Tearing Instability in Gyrotropic MHD: Effects of Equilibrium Pressure Anisotropy

Abstract

Weakly collisional plasmas are widespread in astrophysics and can sustain pressure anisotropy, yet most analytical tearing-mode scalings assume an isotropic equilibrium. We develop a linear theory of resistive tearing in nonideal gyrotropic MHD for a force-free Harris current sheet characterized by perpendicular plasma beta $β_0$ and parallel-minus-perpendicular beta difference $Δβ_0$. In the ideal outer region, anisotropy changes the far-field decay rate, the matching parameter $Δ'$, and the upper wavenumber cutoff for localized tearing, $α\equiv ka<α_c=\sqrt{\mathcal{A}/\mathcal{R}_0}$, with $\mathcal{A}=1-Δβ_0/2$ and $\mathcal{R}_0=1+\frac{1}{2}[(γ_\parallel+γ_\perp-2)β_0+γ_\parallelΔβ_0]$. In the resistive inner layer, anisotropy enters the leading momentum balance through $\mathcal{A}$. We derive modified FKR and Coppi branches and, by matching them at their crossover wavenumber, obtain $γ_{\max}τ_A\sim\mathcal{A}^{1/2}\mathcal{R}_0^{-1/4}S^{-1/2}$. Thus the classical Lundquist-number exponent is retained, while the prefactor depends on the equilibrium anisotropy, plasma beta, and gyrotropic closure. PSECAS eigenvalue calculations support the Coppi branch and are consistent with the FKR branch when a fitted finite-wavelength approximation for $Δ'$ is used. Within the localized-mode and pressure-positive domain, positive $Δβ_0$ generally suppresses tearing and broadens the inner layer, whereas negative $Δβ_0$ enhances growth and shifts the fastest mode to larger wavenumber. This work identifies how prescribed equilibrium pressure anisotropy modifies both ideal outer matching and resistive inner-layer dynamics in the gyrotropic-MHD regime.