Explosion Implosion Duality and the Laboratory Simulation of Astrophysical Systems

The Euler equations of ideal gas dynamics posess a remarkable nonlinear involutional symmetry which allows one to factor out an arbitrary uniform expansion or contraction of the system. The nature of this symmetry (called by cosmologists the transformation to supercomoving variables) is discussed and its origin clarified. It is pointed out that this symmetry allows one to map an explosion problem to a dual implosion problem and vice versa. The application to laboratory simulations of supernova remnants is considered; in principle this duality allows the complete three-dimensional evolution of highly structured explosion ejecta to be modelled using a static target in an implosion facility.