Viscous resistive magnetic reconnection

A unified linear analysis of viscous effects on resistive internal kink and tearing modes in current carrying magnetized plasmas is presented. The plasma is modeled by single‐fluid magnetohydrodynamic (MHD) equations extended to include the dissipative processes caused by finite cross‐field viscosity (μ⊥) and parallel electrical resistivity (η∥). Two parameters suffice to characterize the relevant instability regimes: the ideal stability parameter ΛH, which is proportional to the minimum value of the energy functional δW, and the viscosity parameter V∝μ⊥/η∥. Both positive and negative values of ΛH are considered to simulate the effect of varying the geometry of the plasma. Analytic expressions are found using generalized Fourier techniques for the mode structure and growth rate for arbitrary values of ΛH and V. Within the scope of the present model, the transverse viscosity slows down the growth of the linear mode, but it does not remove the instability. Novel instability regimes are investigated. For moderate values of the plasma viscosity parameter (V<1), the most important effect is on tearing modes, where the usual ordering for the mode growth rate γ∼η3/5∥ is modified into γ∼η5/6∥μ−1/6⊥, while the width of the viscous‐resistive layer is found to scale as δ∼η1/6∥μ1/6⊥. The same scaling for δ is obtained near the ideal‐MHD marginal stability threshold (‖ΛH‖<1); however, this requires a larger viscosity (V>1). The width of the ‘‘viscous‐inertial’’ layer is instead independent of viscosity on the ideal‐MHD unstable side of the spectrum (ΛH>1).