Fast mixing mechanism of two vortex–current filaments

Abstract

We demonstrate fast mixing of vortex–current filaments by means of numerical simulations of collision (strong interaction) between two straight filaments. The two filaments mutually approach, collide, and are rapidly tangled with each other. In fact, the instantaneous Lyapunov exponent shows that the dynamics becomes chaotic. Then there appear many small regions where the two filaments overlap. We consider each overlapping region to be equivalent to the traditional resistive diffusion region. We assume that the overall ‘reconnection rate’ of the two filaments is proportional to the product of the traditional (non-chaotic) resistive reconnection rate and the normalized overlapping volume. The overlapping volume rapidly increases on the time scale of ideal MHD. When many overlapping regions are produced, the overall reconnection probability, i.e. the sum of the probabilities of reconnection in every overlapping region, should be increased compared with that of the single overlapping region. Thus the overall reconnection rate becomes sufficiently large, although the basic reconnection process in each overlapping region is resistive and slow. We conclude that the fast mixing due to chaos may enhance the conventional resistive reconnection. We call this process ‘chaotic reconnection’.