Effects of plasma {beta} on the plasmoid instability
The effects of the initial upstream plasma {beta} on the plasmoid instability are studied via two-dimensional resistive magnetohydrodynamic simulations. For cases with nonuniform {beta} 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 {beta}. The critical Lundquist number is approximately 2000-3000 for {beta}=50 and is 8000-10 000 for {beta}=0.2. The higher the {beta}, the smaller the critical Lundquist number is. Similar to previous studies of high-{beta} systems, the average reconnection rate in low {beta} 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 BV{sub A}, is lower in a low {beta} system than that in a high {beta} system. The magnetic energy spectral index, which characterizes fragmentation of the reconnection layer, is approximately two and is insensitive to {beta} in the high-Lunquist number regime. It is also found that the magnetic reconnection rate becomes similar for different {beta} cases, if the initial force-balance is provided by temperature gradient instead of density gradient. Therefore, it is concluded that the {beta}-dependence mentioned above may be largely attributed to the density variation.