A comprehensive conductivity model for drift and micro-tearing modes

Abstract

The parallel electrical conductivity is a crucial parameter in the study of the linear stability of drift-modes like the micro-tearing mode (MTM). The conductivity enters by closing the electromagnetic tearing layer equations. Recent progress in the understanding of the pedestal suggests that the MTM could play an important role in its structure and evolution. For this reason, we revisit and improve previous model conductivities. This parameter is generally derived from the linearized drift kinetic equation. In the past literature, it has been computed using either simplified collision operators or neglecting the spatial dependence away from the rational surface. A fully consistent expression for the conductivity that would accurately model the pedestal has not been available. By applying a novel variational procedure and with the full Fokker Plank collision operator, including electron–electron collisions, we compute a closed expression for the parallel electrical conductivity in the form of a rational function.

Electromagnetic instabilities and plasma turbulence driven by electron-temperature gradient

“…From the first bracket in , we have which is a (damped) version of the ‘magnetic drift wave’ described in Appendix D.2.1, a purely magnetic oscillation involving the balance between the inductive part of the parallel electric field, the gradient of the equilibrium pressure along the perturbed field line and the resistive force in [or indeed ]: By setting , we have decoupled perturbations of the magnetic field – or, in the electrostatic regime, of the parallel velocity – from those of the density and temperature, as in Appendix D.2.1. Note that this mode can potentially go unstable at lower collisionality, where it is sometimes referred to as a slab micro-tearing mode (see, e.g., Drake et al 1980; Hassam 1980 b ; Larakers et al 2020) – this is discussed in Appendix G.…”

“…The effect is also absent in the collisionless limit (). There is, of course, an intermediate regime in which physics typified by such a term can be important (see, e.g., Larakers et al 2020), but this regime is outside the scope of this paper (and indeed of any perturbative collisional expansion).…”

“…1980; Hassam 1980 a , b ; Zocco et al. 2015; Larakers, Hazeltine & Mahajan 2020; Larakers et al. 2021), later in tokamak geometry (Applegate et al.…”

Microtearing modes as the source of magnetic fluctuations in the JET pedestal

“…This demonstration, in combination with other features of the mode, including predominantly electromagnetic heat flux, a large component of tearing parity, and ω = ω e * , unambiguously identifies the modes as MTMs whose underlying physics connects directly with the earliest literature [10]. Investigations of more comprehensive dispersion relations, which include η (ratio of density gradient scale length to temperature gradient scale length) effects, finite k || effects, and a more sophisticated conductivity [39] are currently being undertaken and will be published elsewhere. We briefly comment on the collisionality scans for 82585, which exhibit a tail in the collisionless limit.…”

Linear stability of the JET H-mode pedestal

“…The discovery of collisional MT driven by the electron temperature gradient is attributed to Hazeltine et al [22] in 1975. They proposed a kinetic description of a slab current sheet destabilized by an electron temperature gradient leading to instability in the collisional regime only, triggering several subsequent developments of linear MT stability theory [23,24,25,26,27,28,29,30,31,32,33,34,35]. Recently, in order to predict the electron heat flux, quasilinear models have been developed and tested against nonlinear simulations of MT turbulence, including one based on a fluid approach, with slab geometry and strong collisionality [33], as well as one in an idealized tokamak core plasma scenario [36].…”