Unveiling a New $β$-Scaling of the Tearing Instability in Weakly Collisional Plasmas

Abstract: We investigate the linear tearing instability in weakly collisional, gyrotropic plasmas via a non-ideal CGL-MHD framework. Even for an initially isotropic equilibrium, our analysis reveals a striking dependence of the maximum growth rate on plasma-$\beta$, with $\gamma_{max}\tau_{A}\propto\beta^{-1/4}$ in the high-$\beta$ regime, thereby challenging the $\beta$-independence predicted by standard MHD theory. We show that this new scaling emerges from the self-consistent fluctuations in pressure anisotropy, which can suppress or enhance the instability depending on the underlying plasma parameters. Systematic scans of the Lundquist number, magnetic Prandtl number, and anisotropy degree $\Delta\beta$ highlight conditions under which the tearing mode departs significantly from classical behavior. Our findings emphasize that weak collisionality and gyrotropic effects must be considered to accurately capture tearing evolution in high-$\beta$ plasma environments.