Visco-resistive tearing in thin current sheets.

Abstract:

How fast magnetic energy release is triggered and occurs in high Lundquist (S) and high Reynolds number ( R ) plasmas such as that of the solar corona is a fundamental problem for understanding phenomena ranging from coronal heating to flares and CMEs. Diffusion or collisional reconnection driven by macroscopic flows in quasi-steady Sweet-Parker (SP) current sheets are processes far too slow to fit observational data. Spontaneous reconnection, driven by the onset of the tearing instability inside current sheets, provides an alternative paradigm to SP reconnection. Nevertheless, as long as macroscopic current layers are considered, the growth of such an instability is also a slow process. Recently it has been shown that SP current sheets are rapidly unstable in high S plasmas, indeed have a growth rate diverging with increasing S. It has been suggested that such instabilities are triggered during the nonlinear stage of the primary tearing instability of a macroscopic layer. The formation of plasmoids in this presumed SP sheet speeds up the reconnection rate to ideal values. Recently, we have suggested that SP sheets can not be realized in quasi-ideal plasmas, and that the plasmoid instability is triggered on a much larger scale (i.e. with current sheets having a much larger ration of thickness to length than SP). Here we present a linear parametric study of the tearing instability for a Harris current sheet, while taking into account both viscosity and current sheets of variable aspect ratios. The present study shows that an explosive growth of the reconnection rate may be reached during the linear stage, once a critical width of the current layer is reached. In the absence of a strong guide field this depends on viscosity and a range of critical aspect ratios can be found for different values of S, R, or S and Prandtl number.