Bounds on the length of magnetic field lines in a two-dimensional plasma -art. no. 037402

Magnetic field lines in ideal turbulent plasmas tend to become quite compli cated and their length to grow in time. Diffusivity allows for reconnection and possible shortening, but this fact has not so far been rigorously quan tified. We show that in a two-dimensional diffusive plasma the mean length of field lines stays bounded for all time. Moreover, these estimates are lo cal, in the sense that the mean values of magnetic field and velocity in th e neighborhood of a ball determine bounds for length within the ball, witho ut recourse to external magnitudes.