Electromagnetic instabilities and plasma turbulence driven by electron-temperature gradient

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 $d_e$ , but below the ion Larmor scale $\rho _i$ , 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 $d_e$ 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 kinetic ballooning mode, which is pressure balanced). A turbulent cascade theory is then constructed, with two energy-injection scales: $d_e$ , 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.

MHD turbulence: a biased review

“…2013; Chen & Boldyrev 2017; Passot, Sulem & Tassi 2017; Loureiro & Boldyrev 2018; Avsarkisov 2020; Adkins et al. 2022; Skoutnev 2022), further bolstering its claim to being a universal physical principle.…”

“…They are straightforward physically and have been quite convincingly verified both observationally and numerically (pace the 'waves vs. structures' confusion: see § 8.3.1). The CB approach also appears to offer an attractive and credible strategy for dealing with turbulence in wave-carrying systems other than MHD, in both plasmas and hydrodynamics (e.g., Schekochihin et al 2009Schekochihin et al , 2016Nazarenko & Schekochihin 2011;Barnes, Parra & Schekochihin 2011;Boldyrev et al 2013;Chen & Boldyrev 2017;Passot, Sulem & Tassi 2017;Avsarkisov 2020;Adkins et al 2022;Skoutnev 2022), further bolstering its claim to being a universal physical principle.…”

Scale invariance and critical balance in electrostatic drift-kinetic turbulence

“…i.e. at perpendicular scales much smaller that those at which electromagnetic effects become important (the 'flux-freezing scale'; see Adkins et al 2022), but much larger than those on which one encounters the effects of electron thermal diffusion due to the finite Larmor motion of the electrons (Hardman et al 2022;Adkins 2023) -both of these bring in a special perpendicular scale that would break the drift-kinetic scale invariance 1 . In other words, (3.8) and (3.9) describe physics on scales…”

“…These are, respectively, the rate of parallel thermal conduction and the drift frequency associated with the electron-temperature gradient. Note that the dispersion relation (3.13) is quadratic in the frequency ω because the parallel velocity u e is determined instantaneously in terms of the other fields, by (3.3), unlike in collisionless ETG theory (Adkins et al 2022).…”

An analytical form of the dispersion function for local linear gyrokinetics in a curved magnetic field

“…the poloidal direction in toroidal geometry). One can think of this geometry as that of a Z-pinch (see Ricci et al 2006;Ivanov et al 2020;Adkins et al 2022;Ivanov, Schekochihin & Dorland 2022) due to the assumption of constant magnetic curvature and lack of magnetic shear, which we have implicitly assumed. Under these assumptions, the system of (2.3), (2.8)-(2.10) is homogeneous in space, allowing us to impose periodic boundary conditions in all three spatial dimensions.…”