High energy density experimental facilities access extreme conditions of temperature and pressure, allowing us to probe states of matter relevant to astrophysics, and planetary and stellar interiors. Laboratory experiments now yield detailed measurements of radiation transport and opacities, equations-of-state and material dynamics at high pressure, and implosions and hydrodynamic instabilities. Developing an understanding of material properties and processes occurring at high energy densities is also the central challenge for inertial confinement fusion (ICF). Current high energy lasers, such as Omega at the University of Rochester Laboratory of Laser Energetics, and others worldwide, and pulsed power machines such as the Z facility at Sandia National Laboratories, conduct experiments at pressures of up to 40 Mbar and temperatures of 200 eV. The National Ignition Facility (NIF) should reach Gbar pressures and temperatures of tens of keV, enabling exploration of new regimes, including attainment of thermonuclear ignition.
The design of high energy density experiments and interpretation of the experimental results rely heavily upon complex codes which treat a full spectrum of physical processes. These codes model heating from intense laser beams, particle beams, or strong electric currents. They model energy transport by soft x-rays over a spectrum of frequencies. Thermal energy transport by electrons and ions is modeled, either in the local or non-local limits, possibly in the presence of evolving magnetic fields. Modeling of thermonuclear burn in ICF capsules necessitates transporting charged particle and neutron products as well. These processes act while the plasma is in motion, often evolving under the action of one or more hydrodynamic instabilities. Thus the transport algorithms employed must be sufficiently economical and efficient to allow highly resolved simulations to proceed on hydrodynamic timescales. The transport algorithms must also scale efficiently for distributed parallel processing to facilitate simulations of targets in three dimensions.
We examine various transport methods employed in high energy density physics simulations. Special emphasis will be placed on methods that have proven practical for everyday use while representing the important physical processes. The propagation and deposition of laser energy are considered in the context of ray tracing models, which include the ponderomotive pressure and scattering effects. We discuss models for electron thermal transport ranging from the local limit to a non-local treatment that employs a delocalization kernel to retain the main features caused by kinetic effects. We examine approaches for modeling of magnetic fields in 3D, considering the complications that arise from wide variations in the Hall parameter and from the Nernst convective term. We outline various methods for calculating thermal x-ray transport and discuss the significance of non-LTE effects. The effectiveness of the methods will be examined through comparisons of simulations with experiments. Results from large-scale simulations run on over 1000 processors, using a combination of massively parallel processing and symmetric multiprocessing, will be described.
*This work performed under the auspices of the U. S. Department of Energy by the University of California Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48.