CURRENT SHEET FORMATION AND DISSIPATION IN GENERAL X-POINT TOPOLOGIES

We consider cylindrical, X-type magnetic equilibria specified by flux functions of the form r(n) cos(ntheta) with n greater-than-or-equal-to 2. It is shown that the excess energy associated with arbitrary disturbances comprises three components: a frictional component that can be dissipated by any form of mechanical damping, a topological component (M(S)) that can be dissipated only by resistive reconnection; and a residual component that is determined by the distribution of normal flux through the outer boundary. We demonstrate that long ''macroscopic'' current sheets should naturally develop in compressible plasmas, even for weak finite amplitude disturbances. In particular, for the simplest topological disturbances the current sheet length scales as L2n approximately M(S). Next we consider the possibility of fast dynamic reconnection for arbitrary, small amplitude perturbations of the X-point. Although the linear theory allows a formal demonstration of fast energy dissipation for the case n = 2, the dissipation rate is expected to slow for higher n due to the weaker equilibrium field in the vicinity of the neutral point. Simple causal arguments imply ''slow'' power law dependences eta1-2/n of the dissipation rate for n > 2.