Toroidal and slab ETG instability dominance in the linear spectrum of JET-ILW pedestals

Abstract

Local linear gyrokinetic simulations show that electron temperature gradient (ETG) instabilities are the fastest growing modes for k y ρ i ≳ 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 ρ i is the ion gyroradius. At k y ρ i ≳ 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 ρ i ∼ (ρ i /ρ e )L Te /R 0 ∼ 1 and at a sufficiently large radial wavenumber that electron finite Larmor radius effects become important; that is, K x ρ e ∼ 1, where K x is the effective radial wavenumber. Here, ρ 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 E × B shear. ETG modes are very resilient to E × B shear. Heuristic quasilinear arguments suggest that the novel toroidal ETG instability is important for transport.

Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

“…We use the gyrokinetic code GS2 [28] to calculate the fastestgrowing linear modes for parameters where we observe extended electron-driven tails in the ballooning eigenfunction. As discussed in the introduction, extended tails have been observed in both electrostatic modes [12,13,15] and (electromagnetic) micro-tearing modes [16][17][18] for a variety of magnetic geometries. In the analytical theory that we have developed, the geometrical factors enter into the equations for the inner region only through the poloidal angle average • θ .…”

Reduced models for ETG transport in the pedestal

“…[31] identified, for an idealized setup targeting pedestal-relevant parameters, a reduction of ETG transport due to interaction with ion-scale microtearing turbulence (or, rather, zonal flows stimulated by it). There is also a possibility of multiscale interaction between different branches of ETG: slab (k y ρ s ∼ 100) and toroidal [22] (k y ρ s ∼ 10). Although a rigorous survey of multiscale effects lies beyond the scope of this work, some simulations were spot-checked with the goal of probing the effects of toroidal ETG modes.…”

“…The extreme density and temperature gradients in the pedestal far surpass those of the background magnetic field, thus circumventing the typical magnetic drift resonances and favoring slab resonances (for an exception to this claim, see Refs. [14,22], which identified toroidal ETG modes destabilized at large radial wavenumbers). This results in turbulence (1) that is isotropic in comparison with the streamer-dominated core ETG [23,24,25]; (2) exhibits high-k z structure, which demands extreme resolution in the parallel direction; and (3) has contributions from a high number (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) of unstable eigenmodes at each wavenumber.…”

Stabilisation of short-wavelength instabilities by parallel-to-the-field shear in long-wavelength E × B flows

“…Parisi et al. (2020), with , and is normalised so that the maximum value of is : this maximum may occur away from . We note that we define the coordinate in the simulations such that is constant in .…”

“…k qR ∼ 1, cf. Parisi et al (2020). Parallel-to-the-field shearing of the ETG fluctuations acts to increase k by imposing a parallel length scale such that k qR 1, and hence stabilises toroidal modes.…”