The vector potential and the magnetic field have been derived for an arrays of quadrupole magnets with thin Cos(2{theta}) current sheet placed at r = R.{sup bc}. The field strength of each coil within the array, varies purely as a Fourier sinusoidal series of the longidutinal coordinate z in proportion to {omega}{sub m}z, where {omega}{sub m} = (2m-1){pi}/L, L denotes the half-period, and m = 1,2,3 etc. The analysis is based on the expansion of the vector potential in the region external to the windings of a linear 3D quad, and a revision of that expansion by the application of the 'Addition Theorem' from that around the coil center to that around any arbitrary point in space.

This report discusses the regulatory issues regarding cattle disease, bovine spongiform encephalopathy (BSE), and a rare, fatal human illness, Creutzfeldt-Jakob disease (CJD).

Thomson scattering has been developed at the Nova laser facility as a direct and accurate diagnostic to characterize inertial confinement fusion plasmas. Measurements from methane-filled, ignition relevant hohlraums apply the theory for two ion species plasmas, which has been tested in separate open geometry experiments, to obtain electron and ion temperatures. The experimental data provide a benchmark for two-dimensional hydrodynamic simulations using LASNEX, which is presently in use to predict he performance of future megajoule laser- driven hohlraums of the National Ignition Facility (NIF). The data are consistent with modeling using significantly inhibited heat transport at the peak of the drive. Furthermore, we find that stagnating plasma regions on the hohlraum axis are well described by the calculations. The result implies that stagnation in gas-filled hohlraums occurs too late to directly affect the capsule implosion in ignition experiments.

The nonlinear systems of equations arising in circuit simulation, structural optimization, closed loop optimal control, chemical engineering of distillation systems, combustion chemistry, CAD/CAM modeling, robotics, computer vision, and orbital mechanics have several properties that make them especially amenable to homotopy methods. Even so, the homotopy zero curves are not trivial to track, and sophisticated curve tracking techniques are sometimes required. The size of typical engineering problems also presents some interesting numerical linear algebra challenges, and the supported work has been geared toward developing parallel sparse matrix techniques specifically tailored to the sparsity structures corresponding to the mentioned problem areas, in the context of homotopy algorithms. There are many different algorithms for tracking the zero curve {gamma}; the previous proposal discussed three such algorithms: ordinary differential equation based, normal flow, and augmented Jacobian matrix. The descriptions of these algorithms are now in the literature for the software package HOMPACK, so will not be repeated here. The development of sparse homotopy algorithms within HOMPACK specifically tailored for various parallel machines (e.g., distributed memory, shared memory, and vector) and problem areas (e.g., circuit simulation, structural optimization, optimal control, and combustion chemistry) was the central theme of this research.

The goal of this research was a feasibility study for vitrifying the organic ion exchange resin in a stirred-tank melter. Tests were conducted to determine the fate of cesium including the feed, exit glass, and offgas streams and to assess any impact of feeding the resin on the melter or its performance.

This document identifies radiological, chemical and physical conditions inside the Fuel Examination Facility. It is located inside the Plutonium Recycle Test Reactor containment structure (309 Building.) The facility was a hot cell used for examination of PRTR fuel and equipment during the 1960`s. Located inside the cell is a PRTR shim rod assembly, reported are radiological conditions of the sample. The conditions were assessed as part of overall 309 Building transition.