| Time-dependent radiative transport is important in inertial confinement of fusion targets. The target must be illuminated with as symmetric a source as possible to ensure an isentropic compression. Once the fusion event begins, energy is taken away from the burn via radiation transport. This process represents a large percentage of the total energy loss. Similarly, neutron transport is important to calculate accurately as it influences neutronic heating and the time-dependent neutron spectrum. Both radiative and neutronic transport are valuable as a diagnostic tools.; Four time-dependent finite media benchmarks were calculated using the time-dependent integral method. The four benchmarks that were produced are: homogeneous Cartesian with uniform source, homogeneous Cartesian with localized source, homogeneous spherical with localized source, and heterogeneous Cartesian with localized source. The benchmarks were calculated using the subtraction of singularity method, solving for the uncollided flux analytically and numerically solving for the collided flux. Time-dependent, heterogeneous, integral kernels were derived for point, line, and planar geometries. These kernels are newly developed to the field of radiative integral transport.; The Time-Dependent Bubble Integral Transport (TBIT) method was introduced. The technique follows the causality of the particles exactly without the need to save the complete history of the problem. The method was benchmarked against the four finite media, time-dependent benchmarks. In Cartesian coordinates, the TBIT method produced errors of no more than 1.6%. In spherical coordinates, the TBIT method produced a maximum error in three-dimensional spherical coordinates of 6.5%.; The TBIT method was applied to two problems typical to Inertial Confinement of Fusion devices. A three-dimensional spherical capsule illumination was simulated for a two, four, and six laser entrance hole spherical hohlraum. As the surface area of the laser entrance hole gets larger, the capsule illumination becomes more non-uniform. The TBIT method predicted that the greater the number of laser entrance holes, for equal surface areas, the more uniform the capsule illumination. The second application was for a neutron time of flight diagnostic found on experimental ICF devices. The simulation showed that scattering effects from the walls would shift the detected spectrum only a small amount. |
