New self-similar solutions for the unsteady one-dimensional expansion of a gas into a vacuum

New simple self-similar solutions for the unsteady expansion of a gas into a vacuum are found. They describe supersonic rarefaction in cylindrical and spherical symmetry for an arbitrary adiabatic index. An inner boundary exists at a constant self-similar coordinate. In the asymptotic region a universal isothermal density law is given which depends only on geometry. Important applications lie in the field of laser-generated plasmas.