The kinetic codes used to model the coupled dynamics of electromagnetic fields and charged particle transport have requirements for spatial, temporal, and charge resolution. These requirements may vary by the solution technique and scope of the problem. In this report, we investigate the resolution limits in the energy-conserving implicit particle-in-cell code CHICAGO. This report has the narrow aim of determining the maximum acceptable grid spacing for the dense plasmas generated in models of z-pinch target gases and power-flow electrode plasmas. In the 2D sample problem, the plasma drifts without external forces with velocity of 10 cm/µs. Simulations are scaled by plasma density to maintain uniform strides across the plasma and from the plasma to the boundaries. Additionally, the cloud-in-cell technique is used with 400 particles per cell and Δt = 0.85× the Courant limit. For the linear cloud distribution, the criterion for conserving energy is ΔE/Etot < 0.01 for 50,000 time steps. The grid resolution is determined to crudely be Δx ≲ 3ls, where ls is the electron collisionless skin depth. For the second-order cloud distribution the criterion is ΔE/Etot < 0.005 yielding Δx ≤ 15ls. These scalings are functions of the chosen vd, Δt, particles-per-cell, and number of steps.
A six-month research effort has advanced the hybrid kinetic-fluid modeling capability required for developing non-thermal warm x-ray sources on Z. The three particle treatments of quasi-neutral, multi-fluid, and kinetic are demonstrated in 1D simulations of an Ar gas puff. The simulations determine required resolutions for the advanced implicit solution techniques and debug hybrid particle treatments with equation-of-state and radiation transport. The kinetic treatment is used in preliminary analysis of the non-Maxwellian nature of a gas target. It is also demonstrates the sensitivity of the cyclotron and collision frequencies in determining the transition from thermal to non-thermal particle populations. Finally, a 2D Ar gas puff simulation of a Z shot demonstrates the readiness to proceed with realistic target configurations. The results put us on a very firm footing to proceed to a full LDRD which includes continued development transition criteria and x-ray yield calculation.
Kinetic simulations of Sandia National Laboratories' Z machine are conducted to understand particle transport in the highly magnetized environment of a multi-MA accelerator. Joule heating leads to the rapid formation of electrode surface plasmas. These plasmas are implicated in reducing accelerator efficiency by diverting current away from the load [M.R. Gomez et al., Phys. Rev. Accel. Beams 20, 010401 (2017)PRABCJ2469-988810.1103/PhysRevAccelBeams.20.010401, N. Bennett et al., Phys. Rev. Accel. Beams 22, 120401 (2019)PRABCJ2469-988810.1103/PhysRevAccelBeams.22.120401]. The fully-relativistic, electromagnetic simulations presented in this paper show that particles emitted in a space-charge-limited manner, in the absence of plasma, are magnetically insulated. However, in the presence of plasma, particles are transported across the magnetic field in spite of being only weakly collisional. The simulated cross-gap currents are well-approximated by the Hall current in the generalized Ohm's law. The Hall conductivities are calculated using the simulated particle densities and energies, and the parameters that increase the Hall current are related to transmission line inductance. Analogous to the generalized Ohm's law, we extend the derivation of the magnetized diffusion coefficients to include the coupling of perpendicular components. These yield a Hall diffusion rate, which is equivalent to the empirical Bohm diffusion.
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.
We have developed a physics-based transmission-line-circuit model of the Z pulsed-power accelerator. The 33-m-diameter Z machine generates a peak electrical power as high as 85 TW, and delivers as much as 25 MA to a physics load. The circuit model is used to design and analyze experiments conducted on Z. The model consists of 36 networks of transmission-line-circuit elements and resistors that represent each of Zs 36 modules. The model of each module includes a Marx generator, intermediate-energy-storage capacitor, laser-triggered gas switch, pulse-forming line, self-break water switches, and tri-plate transmission lines. The circuit model also includes elements that represent Zs water convolute, vacuum insulator stack, four parallel outer magnetically insulated vacuum transmission lines (MITLs), double-post-hole vacuum convolute, inner vacuum MITL, and physics load. Within the vacuum-transmission-line system the model conducts analytic calculations of current loss. To calculate the loss, the model simulates the following processes: (i) electron emission from MITL cathode surfaces wherever an electric-field threshold has been exceeded; (ii) electron loss in the MITLs before magnetic insulation has been established; (iii) flow of electrons emitted by the outer-MITL cathodes after insulation has been established; (iv) closure of MITL anode-cathode (AK) gaps due to expansion of cathode plasma; (v) energy loss to MITL conductors operated at high lineal current densities; (vi) heating of MITL-anode surfaces due to conduction current and deposition of electron kinetic energy; (vii) negative-space-charge-enhanced ion emission from MITL anode surfaces wherever an anode-surface-temperature threshold has been exceeded; and (viii) closure of MITL AK gaps due to expansion of anode plasma. The circuit model is expected to be most accurate when the fractional current loss is small. We have performed circuit simulations of 52 Z experiments conducted with a variety of accelerator configurations and load-impedance time histories. For these experiments, the apparent fractional current loss varies from 0% to 20%. Results of the circuit simulations agree with data acquired on 52 shots to within 2%.
The theory of signal propagation in lossy coaxial transmission lines is revisited and new approximate analytic formulas for the line impedance and attenuation are derived. The accuracy of these formulas from DC to 100 GHz is demonstrated by comparison to numerical solutions of the exact field equations. Based on this analysis, a new circuit model is described which accurately reproduces the line response over the entire frequency range. Circuit model calculations are in excellent agreement with the numerical and analytic results, and with finite-difference-time-domain simulations which resolve the skindepths of the conducting walls.
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.
The propagation of a 30 kA, 3.5 Mev electron beam which was focused into gas and plasma-filled cells was discussed. Gas cells which were used for X-ray radiography were produced using pulsed-power accelerators, onto a high atomic number target to generate bremsstrahlung radiation. The effectiveness of beam focusing using neutral gas, partially ionized gas, and fully ionized (plasma-filled) cells was investigated using numerical simulation. It was observed in an optimized gas cell that an initial plasma density approaching 1016 cm-3 was sufficient to prevent significant net currents and the subsequent beam sweep.
Plasmas are ubiquitous in the high-power electron beam diodes used for radiographic applications. In rod pinch and immersed Bz diodes they are found adjacent to the cathode and anode electrodes, and are suspected of affecting the diodes' impedance characteristics as well as the radiographic spot size. In paraxial diodes, preionized plasmas or beam-formed plasmas are also found in the gas focusing section. A common feature of the plasmas adjacent to the electrodes is that their densities can range from 10 12-1017 cm-3, and their velocity is on the order of 107 cm/s. Researchers from the Naval Research Laboratory have developed a high-sensitivity two-color interferometer that is presently being tested on Gamble II for future use on the Sandia RITS accelerator operating with a Bz diode. This diagnostic is capable of resolving a line-integrated electron density of 2×1012 cm-2, a density that might be capable of even observing the electron beam directly. This paper will present an overview of laser-based and spectroscopic diagnostics that could be used to measure plasmas found in radiographic diodes with spatial and temporal resolutions on the order of 1-5 mm and 5 ns, respectively. Plans for the use of this diagnostic on a preionized plasma cell of a paraxial diode on the Sandia RITS experiment will be discussed.
SNL is developing intense sources for flash x-ray radiography. The goals of the experiments presented here were to assess power flow issues and to help benchmark the LSP particle-in-cell code used to design the experiment. Comparisons between LSP simulations and experimental data are presented.
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.