Reconnection rates of magnetic fields including the effects of viscosity

TLDR

The authors extend Sweet–Parker and Petschek reconnection scalings to include viscosity and validate the modified theory against tokamak simulations of forced reconnection, m = 1 kink, and m = 2 tearing modes. The results show that viscosity significantly affects reconnection in high‑β plasmas, with large viscosity yielding rates consistent with the modified Sweet–Parker scaling, negligible viscosity producing non‑steady or slower resistive behavior, and experimental m = 1 kink data agreeing with the theory.

Abstract

The Sweet–Parker and Petschek scalings of the magnetic reconnection rate are modified to include the effect of the viscosity. The modified scalings show that the viscous effect can be important in high-β plasmas. The theoretical reconnection scalings are compared with numerical simulation results in a tokamak geometry for three different cases: a forced reconnection driven by external coils, the nonlinear m=1 resistive internal kink, and the nonlinear m=2 tearing mode. In the first two cases, the numerical reconnection rate agrees well with the modified Sweet–Parker scaling when the viscosity is sufficiently large. When the viscosity is negligible, a steady state which was assumed in the derivation of the reconnection scalings is not reached and the current sheet in the reconnection layer either remains stable through sloshing motions of the plasma or breaks up to higher m modes. When the current sheet remains stable, a rough comparison with the Sweet–Parker scaling is obtained. In the nonlinear m=2 tearing mode case where the instability is purely resistive, the reconnection occurs on the slower dissipation time scale (ψ̇s∼η). In addition, experimental data of the nonlinear m=1 resistive internal kink in tokamak discharges are analyzed and are found to give reasonable agreement with the modified Sweet–Parker scaling.