Impact of electron temperature anisotropy on the collisionless tearing mode instability in the presence of a strong guide field

TL;DR

This paper derives an analytical dispersion relation for collisionless tearing modes considering electron temperature anisotropy in a strong guide field, revealing damping effects and validating predictions with numerical simulations.

Contribution

A new gyrofluid model and dispersion relation are developed to analyze electron temperature anisotropy effects on tearing modes in strong guide fields.

Findings

Tearing mode gets weakly damped as electron temperature anisotropy increases.

The derived dispersion relation reduces to known formulas in the isotropic limit.

Numerical simulations confirm the analytical predictions with high accuracy.

Abstract

We derive and analyze a dispersion relation for the growth rate of collisionless tearing modes, driven by electron inertia and accounting for equilibrium electron temperature anisotropy in a strong guide field regime. For this purpose, a new gyrofluid model is derived and subsequently simplified to make the derivation of the dispersion relation treatable analytically. The main simplifying assumptions consist in assuming cold ions, neglecting electron finite Larmor radius effects, decoupling ion gyrocenter fluctuations and considering $\beta_{\perp_e} \ll 1$, with $\beta_{\perp_e}$ indicating the ratio between the perpendicular electron thermal pressure and the magnetic pressure exerted by the guide field. This simplified version of the gyrofluid model is shown to possess a noncanonical Hamiltonian structure. The dispersion relation is obtained by applying the theory of asymptotic matching and does not predict an enhancement of the growth rate as the ratio $\Theta_e$, between perpendicular and parallel equilibrium electron temperatures, increases. This indicates a significant difference with respect to the case of absent or moderate guide field. For an equilibrium magnetic shear length of the order of the perpendicular sonic Larmor radius and at a fixed $\beta_{\perp_e}$, we obtain that the tearing mode in the strong guide field regime gets actually weakly damped, as $\Theta_e$ increases. In the isotropic limit $\Theta_e=1$, the dispersion relation reduces to a previously known formula. The analytical predictions are tested against numerical simulations showing a very good quantitative agreement. We also provide a detailed discussion of the range of validity of the derived dispersion relation and of the compatibility among the different adopted assumptions.