  The problem of collisionless plasma slab expansion into vacuum is solved
within a two-temperature hydrodynamic approximation in the dispersionless limit
of zero Debye radius. In the framework of such an approach, the solution by the
Riemann method provides quite accurate description of the whole process of
plasma dynamics. It is shown that the dispersionless approximation agrees very
well with exact numerical solution of the full system of plasma hydrodynamic
equations.
