Bounds on the length of magnetic field lines in a two-dimensional plasma.

Abstract

Magnetic field lines in ideal turbulent plasmas tend to become quite complicated and their length to grow in time. Diffusivity allows for reconnection and possible shortening, but this fact has not so far been rigorously quantified. We show that in a two-dimensional diffusive plasma the mean length of field lines stays bounded for all time. Moreover, these estimates are local, in the sense that the mean values of magnetic field and velocity in the neighborhood of a ball determine bounds for length within the ball, without recourse to external magnitudes.