Forced Reconnection in Voigt-Regularized MHD

Abstract

Forced reconnection in Voigt-regularized MHD is investigated in the Hahm-Kulsrud-Taylor problem. It is shown that Voigt regularization introduces an early linear phase of reconnection that partially bypasses the ideal current sheet formation phase. A Rutherford-like model of nonlinear island growth and saturation is introduced, including time-dependent spatial variation in the island current distribution and the braking effects of regularization and viscosity. It is conjectured, with numerical justification, that the inclusion of drag in the momentum equation results in precise MHS equilibria in the long-time limit.

Figures (8)

• Figure 1: The linear reconnection phase in the Voigt-HKT problem for $\alpha_1 = \alpha_2 = 0.1, 0.01, 0.001$. Dashed lines show $\psi_1 = \delta \alpha_2t^2$. Note the rapid deviation from linear, ideal behavior.
• Figure 2: Current density at $y=0$, $t=196$ with $\mu = \nu = 10^{-3}$, $\eta = 10^{-4}$, $\delta = 0.1$ for $\alpha_1 = \alpha_2 = {0.5, 0.1, 10^{-2}, 10^{-5}}$ with timestep $0.05$, showing how increasing regularization spreads the current density.
• Figure 3: Current density at $t=210$ with $\mu = \nu = 10^{-3}$, $\eta = 10^{-4}$, $\delta = 0.1$ for $\alpha_1 = \alpha_2 = 0.5$ with timestep $0.05$. Note the variation in $J$ across the island.
• Figure 4: The saturated pressure in the case from figure \ref{['fig:j-psi']}. The final island width $w=0.42787$ is the same as that found in all other cases with $\delta=0.1$.
• Figure 5: Island width evolution for cases (a) $\delta=0.03, L_y = 7$; (b) $\delta = 0.01, L_y = 1.5$; and (c) $\delta = 10^{-3}, L_y = 3.5$.