Abstract
It is found that the mean length of magnetic field lines in a two-dimensional plasma is a lower bound of the total current in it, and this estimate does not depend on the value of the resistivity. In a turbulent plasma, the current is often localized in current sheets (of finite thickness). Since the length of curves transported by chaotic flows tends to grow exponentially in time, the same must happen to the current density at these sheets. This fact was previously known by numerical methods.
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