Deep geologic repositories are being widely studied as the most favored method of disposal of nuclear waste. Scientists search for repository sites in salt, basalt, tuff and granite that are geologically and hydrologically suitable. The systematic evaluation of the safety and reliability of deep geologic disposal centers around the concept of interacting multiple barriers. The simplest element to describe of the geologic barrier is the physical isolation of the waste in a remote region at some depth within the rock unit. Of greater complexity is the hydrologic barrier which is determined by the waste dilution factors and groundwater flow rates. The least understood is the geochemical barrier, identified as a series of waste/water/rock interactions involving sorption, membrane filtration, precipitation and complexing. In addition to the natural barriers are the engineered barriers, which include the waste form and waste package. The relative effectiveness of these barriers to provide long-term isolation of nuclear waste from the human environment is being assessed through the use of analytical and numerical models. The data used in the models is generally adequate for parameter sensitivity studies which bound the uncertainties in the release and transport predictions; however, much of the data comes from laboratory testing, and …

This paper discusses recent theoretical work on the equilibrium and stability of quadrupole tandem mirrors in the paraxial limit. It reviews calculations of three-dimensional equilibria by means of a ..beta..-expansion technique which lead to an understanding of the important role played by parallel currents and the corollary importance of careful design of the structure of the vacuum geodesic curvature. The previously predicted scaling with central-cell length of the finite-..beta.. distortion of vacuum flux surfaces is shown to saturate because of finite orbit effects. An adaptation to tandem geometries of the reduced MHD technique for calculating high-..beta.. three-dimensional equilibria is described. This approach uses the paraxial expansion to resolve the time-dependent relaxation to equilibrium into three distinct timescales on which the motion can be followed independently. Regarding stability, it is shown that kinetic effects suppress ballooning modes of short-to-moderate perpendicular wavelength; in the limit that such effects are dominant only rigid modes are possible. The stability of the latter modes is investigated within the context of the energy principle. Results of equilibrium and stability calculations for the TMX-U and MFTF-B experiments at Livermore are presented.