The rudiments of a particle-based single-fluid two-temperature magnetohydrodynamic (MHD) algorithm have been outlined in Thoma et al. (2013). The extension of this algorithm to include the effect of Hall physics is described in this paper. An implicit leapfrog version of the algorithm, which allows timesteps large compared to the resistive decay time and other relevant timescales, has recently been added to a hybrid particle-in-cell code. In standard MHD the Hall term in the generalized Ohm’s law can often be neglected when the Hall parameter is small. This term must, however, be retained in regimes where it is non-negligible. The retention of displacement current in Maxwell’s equations avoids the numerical difficulties associated with the whistler mode, which are encountered in standard explicit Hall-MHD codes, and allows the algorithm to be incorporated into hybrid particle-in-cell codes, for which particles may migrate from a kinetic to fluid to MHD description based upon local ambient plasma conditions. A highly-coupled implicit Hall-MHD formalism is presented, in which displacement current can either be retained or neglected. Even when displacement current is neglected, the highly-coupled implicit formalism avoids the restrictive timesteps for the whistler mode in explicit Hall-MHD codes. A comparison of numerical and analytic dispersion analysis demonstrates the feasibility of this approach and establishes relevant constraints to assure numerical stability. The implementation of the algorithm is described, and test simulation results in 1D and 2D in both linear and nonlinear regimes are presented.
This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.
Current loss in magnetically insulated transmission lines (MITLs) was investigated using data from experiments conducted on Z and Mykonos. Data from experiments conducted on Z were used to optimize an ion diode current loss model that has been implemented into the transmission line circuit model of Z. Details on the current loss model and comparisons to data from Z experiments have been previously published in a peer-reviewed journal [Hutsel, et al., Phys. Rev. Accel. Beams 21, 030401]. Dedicated power flow experiments conducted on Mykonos investigated current loss in a millimeter-scale anode-cathode gap MITL operated at lineal current densities greater than 410 kA/cm and with electric field stresses in excess of 240 kV/cm where it is expected that both anode and cathode plasmas are formed. The experiment MITLs were exposed to varying vacuum conditions; including vacuum pressure at shot time, time under vacuum, and vacuum storage protocols. The results indicate that the vacuum conditions have an effect on current loss in high lineal current density MITLs.
A series of simulations and experiments to resolve questions about the operation of arrays of closely spaced small aspect ratio rod pinches has been performed. Design and postshot analysis of the experimental results are supported by 3-D particle-in-cell simulations. Both simulations and experiments support these conclusions. Penetration of current to the interior of the array appears to be efficient, as the current on the center rods is essentially equal to the current on the outer rods. Current loss in the feed due to the formation of magnetic nulls was avoided in these experiments by design of the feed surface of the cathode and control of the gap to keep the electric fields on the cathode below the emission threshold. Some asymmetry in the electron flow to the rod was observed, but the flow appeared to symmetrize as it reached the end of the rod. Interaction between the rod pinches can be controlled to allow the stable and consistent operation of arrays of rod pinches.
High-brightness flash x-ray sources are needed for penetrating dynamic radiography for a variety of applications. Various bremsstrahlung source experiments have been conducted on the TriMeV accelerator (3MV, 60 {Omega}, 20 ns) to determine the best diode and focusing configuration in the 2-3 MV range. Three classes of candidate diodes were examined: gas cell focusing, magnetically immersed, and rod pinch. The best result for the gas cell diode was 6 rad at 1 meter from the source with a 5 mm diameter x-ray spot. Using a 0.5 mm diameter cathode immersed in a 17 T solenoidal magnetic field, the best shot produced 4.1 rad with a 2.9 mm spot. The rod pinch diode demonstrated very reproducible radiographic spots between 0.75 and 0.8 mm in diameter, producing 1.2 rad. This represents a factor of eight improvement in the TriMeV flash radiographic capability above the original gas cell diode to a figure of merit (dose/spot diameter) > 1.8 rad/mm. These results clearly show the rod pinch diode to be the choice x-ray source for flash radiography at 2-3 M V endpoint.