We present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L-2 norm.

We have developed a new 3D multi-physics multi-material code, ALE-AMR, for modeling laser/target effects including debris/shrapnel generation. The code combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR) to connect the continuum to microstructural regimes. The code is unique in its ability to model hot radiating plasmas and cold fragmenting solids. New numerical techniques were developed for many of the physics packages to work efficiency on a dynamically moving and adapting mesh. A flexible strength/failure framework allows for pluggable material models. Material history arrays are used to store persistent data required by the material models, for instance, the level of accumulated damage or the evolving yield stress in J2 plasticity models. We model ductile metals as well as brittle materials such as Si, Be, and B4C. We use interface reconstruction based on volume fractions of the material components within mixed zones and reconstruct interfaces as needed. This interface reconstruction model is also used for void coalescence and fragmentation. The AMR framework allows for hierarchical material modeling (HMM) with different material models at different levels of refinement. Laser rays are propagated through a virtual composite mesh consisting of the finest resolution representation of the modeled space. A new 2nd order accurate diffusion solver has been implemented for the thermal conduction and radiation transport packages. The code is validated using laser and x-ray driven spall experiments in the US and France. We present an overview of the code and simulation results.

The ALE-AMR code developed for NIF is a multi-material hydro-code that models target assembly fragmentation in the aftermath of a shot. The combination of ALE (Arbitrary Lagrangian Eulerian) hydro with AMR (Adaptive Mesh Refinement) allows the code to model a wide range of physical conditions and spatial scales. The large range of temperatures encountered in the NIF target chamber can lead to significant fluxes of energy due to thermal conduction and radiative transport. These physical effects can be modeled approximately with the aid of the diffusion equation. We present a novel method for the solution of the diffusion equation on a composite mesh in order to capture these physical effects.

The generation of neutron/gamma radiation, electromagnetic pulses (EMP), debris and shrapnel at mega-Joule class laser facilities (NIF and LMJ) impacts experiments conducted at these facilities. The complex 3D numerical codes used to assess these impacts range from an established code that required minor modifications (MCNP - calculates neutron and gamma radiation levels in complex geometries), through a code that required significant modifications to treat new phenomena (EMSolve - calculates EMP from electrons escaping from laser targets), to a new code, ALE-AMR, that is being developed through a joint collaboration between LLNL, CEA, and UC (UCSD, UCLA, and LBL) for debris and shrapnel modelling.

ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray tracing in ALE-AMR. We present the basic concepts of laser ray tracing and our approach to efficiently traverse the adaptive mesh hierarchy.

The critical issue of divertor configuration for heat and particle flux control in a conceptual ARIES compact stellarator (CS) reactor is addressed. The goal is to determine a divertor location and geometry with a peak heat load of not more than 10 MW/m(2) for a CS equilibrium based on the configuration to be used in the NCSX experiment, optimized for high beta (6.4%) and designed for low alpha-particle power loss fraction (<= 5%). The surface heat flux on the target has three components: thermal particles, lost energetic alphas, and radiation from the core and the scrape-off layer. The first two components are dominant and their magnitudes can be comparable. To maintain a tritium-breeding ratio of 1.1, the total target area should not exceed 15% of the boundary plasma surface area. The divertor concept consists of two pairs of target plates per field period, one pair each at the top and bottom of the plasma. The heat flux profile is assessed by assuming that the parallel transport can be represented by field line mapping and that cross-field transport can be modeled with a prescribed field line diffusion scheme. In this manner, the poloidal and toroidal extents of the plates and their shape and distance to the plasma are designed to intercept all the heat flux and to minimize the peak thermal heat load. An approximate scheme, based on particle drift orbits in the core and field line tracing in the edge, is derived to estimate the alpha-particle heat load distribution over the plates and the first wall. The best plate configuration to date yields total peak heat loads (thermal + alpha) ranging from 5 to 18 MW/m(2). Further optimization of the target plates is required to reach the design goal, which will be addressed in a future study.

An integrated study of compact stellarator power plants, ARIES-CS, has been conducted to explore attrac- tive compact stellarator configurations and to define key research and development (R&D) areas. The large size and mass predicted by earlier stellarator power plant studies had led to cost projections much higher than those of the advanced tokamak power plant. As such, the first major goal of the ARIES-CS research was to inves- tigate if stellarator power plants can be made to be com- parable in size to advanced tokamak variants while maintaining desirable stellarator properties. As stellar- ator fusion core components would have complex shapes and geometry, the second major goal of the ARIES-CS study was to understand and quantify, as much as pos- sible, the impact of the complex shape and geometry of fusion core components. This paper focuses on the direc- tions we pursued to optimize the compact stellarator as a fusion power plant, summarizes the major findings from the study, highlights the key design aspects and con- straints associated with a compact stellarator, and iden- tifies the major issues to help guide future R&D.

Divertor heat load distributions due to thermal and alpha particles have been assessed in an NCSX-based compact stellarator reactor. A divertor plate system is envisaged, with 4 plates per field period and covering 7% of the plasma surface area. The field-line tracing technique is employed; for thermal flux, the conventional approach is used, while for alphas, their characteristic exit pattern from the plasma and subsequent gyro- orbits are approximated. For the ARIES-CS reference design point (R=7.75 m, A=4.5, B=5.7 T, beta=6.4% and P net =1000 MW), combined peak heat loads in the 5 -18 MW/m 2 range on the plates have been obtained, assuming a 75% radiation fraction both in the core and at the edge, and a 5% alpha loss fraction. The alpha heat flux could be a dominant determining factor. Further optimization study is warranted to lower all peak heat loads to satisfy the accepted limit of les10 MW/m 2 .

The National Compact Stellarator Experiment (NCSX) is a three-field period compact stellarator presently in the construction phase at Princeton, NJ. The design parameters of the device are major radius R=1.4m, average minor radius = 0.32m, 1.2 {le} toroidal field (B{sub t}) {le} 1.7 T, and auxiliary input power up to 12 MW with neutral beams and radio-frequency heating. The NCSX average aspect ratio of 4.4 lies well below present stellarator experiments and designs, enabling the investigation of high {beta} physics in a compact stellarator geometry. Also the NCSX design choice for a quasi-axisymmetric configuration aims toward the achievement of tokamak-like transport. In this paper, we report on the magnetic field line tracing calculations used to evaluate conceptual plasma facing component (PFC) designs. In contrast to tokamaks, axisymmetric target plates are not required to intercept the majority of the heat flux in stellarators, owing to the nature of the 3-D magnetic field footprint. The divertor plate design investigated in this study covers approximately one half of the toroidal extent in each period. Typical Poincare plots in Figure 1 illustrate the plasma cross-section at several toroidal angles for a computed NCSX high-beta equilibrium. The plates used for these calculations aremore » centered in each period about the elongated cross-section shown in Figure 1a, extending to +/- {pi}/6 in each direction. Two methods for tracing the edge field line topology were used in this study. The first entails use of the VMEC/MFBE-2001 packages, whereas the second entails use of the PIES code with a post-processor by Michael Drevlak; the same field line integration routine was used to evaluate the equilibria for this comparison. Both inputs were generated based on the {beta}=4%, =iota=0.5 equilibrium computed from the final NCSX coil set. We first compare these two methods for a specific plate geometry, and conclude with a comparison of the strike characteristics for two different target plate poloidal lengths using the latter method. The details of the magnetic topology differ when computed with VMEC/MFBE as compared with an iterated PIES solution. This difference is illustrated in Figure 2. The presence of islands in the PIES solution effectively reduces the radius of the last closed magnetic surface (LCMS) by about 8 cm. As expected, this difference in the edge topology translates to a difference in field line terminations.« less

Toroidal plasmas created with negative magnetic shear in the core region offer advantages in terms of MHD stability properties. These plasmas, transiently created in several tokamaks, have exhibited high-performance as measured by normalized stored energy and neutron production rates. A critical issue with extending the duration of these plasmas is the need to maintain the off-axis-peaked current distribution required to support the minimum in the safety factor q at large radii. We present equilibrium and transport simulations that explore the use of electron cyclotron heating and current drive to maintain this negative shear configuration. Using parameters consistent with DIII-D tokamak operation (Strait E et al 1995 Phys. Rev. Lett. 75 4421, Rice B W et al 1996 Nucl. Fusion 36 1271), we find that with sufficiently high injected power, it is possible to achieve steady-state conditions employing well aligned electron cyclotron and bootstrap current drive in fully non-inductively current-driven configurations.