Dr Plamen Ivanov

Abstract:

Electromagnetic (EM) instabilities and turbulence driven by the electron-temperature gradient (ETG) 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 ρi, capturing both electrostatic and EM regimes of turbulence. The well-known electrostatic instabilities – slab and curvature-mediated ETG – are recovered, and a new instability is found in the EM regime, called the thermo-Alfvénic instability (TAI). It exists in both a slab version (sTAI, destabilising kinetic Alfvén waves) and a curvature-mediated version (cTAI), which is a cousin of the (electron-scale) kinetic ballooning mode. The cTAI turns out to be dominant at the largest scales covered by the model (greater than de but smaller than ρi), its physical mechanism hinging on the fast equalisation of the total temperature along perturbed magnetic field lines (in contrast to kinetic ballooning mode, 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). While the model is simplistic, the new physics that is revealed by it should be of interest to those attempting to model the effect of EM turbulence in tokamak-relevant configurations with high beta and large ETGs.

Abstract:

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for $k_y \rho_i \gtrsim 0.1$ in the steep gradient region for a JET pedestal discharge (92174) where the electron temperature gradient is steeper than the ion temperature gradient. Here, $k_y$ is the wavenumber in the direction perpendicular to both the magnetic field and the radial direction, and $\rho_i$ is the ion gyroradius. At $k_y \rho_i \gtrsim 1$, the fastest growing mode is often a novel type of toroidal ETG instability. This toroidal ETG mode is driven at scales as large as $k_y \rho_i \sim (\rho_i/\rho_e) L_{Te} / R_0 \sim 1$ and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, $K_x \rho_e \sim 1$, where $K_x$ is the effective radial wavenumber. Here, $\rho_e$ is the electron gyroradius, $R_0$ is the major radius of the last closed flux surface, and $1/L_{Te}$ is an inverse length proportional to the logarithmic gradient of the equilibrium electron temperature. The fastest growing toroidal ETG modes are often driven far away from the outboard midplane. In this equilibrium, ion temperature gradient instability is subdominant at all scales and kinetic ballooning modes are shown to be suppressed by $\mathbf{ E} \times \mathbf{ B} $ shear. ETG modes are very resilient to $\mathbf{ E} \times \mathbf{ B}$ shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport.

Abstract:

The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a 𝑍-pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations (Dimits et al., Phys. Plasmas, vol. 7, 2000, 969). A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear (van Wyk et al., J. Plasma Phys., vol. 82, 2016, 905820609). The breakup of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system – the Reynolds stress and the advection of the diamagnetic flow by the 𝐸×𝐵 flow. By analysing the linear ion-temperature-gradient modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.

Abstract:

Abstract:

Refer to readme.pdf in the repository.