Self-similar multishock implosions for ultrahigh compression of matter

We present a class of self-similar solutions describing ultrahigh compression of a uniform-density target by spherically converging, stacked shock waves. Extending the classical Guderley model, we derive a scaling law for the final density of the form ${\rho }_r\mathrm{/}{\rho }_0\propto {\widehat{P}}^{\beta (N-1)}$, where $N$ is the number of shocks, $\widehat{P}$ the stage pressure ratio, and $\beta$ a numerical exponent determined by the adiabatic index $\gamma$. One-dimensional hydrodynamic simulations confirm the validity of this scaling across a broad parameter range. Notably, the relation remains accurate even in the strongly nonlinear regime up to $\widehat{P}\sim 70$, well beyond the perturbative limit, highlighting the robustness and practical relevance of the model. Owing to its volumetric geometry, this compression scheme inherently avoids the Rayleigh–Taylor instability, which typically compromises shell-based implosions, and thereby establishes a theoretical benchmark for instability-free compression in inertial confinement fusion.