High frequency geodesic acoustic modes in electron scale turbulence

Experimental investigations has elucidated on the complex dynamics of the low to high (L-H) plasma confinement mode transition. Evidence of interactions between the the turbulence driven E⃗ × B⃗ zonal flow oscillation or Geodesic Acoustic Mode (GAM) [1], turbulence and the mean equilibrium flows during this transition was found. Furthermore, periodic modulation of flow and turbulence level with the characteristic limit cycle oscillation at the GAM frequency was present [2]. The GAMs are weakly damped by Landau resonances and moreover this damping effect is weaker at the edge suggesting that GAMs are more prominent in the region where transport barriers are expected [3]. During recent years investigations on coherent structures such as vortices, streamers and zonal flows (m = n = 0, where m and n are the poloidal and toroidal modenumbers respectively) revealed that they play a critical role in determining the overall transport in magnetically confined plasmas [4]. Zonal flows impede transport by shear decorrelation [4], whereas the GAM is the oscillatory counterpart of the zonal flow (m = n = 0 in the potential perturbation, m= 1, n= 0 in the perturbations in density, temperature and parallel velocity) and thus a weaker effect on turbulence is expected [5, 6]. The electron-temperature-gradient (ETG) mode driven by a combination of electron temperature gradients and field line curvature effects is a likely candidate for driving electron heat transport [7]. The ETG driven electron heat transport is determined by short scale fluctuations that do not influence ion heat transport and is largely unaffected by the large scale flows stabilizing ion-temperature-gradient (ITG) modes. In this work the electron branch of the geodesic acoustic mode (el-GAM) driven by electron temperature gradient (ETG) modes is presented including finite β -effects [8] in similar way as in Ref. [9]. The frequency of the el-Gam is higher compared to the ion GAM by the square root of the ion-to-electron mass ratio (Ωq(electron)/Ωq(ion) ≈ √ mi/me where Ωq(electron) and Ωq(ion) are the real frequencies of the electron and ion GAMs, respectively.).