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

TL;DR

This paper develops a theoretical and numerical framework for multi-shock implosions that achieve ultrahigh, quasi-isentropic compression with suppressed instabilities, advancing inertial confinement fusion techniques.

Contribution

It extends classical models to N stacked shocks, deriving self-similar solutions and scaling laws validated by simulations, enabling more stable high compression schemes.

Findings

Cumulative compression increases with the number of shocks.

Entropy generation is strongly suppressed as the number of shocks increases.

The scheme reduces Rayleigh Taylor instability, improving stability in inertial confinement fusion.

Abstract

We present a unified theoretical and numerical framework for self-similar multi-shock implosions achieving ultrahigh compression in a uniform solid spherical target. Extending the classical Guderley model to N stacked, spherically converging shocks, we derive selfsimilar solutions and the scaling law for the final density. One dimensional Lagrangian hydrodynamic simulations confirm this relation over a broad range of parameters, from the weakly to the strongly nonlinear regime. 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 increases infinity. 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.