Self-similar motions in Z-pinch dynamics

New self-similar solutions of the equations of ideal magnetohydrodynamics for a cylindrically symmetric plasma carrying an axial current are presented. They describe the collapse of shock waves and cavities (hollow plasma liners) on the axis, the outward propagation of shock waves reflected from the axis, inverse Z-pinch flows and related phenomena. The current sheaths at the outer plasma boundary can (and, in fact, should) be included explicitly in these solutions. A comparison of the self-similar solutions with calculations based on the snowplow model show the limits of validity of the latter. (author)