Hydrodynamic instabilities, such as the Rayleigh–Taylor
and Richtmyer–Meshkov instabilities, play a central
role when trying to achieve net thermonuclear fusion energy
via the method of inertial confinement fusion
(ICF). The development of hydrodynamic instabilities on
both sides of the compressed shell may cause shell breakup
and ignition failure. A newly developed statistical mechanics
model describing the evolution of the turbulent mixing
zone from an initial random perturbation is presented.
The model will be shown to compare very well both with
full numerical simulations and with experiments, performed
using high power laser systems, and using shock tubes.
Applying the model to typical ICF implosion conditions,
an estimation of the maximum allowed target, in-flight
aspect ratio as a function of equivalent surface roughness,
will be derived.