Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics is presented. The simulations start from two interlocking magnetic flux 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 $\Vert J{\Vert }_{\infty }\sim 1/(t_c-t)$ for a range of sound speeds and initial conditions. For the incompressible calculations $\Vert \mathit{\omega }{\Vert }_{\infty }/\Vert \mathbf{J}{\Vert }_{\infty }\to \mathrm{const}$. In resistive reconnection the magnetic helicity is nearly conserved while energy is dissipated.

• Received 10 December 1998

DOI:https://doi.org/10.1103/PhysRevLett.83.1155