Radiative Hydrodynamics

In inertial confinement fusion, a shell of solid thermonuclear fuel (deuterium and tritium) is imploded by irradiating its surface directly with UV laser light (direct drive) or indirectly with laser-produced x rays (indirect drive). In both cases, the dynamics of the implosion is governed by the laws of hydrodynamics. Conservation of mass and momentum are the same as the ones describing classical fluid mechanics. The conservation of energy is complicated by the energy transfer between the laser or x-ray radiation field and the plasma internal or kinetic energy. Classical fluid mechanics including radiation energy transport is usually referred to as “radiative hydrodynamics.” The latter is a well-known discipline in astrophysics. In ICF, radiative hydrodynamics is used to predict the implosion dynamics and the level of shell distortion induced by hydrodynamic instabilities. In astrophysics, radiative hydrodynamics is used to study the dynamics of stars. The main obstacle to reaching thermonuclear ignition is the onset of the so-called “Rayleigh-Taylor instability (RTI)” at the outer and inner surfaces of the imploding shell. The RTI occurs when a heavy fluid is accelerated against a light fluid. In ICF, the heavy fluid is the compressed target accelerated by the low-density ablating plasma (the light fluid). Because of its devastating effects on ICF implosions (a small perturbation could grow thousands of times during the implosion), it is important to fully understand the physics and the stabilizing mechanisms of such instability. Although the physics of the RTI for two inviscid superimposed fluids is well known, the RTI in laser-accelerated targets is strongly affected by the laser ablation, the electron and radiation energy transport, and the complicated density profiles. Two- and three-dimensional numerical simulations as well as complicated analytic theories have been developed at LLE to predict the evolution of the RTI. Such theories and simulations have been compared with detailed experimental observations. The experimental campaigns carried out using the OMEGA laser system have produced a set of reliable data allowing the validation of the hydrodynamic codes and theories developed at LLE. The RTI also plays an important role in the dynamics of astrophysical objects such as supernovae. Recent images from the Hubble Space Telescope of the supernova SN1987A remnant have indicated the development of the RTI in the supernova ejecta as denser ejecta are being accelerated by less-dense ejecta.

Rayleigh–Taylor instability diagram
Rayleigh–Taylor Instability graphs: two and three dimensional numerical simulations predict the evolution of RTI

High compression is usually attained through several laser-driven shocks or continuous compression. The propagation of such strong shocks depends on the material equation of state (the EOS is another equation of radiative hydrodynamics). The EOS of most materials is not well known in the Mbar and gigabar range of pressure. A better determination of the EOS at such high pressures also has important applications in astrophysics as to the understanding of the dynamic behavior of the cores of stars and planets. Until recently, EOS data could be obtained only through underground nuclear explosions. Using high-power lasers, we are now able to collect important information on the equation of state of many materials in the high-energy-density regime. The laws of radiative hydrodynamics describe the compression of matter into the parameter space of high-energy-density physics. At full compression, the plasma pressure in an ICF capsule is of the order of billions of bars. The high temperature and high densities trigger the thermonuclear ignition and propagating burn wave. To study the ignition process, the equations of radiative hydrodynamics must be improved by including models of nuclear reaction rates and alpha-particle energy deposition in the core of the compressed capsule. At the Laboratory for Laser Energetics, full two-dimensional simulations of the implosion, ignition, and burn of a DT capsule are routinely performed to determine the optimum design of the high-gain target to be used in the National Ignition Facility. Faculty in Mechanical Engineering and Physics are actively involved in the study of radiative hydrodynamics and hydrodynamic instability in inertial confinement fusion and astrophysics.

For more information, please contact  or Prof. Adam Frank.

Rayleigh–Taylor instability: growth of imposed mass perturbations is measured with time-gated x-ray radiography