Radiation hydrodynamics

This course was intended to provide the participant with an introduction to the theory of radiative transfer, and an understanding of the coupling of radiative processes to the equations describing compressible flow. At moderate temperatures (thousands of degrees), the role of the radiation is primarily one of transporting energy by radiative processes. At higher temperatures (millions of degrees), the energy and momentum densities of the radiation field may become comparable to or even dominate the corresponding fluid quantities. In this case, the radiation field significantly affects the dynamics of the fluid, and it is the description of this regime which is generally the charter of radiation hydrodynamics. The course provided a discussion of the relevant physics and a derivation of the corresponding equations, as well as an examination of several simplified models. Practical applications include astrophysics and nuclear weapons effects phenomena

Linear kinetic theory and particle transport in stochastic mixtures. Third year and final report, June 15, 1993--December 14, 1996

The goal in this research was to continue the development of a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. Such a theory should predict the ensemble average and higher moments, such as the variance, of the particle or energy density described by the underlying transport/kinetic equation. The statistics studied correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components in the mixture. The mixing statistics considered were Markovian as well as more general statistics. In the absence of time dependence and scattering, the theory is well developed and described exactly by the master (Liouville) equation for Markovian mixing, and by renewal equations for non-Markovian mixing. The intent of this research was to generalize these treatments to include both time dependence and scattering. A further goal of this research was to develop approximate, but simpler, models from any comprehensive theory. In particular, a specific goal was to formulate a renormalized transport/kinetic theory of the usual nonstochastic form, but with effective interaction coefficients and sources to account for the stochastic nature of the problem. In the three and one-half year period of research summarized in this final report, they have made substantial progress in the development of a comprehensive theory of kinetic processes in stochastic mixtures. This progress is summarized in 16 archival journal articles, 7 published proceedings papers, and 2 comprehensive review articles. In addition, 17 oral presentations were made describing these research results

Transport in statistical media. Final report, May 1, 1988--May 1, 1990

The technical content of these five papers is summarized in this report: Benchmark results for particle transport in a binary Markov statistical medium; Statistics, renewal theory, and particle transport; asymptotic limits of a statistical transport description; renormalized equations for linear transport in stochastic media; and solution methods for discrete state Markovian initial value problems

Variational correction to the FERMI beam solution

We consider the time-independent, monoenergetic searchlight problem for a purely scattering, homogeneous slab with a pencil beam of nuclear particles impinging upon one surface. The scattering process is assumed sufficiently peaked in the forward direction so that the Fokker-Planck differential scattering operator can be used. Further, the slab is assumed sufficiently thin so that backscattering is negligibly small. Generally, this problem is approximated by the classic Fermi solution. A number of modifications of Fermi theory, aiming at improved accuracy, have been proposed. Here, we show that the classic Fermi solution (or any approximate solution) can I be improved via a variational formalism

A CLASS OF TRANSPORT PROBLEMS IN STATISTICAL MIXTURES WITH SCATTERING

Pour un transport indépendant du temps en systèmes monodimensionnels, un formalisme est discuté pour le traitement du transfert radiatif dans les mélanges statistiques, y compris l'interaction de la dispersion, pour une certaine catégorie de problèmes. A titre d'exemple particulier, les statistiques homogènes binaires de Markov sont traitées en détail, pour le modèle de transport en "ligne", ainsi que en géométrie plane. Des résultats sont donnés pour plusieurs problèmes de transport classiques. Dans le cas du problème de Milne, une ambiguïté dans sa définition est mise en exergue et la solution est discutée pour deux interprétations possibles.For time independent transport in one dimensional systems, a formalism is discussed to treat radiative transfer in statistical mixtures, including the scattering interaction, for a certain class of problems. As a special case, binary homogeneous Markov statistics are treated in detail, for both the "rod" model of transport and planar geometry. Results are given for several classical transport problems. In the case of the Milne problem, an ambiguity in its definition is pointed out, and the solution is discussed for two different interpretations

Application of diffusion theory to neutral atom transport in fusion plasmas

It is found that energy dependent diffusion theory provides excellent accuracy in the modelling of transport of neutral atoms in fusion plasmas. Two reasons in particular explain the good accuracy. First, while the plasma is optically thick for low energy neutrals, it is optically thin for high energy neutrals and diffusion theory with Marshak boundary conditions gives accurate results for an optically thin medium even for small values of 'c', the ratio of the scattering to the total cross section. Second, the effective value of 'c' at low energy becomes very close to one due to the down-scattering via collisions of high energy neutrals. The first reason is proven both computationally and theoretically by solving the transport equation in a power series in 'c' and the diffusion equation with 'general' Marshak boundary conditions. The second reason is established numerically by comparing the results from a one-dimensional, general geometry, multigroup diffusion theory code, written for this purpose, with the results obtained using the transport code ANISN