma condition, can be counteracted in DT by the long correlation zonal flow activity if the plasma β is high enough. The link between electromagnetic effects and stronger zonal flow activity has been studied in several previous studies [15,16], therefore we hope that the fact that there is an extra element playing a role, i.e. the mass, may trigger further studies regarding the detailed mechanisms at play.…”

High frequency geodesic acoustic modes in electron scale turbulence

“…The finite β-effects are added in an analogous way compared to the recent work on zonal flows in Ref. [32,33]. In particular the Maxwell stress is included in the generation of the el-GAM.…”

“…It is well known that a linear drift wave can be significantly damped by finite β effects and it was recently shown that finite β can have a significant impact on secondarily generated modes such as zonal flows, see [4,32]. Although the electron GAM (el-GAM) was previously explored in [30,31], vital physics were, however, neglected.…”

“…In this work the finite β-effects are elaborated on, and numerical quantifications of the frequency and growth rate are given. The finite β-effects are added in an analogous way compared with the recent work on zonal flows in [32,33]. In particular the Maxwell stress is included in the generation of the el-GAM.…”

Effects of the Second Harmonic on the GAM in Electron Scale Turbulence

“…The finite β-effects were added in an analogous way compared to the recent work on zonal flows in Ref. [29,30]. In particular, the Maxwell stress was included in the generation of the el-GAM.…”