Stability of tearing modes in finite-beta plasmas

The linear stability of classical tearing modes in a finite-beta, cylindrical plasma is reconsidered. The different regimes of tearing mode instability are delineated by means of critical Lundquist numbers. The well-known criterion Δ′>Δ_c due to Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)] defines a critical Lundquist number above which the plasma is stable. However, the physical importance of this Lundquist number is diminished by the fact that there is another critical Lundquist number, which is typically an order of magnitude smaller, above which the mode changes qualitatively in that the growth rate scales linearly with resistivity, and eventually becomes indistinguishable from resistive diffusion. The effect of parallel viscosity, which reduces the stabilizing coupling to the sound wave, is also considered. For large parallel viscosity, it is shown that Δ_c tends to zero. Thus, the stability criterion Δ′>Δ_c for a finite-beta plasma is simply replaced by the criterion Δ′>0. These analytical results are shown to be in good agreement with numerical results.