Compression of matter by hyperspherical shock waves

A novel compression scheme is proposed, in which hollow targets with specifically curved structures initially filled with uniform matter, are driven by a converging shock waves. The self-similar dynamics are analyzed for converging and diverging shock waves. Owing to the geometrical accumulation, the shock-compressed densities and pressures are substantially higher than those achieved using spherical shocks. Two-dimensional hydrodynamic simulations are developed. A linear stability analysis for the spherical geometry reveals a dispersion relation with cut-off mode numbers that are a function of the specific heat ratio, above which eigenmode perturbations are smeared out in the converging phase.