Formation of plasmoids during sawtooth crashes

Abstract

The nonlinear growth of the internal kink mode is studied numerically using reduced magnetohydrodynamic equations in cylinder geometry. For low Lundquist numbers, S < 107, the already well-known results have been reproduced: a m/n = 1/1 magnetic island (m: poloidal, n: toroidal mode number) grows while the original core shrinks until full reconnection is achieved. For higher S values, however, the dynamics is found to be qualitatively different from the well-known Kadomtsev's model (Kadomtsev 1975 Sov. J. Plasma Phys. 1 389). The growth of the 1/1 island causes the development of a very thin current sheet which becomes tearing unstable. The current sheet is thus broken up and secondary islands (plasmoids) form. These plasmoids strongly speed up the reconnection and eventually coalesce into one secondary island. The formation of a large secondary island stops the fast reconnection process, leading even to a partial reversal of this process. The final state of sawtooth reconnection is thus no longer an axis-symmetric equilibrium as in the case of complete reconnection for low S values, but a helical equilibrium with two coexisting magnetic islands.