Electron fluxes in low density pinches

The pinches with the current velocity more than Alfven velocity are considereJ. The class of exact solutions of electron hydrodynamics has been found. Arguments in favour of such pinches agains the sausage instability are presented, the new heating mechanism related to the electron current velocity infinity is considered. Sharp focusing observed on the anode surface of the REB diode is explained by electron freezing-in and plasma inhomogeneity. The basic heating mechanism in the z-pinch is electron flow from the low-density plasma into the dense one. The z-pinch neck stabilization occurs at the current velocity of Alfven order