Scaling laws of multi-shock implosions toward the quasi-isentropic limit

We present a unified theoretical and numerical framework for self-similar multi-shock implosions achieving ultra-high compression in a uniform solid spherical target. Extending the classical Guderley model to N-stacked, spherically converging shocks, we derive self-similar solutions and the scaling law for the final density of the form ρr/ρ0∝P̂β(N−1), where P̂ is the stage pressure ratio and β is determined by the adiabatic index γ. One-dimensional Lagrangian hydrodynamic simulations confirm this relation over a broad range of parameters, from the weakly to the strongly nonlinear regime (P̂∼70). The results show that cumulative compression increases systematically with the number of stacked shocks while entropy generation is strongly suppressed, asymptotically approaching a quasi-isentropic limit as N→∞. This volumetric scheme strongly suppresses the Rayleigh–Taylor instability that plagues shell-based implosions and thus provides a robust, largely instability-resistant compression pathway applicable to inertial confinement fusion and other high-energy-density systems. The framework bridges similarity theory with realistic multi-shock dynamics, guiding the design of advanced laser-driven compression schemes.