AbstractSelf similar flow patterns are studied which arise when a cylindrical symmetric strong shock or detonation wave propagates outwards into a gas at rest in which the ambient density varies as the inverse square of the distance from the axis of symmetry along which flows a line current of either zero or finite constant strength. The electrical conductivity of the gas is supposed zero ahead and infinite behind, so that the wave is an ionizing wave. It is shown that self similar solutions exist for both shock and detonation waves for which detailed flow patterns are present.