Dissipative Collapse of a Magnetic Flux Rope with a Force-Free Internal Field

We have obtained new exact solutions describing the self-similar, uniform compression of twisted magnetic flux tubes (a magnetic flux rope) with a linear, force-free internal field with alpha = const in a resistive medium during the course of their dissipative evolution. Formally, the radius of the rope a decreases to zero over a finite time. This time turns out to be relatively short (several hours) for a rope with a radius of several hundred kilometers, if the helicity of the magnetic field in the rope is high: alpha alpha >> 1.