High frequency geodesic acoustic modes in electron scale turbulence

Abstract

In this work the finite β-effects of an electron branch of the geodesic acoustic mode (el-GAM) driven by electron temperature gradient (ETG) modes is presented. The work is based on a fluid description of the ETG mode retaining nonadiabatic ions and the dispersion relation for el-GAMs driven non-linearly by ETG modes is derived. The ETG growth rate from the fluid model is compared to the results found from gyrokinetic simulations with good agreement. A new saturation mechanism for ETG turbulence through the interaction with el-GAMs is found, resulting in a significantly enhanced ETG turbulence saturation level compared to the mixing length estimate. It is shown that the el-GAM may be stabilized by an increase in finite β as well as by increasing non-adiabaticity. The decreased GAM growth rates is due to the inclusion of the Maxwell stress.

Effects of the Second Harmonic and Plasma Shaping on the Geodesic Acoustic Mode

“…The frequency decreases with increasing safety factor q 0 in the same manner as found in Ref. [4]. The scaling is however independent of ε n = 2L n /R and the frequency is increased by about 10% by including the m = 2 mode in the analysis.…”

“…The geometrical quantities will first be considered in the strong ballooning limit (θ = 0, g (θ = 0, κ) = 1/κ [3] where g (θ ) is defined by ω D (θ ) = ω ⋆ ε n g (θ )). Moreover we will also employ semi-local approximation as follows [4], k = k , k ⊥ = k ⊥ and ω D = ω D will be replaced by the averages defined through the integrals…”

“…The effects of geometry is determined by a semi-local analysis similar to the work done in Ref. [4] however here modified to allow for varying elongation as well as magnetic shear and safety factor. The other parameters are close to those of the cyclone base case η i = 3.14, ε n = 0.909, s = 0.8 and k 2 ⊥ = 0.1.…”

“…This analysis is based on the coupling of the micro-scale turbulence with the GAM through the WKE under the assumptions that there is a large separation of scales in space and time [1]. In the present work the effects of the second harmonics of the density and temperature perturbations on the linear GAM frequency and non-linear generation of the GAM, using a fluid model [3,4] are investigated.…”

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

“…[23,13,24,25,10,26] In recent work the el-GAM, the finite β-effects were elaborated on, and numerical quantifications of the frequency and growth rate were given in Refs. [27,28]. The finite β-effects were added in an analogous way compared to the recent work on zonal flows in Ref.…”