Effects of plasma β on the plasmoid instability

The effects of the initial upstream plasma β on the plasmoid instability are studied via two-dimensional resistive magnetohydrodynamic simulations. For cases with nonuniform β dependent initial plasma mass density and uniform temperature, our numerical results indicate that the critical Lundquist number for onset of the plasmoid instability depends on the initial plasma β. The critical Lundquist number is approximately 2000 - 3000 for β 50 and is 8000 - 10 000 for β 0.2. The higher the β, the smaller the critical Lundquist number is. Similar to previous studies of high-β systems, the average reconnection rate in low β systems is found to become weakly dependent on the Lundquist number in the plasmoid-unstable regime. However, the average reconnection rate, normalized to the asymptotic value of upstream B V A, is lower in a low β system than that in a high β system. The magnetic energy spectral index, which characterizes fragmentation of the reconnection layer, is approximately two and is insensitive to β in the high-Lunquist number regime. It is also found that the magnetic reconnection rate becomes similar for different β cases, if the initial force-balance is provided by temperature gradient instead of density gradient. Therefore, it is concluded that the β-dependence mentioned above may be largely attributed to the density variation.