Degradation of performance in ICF implosions due to Rayleigh--Taylor instabilities: a Hamiltonian perspective

TL;DR

This paper develops a Hamiltonian-based variational theory to analytically study how Rayleigh--Taylor instabilities degrade performance in inertial-confinement-fusion implosions, highlighting the importance of polar flows and convergence ratios.

Contribution

It introduces a first-principle variational model for RTI in spherical ICF implosions, including shell-fluid coupling, and compares analytical and numerical results to understand performance degradation.

Findings

Higher convergence ratios cause greater performance degradation.

Polar flows significantly affect residual kinetic energy calculations.

Analytical results align with nonlinear numerical simulations.

Abstract

The Rayleigh--Taylor instability (RTI) is an ubiquitous phenomenon that occurs in inertial-confinement-fusion (ICF) implosions and is recognized as an important limiting factor of ICF performance. To analytically understand the RTI dynamics and its impact on ICF capsule implosions, we develop a first-principle variational theory that describes an imploding spherical shell undergoing RTI. The model is based on a thin-shell approximation and includes the dynamical coupling between the imploding spherical shell and an adiabatically compressed fluid within its interior. Using a quasilinear analysis, we study the degradation trends of key ICF performance metrics (e.g., stagnation pressure, residual kinetic energy, and aerial density) as functions of initial RTI parameters (e.g., the initial amplitude and Legendre mode), as well as the 1D implosion characteristics (e.g., the convergence ratio). We compare analytical results from the theory against nonlinear results obtained by numerically integrating the governing equations of this reduced model. Our findings emphasize the need to incorporate polar flows in the calculation of residual kinetic energy and demonstrate that higher convergence ratios in ICF implosions lead to significantly greater degradation of key performance metrics.