3-DIMENSIONAL MAGNETIC-FIELD ANNIHILATION

We present a family of three-dimensional nonlinear solutions for magne tic field annihilation in a current sheet, including the effects of re sistivity and viscosity. The different members of the family are chara cterized by the imposed vorticity of the flow that brings the field li nes together. Since in a three-dimensional flow the, vorticity can be increased by the stretching of vortex lines (an effect that is absent in two dimensions), we find some striking differences to our previous two-dimensional analysis. In both the two-dimensional and three-dimens ional analyses, above a certain critical imposed vorticity omega(crit) , the flow breaks up into cells with current sheets at their boundarie s. The nature of the original central current sheet is completely alte red. In the two-dimensional analysis, omega(crit) is a steeply increas ing function of the viscous Reynolds number R, whereas in the three-di mensional case, it quickly asymptotes to only omega(crit) = 2nu0/L whe re nu0 and L are the characteristic velocity and length scale of the f low, respectively. The width of the current sheet, which depends on th e speed at which field lines are, carried into it, also responds diffe rently to an increase in R. In two dimensions, the current sheet narro ws for an vorticities, but in three dimensions, it narrows when the im posed vorticity is negative and widens when it is positive. Also we fi nd that the current density within the current sheet, varies as the na ture of the flow is changed, rather than being constant as in the two- dimensional case. Finally, we find that there is a minimum value of th e plasma beta beta(min) below which the plasma pressure is negative. F or the nonsheared (neutral current sheet) case beta(min) increases rap idly with the magnetic Reynolds number R(m) such that this type of ann ihilation is only possible for a high-beta plasma. For a sheared magne tic field, however, beta(min) is much lower, making this type of annih ilation more relevant to the solar corona.