Evidence for a singularity in ideal magnetohydrodynamics: Implications forfast reconnection

Numerical evidence for a finite-time singularity in ideal 3D magnetohydrody namics is presented. The simulations start from two interlocking magnetic f lux rings with no initial velocity. Curvature shrinks the rings until they touch and current sheets form between them. The evidence for a singularity in a finite time t(c) is that the peak current density behaves like \\J\\(i nfinity) similar to 1/(t(c) - t) for a range of sound speeds and initial co nditions. For the incompressible calculations \\omega\\(infinity)/\\J\\(inf inity) --> const. In resistive reconnection the magnetic helicity is nearly conserved while energy is dissipated.