In problems involving highly forward-peaked scattering, the Boltzmann transport equation can be simplified using the Fokker-Planck model. The purpose of this project was to develop an analytical solution to the resulting Fokker-Planck equation. This analytical solution can then be used to benchmark numerical transport codes. A numerical solution to the Fokker-Planck equation was also developed. The analytical solution found is a generalized function. It satisfies the purpose of the project with two limitations. The first limitation is that the solution can only be evaluated for certain sources. The second limitation is that the solution can only be evaluated for small times. The moments of the Fokker-Planck equation can be evaluated for any time. The numerical solution developed works for all sources and all times. The analytical solution, then, provides an accurate and precise benchmark under certain conditions. The numerical solution provides a less accurate benchmark under all conditions.

Two-dimensional numerical simulations of ablatively accelerated thin-shells subject to Rayleigh-Taylor instability are presented. Results for both single wavelength and multiwavelength perturbations show that the nonlinear effects of the instability are evident mainly in the "bubble" rather than the "spike." Approximate roles for predicting the dominant nonlinear mode-mode interactions, which limit shell performance, are also discussed. The work concludes with a discussion of recommendations for future work in this area.

The steady flow model is applied to ablatively accelerated spherical targets for inertial confinement fusion. A parameter study is conducted which identifies regions of good hydrodynamic efficiency. In the limit of very large acceleration the model is seen to become planar and can be used to treat some large aspect ratio shells. A model of charged particle beam driven ablation is presented. The ablation resulting from this form of energy deposition can resemble laser driven albation in some cases, but qualitatively different behavior occurs in certain regimes of the beam power and range. Laser energy deposition by inverse bremsstrahlung is also included. A procedure for descaling the dimensionless results of the steady flow model is presented. This allows for comparison of the model with experiments and numerical simulations.

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