Bulk hydrodynamic stability and turbulent saturation in compressing hot spots

TL;DR

This paper develops a hydrodynamic stability criterion for hot spots under compression, predicting energy behavior of non-radial motions and their saturation, with implications for hot-spot energy at burn time.

Contribution

It introduces a point-wise stability criterion based on $ ho R$, $T$, and trajectory slope, and calculates saturated hydrodynamic energy levels during compression.

Findings

Hydrodynamic energy can reach saturation levels during compression.

Certain trajectories lead to bounded or decreasing hydrodynamic motion.

Simulation results show velocities approach the predicted saturated values.

Abstract

For hot spots compressed at constant velocity, we give a hydrodynamic stability criterion that describes the expected energy behavior of non-radial hydrodynamic motion for different classes of trajectories (in $\rho R$ --- $T$ space). For a given compression velocity, this criterion depends on $\rho R$, $T$, and $\mathrm{d}T/\mathrm{d}(\rho R)$ (the trajectory slope), and applies point-wise, so that the expected behavior can be determined instantaneously along the trajectory. Among the classes of trajectories are those where the hydromotion is guaranteed to decrease, and those where the hydromotion is bounded by a saturated value. We calculate this saturated value, and find the compression velocities for which hydromotion may be a substantial fraction of hot-spot energy at burn time. The Lindl "attractor" trajectory (Lindl, 1995) is shown to experience non-radial hydrodynamic energy that grows towards this saturated state. Comparing the saturation value to available detailed 3D simulation results, we find that the fluctuating velocities in these simulations reach substantial fractions of the saturated value.