Recent results from the SSPX spheromak experiment demonstrate the potential for obtaining good energy confinement (Te> 350eV and radial electron thermal diffusivity comparable to tokamak L-mode values) in a completely self-organized toroidal plasma. A strong decrease in thermal conductivity with temperature is observed and at the highest temperatures, transport is well below that expected from the Rechester-Rosenbluth model. Addition of a new capacitor bank has produced 60% higher magnetic fields and almost tripled the pulse length to 11ms. For plasmas with T{sub e}> 300eV, it becomes feasible to use modest (1.8MW) neutral beam injection (NBI) heating to significantly change the power balance in the core plasma, making it an effective tool for improving transport analysis. We are now developing detailed designs for adding NBI to SSPX and have developed a new module for the CORSICA transport code to compute the correct fast-ion orbits in SSPX so that we can simulate the effect of adding NBI; initial results predict that such heating can raise the electron temperature and total plasma pressure in the core by a factor of two.

We developed a reduced description of kinetic effects that is included in a fluid model of stimulated Brillouin backscattering (SBS) in low Z plasmas (e.g. He, Be). Following hybrid-PIC simulations, the modified ion distribution function is parametrized by the width {delta} of the plateau created by trapping around the phase velocity of the SBS-driven acoustic wave. An evolution equation is derived for {delta}, which affects SBS through a frequency shift and a reduced Landau damping. This model recovers the linear Landau damping value for small waves and the time-asymptotic nonlinear frequency shift calculated by Morales and O'Neil. Finally we compare our reduced model with Bzohar simulations of a Be plasma representative of experiments that have shown evidence of ion trapping.

The Plasma Theory and Simulation Group (PTSG) is collaborating with LLNL in order to model the edge region of a tokamak plasma and its interaction with the diverter plate. In the overall framework of the project, MHD will be used to model the bulk plasma. Near the edge, the MHD model will interface with the gyrokinetic code UEDGE developed at LLNL. Since the UEDGE model approximations may not be accurate within a few cyclotron radii of the diverter plate, the UEDGE code will interface with a collisional PIC-hybrid code developed by the PTSG under this project. The PTSG PIC code will include a self-consistent potential with kinetic or fixed hydrogen ions. The sputtering profile of the plate, under development at LLNL, will be used as input to the PIC code in order to correctly model the kinetic behavior of sputtered carbon. These carbon products will interact with hydrogen according to known chemistry cross-sections. While some kinetic electrons may be used to model the fast tail of the distribution function (if necessary), the bulk of the electron population will be modeled as being in thermal equilibrium using the Boltzmann relation, resulting in a significant improvement in code speed. Coulomb collisions may also be considered. The Boltzmann model has been implemented with various features in three of the PTSG codes: XPDP1 and OOPD1 (both 1d-3v), and OOPIC (2d-3v), according to the methodology of Cartwright [1]. When the model is fully implemented, it will include fluid interaction with the boundaries, energy conservation through the temperature term, and take into account collisions with the Boltzmann species. A more rigorous convergence analysis has been developed than is outlined in [1]; boundary effects are included explicitly in a formulation valid in arbitrary coordinate systems. In OOPD1, the Boltzmann model is included in an object-oriented manner as part of a general fluid model framework. The basic Boltzmann solver has been implemented and shown to give self-consistent results. The details and results were described in detail in a talk presented at LLNL (updated slides attached). Currently, the output of the three codes is being compared for a test case of a current-driven DC discharge. Computational speed-up and accuracy will be compared between PIC and the Boltzmann-PIC hybrid. A framework for general binary and three-body collisions is being developed for OOPD1. Given known cross-sections or reaction rates, this will function as a chemistry model for the code. The framework may then be imported into OOPIC.

The first experiments on the National Ignition Facility (NIF) have employed the first four beams to measure propagation and laser backscattering losses in large ignition-size plasmas. Gas-filled targets between 2 mm and 7 mm length have been heated from one side by overlapping the focal spots of the four beams from one quad operated at 351 nm (3{omega}) with a total intensity of 2 x 10{sup 15} W cm{sup -2}. The targets were filled with 1 atm of CO{sub 2} producing of up to 7 mm long homogeneously heated plasmas with densities of n{sub e} = 6 x 10{sup 20} cm{sup -3} and temperatures of T{sub e} = 2 keV. The high energy in a NIF quad of beams of 16kJ, illuminating the target from one direction, creates unique conditions for the study of laser plasma interactions at scale lengths not previously accessible. The propagation through the large-scale plasma was measured with a gated x-ray imager that was filtered for 3.5 keV x rays. These data indicate that the beams interact with the full length of this ignition-scale plasma during the last {approx}1 ns of the experiment. During that time, the full aperture measurements of the stimulated Brillouin scattering and stimulated Raman scattering show scattering into the four focusing lenses of 6% for the smallest length ({approx}2 mm). increasing to 12% for {approx}7 mm. These results demonstrate the NIF experimental capabilities and further provide a benchmark for three-dimensional modeling of the laser-plasma interactions at ignition-size scale lengths.