Electromagnetic instabilities and plasma turbulence driven by the electron-temperature gradient - Adkins, T (2022)
Electromagnetic instabilities and turbulence driven by the electron-temperature gradient are considered in a local slab model of a tokamak-like plasma. Derived in a low-beta asymptotic limit of gyrokinetics, the model describes perturbations at scales both larger and smaller than the electron inertial length de, but below the ion Larmor scale rho i, capturing both electrostatic and electromagnetic regimes of turbulence. The well-known electrostatic instabilities --- slab and curvature-mediated ETG --- are recovered, and a new instability is found in the electromagnetic regime, called the Thermo-Alfv\'enic instability (TAI). It exists in both a slab version (sTAI, destabilising kinetic Alfv\'en waves) and a curvature-mediated version (cTAI), which is a cousin of the (electron-scale) kinetic ballooning mode (KBM). The cTAI turns out to be dominant at the largest scales covered by the model (greater than de but smaller than rho i), its physical mechanism hinging on the fast equalisation of the total temperature along perturbed magnetic field lines (in contrast to KBM, which is pressure balanced). A turbulent cascade theory is then constructed, with two energy-injection scales: de, where the drivers are slab ETG and sTAI, and a larger (parallel-system-size-dependent) scale, where the driver is cTAI. The latter dominates the turbulent transport if the temperature gradient is greater than a certain critical value, which scales inversely with the electron beta. The resulting heat flux scales more steeply with the temperature gradient than that due to electrostatic ETG turbulence, giving rise to stiffer transport. This can be viewed as a physical argument in favour of near-marginal steady-state in electron-transport-controlled plasmas (e.g., the pedestal) at sufficiently high values of the electron beta. Numerical simulations are then used to demonstrate that electrostatic turbulence driven by the slab ETG does indeed saturate via a critically-balanced, constant-flux cascade of free-energy, which is shown to be the dynamical manifestation of the scale-invariance of electrostatic drift kinetics. Data from simulations shows excellent agreement with the theoretically predicated one- and two-dimensional spectra of the perturbations. Failure of saturation in electromagnetic turbulence driven by the sTAI is then identified, characterised and discussed. While the model in which these results are derived is simplistic, the new physics that is revealed by it should be of interest to those attempting to model the effect of gradient-driven turbulence in tokamak-relevant configurations, particularly those with high beta and large electron-temperature gradients, in which electromagnetic effects play a significant role.