Publications

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Recent studies of power flow and particle transport in multi-MA pulsed-power accelerators demonstrate that electrode plasmas may reduce accelerator efficiency by shunting current upstream from the load. The detailed generation and evolution of these electrode plasmas are examined here using fully relativistic, Monte Carlo particle-in-cell (PIC) and magnetohydrodynamic (MHD) simulations over a range of peak currents (8–48 MA). The PIC calculations, informed by vacuum science, describe the electrode surface breakdown and particle transport prior to electrode melt. The MHD calculations show the bulk electrode evolution during melt. The physical description provided by this combined study begins with the rising local magnetic field that increases the local electrode surface temperature. This initiates the thermal desorption of contaminants from the electrode surface, with contributions from atoms outgassing from the bulk metal. The contaminants rapidly ionize forming a 10¹⁵-10¹⁸ cm^-3 plasma that is effectively resistive while weakly collisional because it is created within, and rapidly penetrated by, a strong magnetic field (> 30 T). Prior to melting, the density of this surface plasma is limited by the concentration of absorbed contaminants in the bulk (~10¹⁹ cm^-3 for hydrogen), its diffusion, and ionization. Eventually, the melting electrodes form a conducting plasma (10²¹-10²³ cm^-3) that experiences j × B compression and a typical decaying magnetic diffusion profile. This physical sequence ignores the transport of collisional plasmas of 10¹⁹ cm^-3 which may arise from electrode defects and associated instabilities. Nonetheless, this picture of plasma formation and melt may be extrapolated to higher-energy pulsed-power systems.

Power-flow studies on the 30-MA, 100-ns Z facility at Sandia National Labs have shown that plasmas in the facility's magnetically insulated transmission lines can result in a loss of current to the load.1 During the current pulse, electrode heating causes neutral surface contaminants (water, hydrogen, hydrocarbons, etc.) to desorb, ionize, and form plasmas in the anode-cathode gap.2 Shrinking typical electrode thicknesses (∼1 cm) to thin foils (5-200 μm) produces observable amounts of plasma on smaller pulsed power drivers <1 MA).3 We suspect that as electrode material bulk thickness decreases relative to the skin depth (50-100 μm for a 100-500-ns pulse in aluminum), the thermal energy delivered to the neutral surface contaminants increases, and thus desorb faster from the current carrying surface.

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Detailed analysis of both the line-intensity ratios and line shapes of the K-lines of elements of different abundances (Fe, Cr, Ni, and Mn) emitted from the stagnation of a steel wire-array implosion on Z, were used to determine the line opacities. While the opacities at the early time of stagnation appear to be consistent with a nearly uniform hot-plasma cylinder on-axis surrounded by a colder annulus, the opacities during the peak K-emission strongly suggest that the main K-emission is due to small hot regions (spots) spread over the stagnating column. The spots are shown to be at least 4× denser than expected based on a uniform-cylinder emission (namely, ni > 3 ×1020 cm-3 ), are of diameters of about 200 μ or less (where the smaller the spots the higher are the densities), and are thousands in number. The total mass of the spots was determined to be 3-10 % of the load mass, and their total volume 3-15 % of the O 1.2-mm stagnation-column volume, both are less than the respective values for the earlier period of lower K power.

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The Z Machine at Sandia National Laboratories uses current pulses with peaks up to 27 MA to drive target implosions and generate high energy density conditions of interest for stockpile stewardship programs pertinent to the NNSA program portfolio . Physical processes in the region near the Z Machine target create electrode plasmas which seed parasitic current loss that reduce the performance and output of a Z experiment. Electrode surface contaminants (hydrogen, water, hydrocarbons) are thought to be the primary constituent of electrode plasmas which contribute to loss mechanisms. The Sandia team explore d in situ heating and plasma discharge techniques by integrating requisite infrastructure into Sandia's Mykonos LTD accelerator, addressing potential impacts to accelerator operation, and reporting on the impact of these techniques on electrode plasma formation and shot performance. The in situ discharge cleaning utilizes the electrodes of the accelerator to excite an argon-oxygen plasma to sputter and chemically react contaminants from electrode surfaces. Insulating breaks are required to isolate the plasma in electrode regions where loss processes are most likely to occur. The shots on Mykonos validate that these breaks do not perturb experiment performance, reducing the uncertainty on the largest unknown about the in situ cleaning system. Preliminary observations with electrical and optical diagnostics suggest that electrode plasma formation is delayed, and overall inventory has been substantively reduced. In situ heating embeds cartridge heaters into accelerator electrodes and employs a thermal bakeout to rapidly desorb contaminants from electrode surfaces. For the first time, additively manufactured (AM) electrode assemblies were used on a low impedance accelerator to integrate cooling channels and manage thermal gradients. Challenges with poor supplier fabrication to specifications, load alignment, thermal expansion and hardware movement and warpage appears to have introduced large variability in observed loss, though, preventing strong assertions of loss reduction via in situ heating. At this time, an in situ discharge cleaning process offers the lowest risk path to reduce electrode contaminant inventories on Z, though we recommend continuing to develop both approaches. Additional engineering and testing are required to improve the implementation of both systems. .

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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.

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.

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Large pulsed power accelerators deliver multi-MJ pulses of electrical energy to a variety of high energy density (HED) physics experiments that support stockpile science programs. Understanding the plasma formation mechanisms and resulting electrical power transport (or "power flow") in the vacuum magnetically insulated transmission lines (MITLs) is an important area of ongoing research, and could provide a means to improve the performance of today's pulsed power accelerators while improving confidence in the design options for next-generation pulsed power concepts. Power flow science has been studied for decades, but these studies have not provided a predictive understanding of plasma formation and expansion in MITL systems. Several recent factors in pulsed power system design have generated a renewed (and urgent) interest in developing validated, multi-physics power flow engineering models with increased scrutiny and understanding. Examples of these factors include (i) the use of high inductance experimental configurations that could increase current "loss", (ii) interest in long-pulse applications that require predictable pulse shapes, and (iii) the desire to develop a deeper understanding of how current loss phenomena scale to larger accelerator configurations. This work is directed to support the validation of multi-physics power flow engineering models required to realize pulsed power systems for the NNSA mission.

Two-dimensional electromagnetic (EM) particle-in-cell (PIC) simulations of a radial magnetically-insulated-transmission-line are presented and compared to the model of E. M. Waisman, M. P. Desjarlais, and M. E. Cuneo [Phys. Rev. Accel. Beams 22, 030402 (2019) in the “high-enhancement” (WDC-HE) limit. The simulations use quasi-equilibrium current and voltage values based on the Sandia National Laboratories Z accelerator, with prescribed injection of an electron sheath that gives electron density profiles qualitatively similar to those used in the WDC-HE model. We find that the WDC-HE model accurately predicts the quasiequilibrium ion current losses in the EM PIC simulations for a wide range of current and voltage values. For the case of two ion species where one is magnetically insulated by the ambient magnetic field and the other is not, the charge of the lighter insulated species in the anode-cathode gap can modify the electric field profile, reducing the ion current density enhancement for the heavier ion species. On the other hand, for multiple ion species, when the lighter ions are not magnetically insulated and are a significant fraction of the anode plasma, they dominate the current loss, producing loss currents which are a significant fraction of the lighter ion WDC values. The observation of this effect in the present work is new to the field and may significantly impact the analysis of ion current losses in the Z machine inner MITL and convolute.

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We introduce a 1D planar static model to elucidate the underlying mechanism of large ion current losses in the vacuum convolute and the inner magnetically insulated transmission line (MITL) of the Z machine. We consider E×B electron flow, parallel to the electrodes, and ion motion across the vacuum gap, for given voltage V, gap distance d, anode magnetic field Ba, and vacuum electron current ΔI. This model has been introduced and solved before by Desjarlais [Phys. Rev. Lett. 59, 2295 (1987)PRLTAO0031-900710.1103/PhysRevLett.59.2295] for the applied magnetic field ion diode. Here we apply it to convolute and inner MITL ion losses of Z, relaxing the fix magnetic flux condition of that reference. In the absence of ions we show that the electron vacuum flow must be close to the anode if its current exceeds the value given by the local flow impedance, implying high electric fields there. We then introduce space charge limited ion emission from the anode, neglecting the magnetic force on ions. We obtain the solution of the steady state equations for two special cases: (a) when both the electric potential and the electric field are zero inside the gap, and there is a layer of electrons not carrying current that neutralizes the ion charge between the virtual and the electrode cathode, making that region electric field free, and (b) when the electric field is zero inside the gap, but the potential is not, and zero electron charge between that point and the physical cathode. For case (a) we obtain an ion current density which we conjecture is the maximum attainable for any electron charge distribution in the electron current carrying layer, given V,d,Ba,ΔI an ion species. We obtain the enhancement factor for both cases with respect to the ion-only Child-Langmuir ion current density, and show that it can be significantly larger than that of the electron saturated flow case. Furthermore, imposing electron current conservation as the flow enters the inner MITL from the four outer MITLs, we recover the well-known dependence jion∼V3/2/d2, where voltage and gap are taken near the joining point of those outer MITLs. The implications and limitations of the proposed model are discussed.

Herein we present details of the design, simulation, and performance of a 100-GW linear transformer driver (LTD) cavity at Sandia National Laboratories. The cavity consists of 20 "bricks." Each brick is comprised of two 80 nF, 100 kV capacitors connected electrically in series with a custom, 200 kV, three-electrode, field-distortion gas switch. The brick capacitors are bipolar charged to ±100 kV for a total switch voltage of 200 kV. Typical brick circuit parameters are 40 nF capacitance (two 80 nF capacitors in series) and 160 nH inductance. The switch electrodes are fabricated from a WCu alloy and are operated with breathable air. Over the course of 6,556 shots the cavity generated a peak electrical current and power of 1.03 MA (±1.8%) and 106 GW (±3.1%). Experimental results are consistent (to within uncertainties) with circuit simulations for normal operation, and expected failure modes including prefire and late-fire events. New features of this development that are reported here in detail include: (1) 100 ns, 1 MA, 100-GW output from a 2.2 m diameter LTD into a 0.1 Ω load, (2) high-impedance solid charging resistors that are optimized for this application, and (3) evaluation of maintenance-free trigger circuits using capacitive coupling and inductive isolation.

In relativistic electron beam diodes, the self-generated magnetic field causes electron-beam focusing at the center of the anode. Generally, plasma is formed all over the anode surface during and after the process of the beam focusing. In this work, we use visible-light Zeeman-effect spectroscopy for the determination of the magnetic field in the anode plasma in the Sandia 10 MV, 200 kA (RITS-6) electron beam diode. The magnetic field is determined from the Zeeman-dominated shapes of the Al III 4s–4p and C IV 3s–3p doublet emissions from various radial positions. Near the anode surface, due to the high plasma density, the spectral line-shapes are Stark-dominated, and only an upper limit of the magnetic field can be determined. The line-shape analysis also yields the plasma density. The data yield quantitatively the magnetic-field shielding in the plasma. In conclusion, the magnetic-field distribution in the plasma is compared to the field-diffusion prediction and found to be consistent with the Spitzer resistivity, estimated using the electron temperature and charge-state distribution determined from line intensity ratios.

The Magnetized Liner Inertial Fusion concept (MagLIF) [Slutz et al., Phys. Plasmas 17, 056303 (2010)] is being studied on the Z facility at Sandia National Laboratories. Neutron yields greater than 1012 have been achieved with a drive current in the range of 17-18 MA and pure deuterium fuel [Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)]. We show that 2D simulated yields are about twice the best yields obtained on Z and that a likely cause of this difference is the mix of material into the fuel. Mitigation strategies are presented. Previous numerical studies indicate that much larger yields (10-1000 MJ) should be possible with pulsed power machines producing larger drive currents (45-60 MA) than can be produced by the Z machine [Slutz et al., Phys. Plasmas 23, 022702 (2016)]. To test the accuracy of these 2D simulations, we present modifications to MagLIF experiments using the existing Z facility, for which 2D simulations predict a 100-fold enhancement of MagLIF fusion yields and considerable increases in burn temperatures. Experimental verification of these predictions would increase the credibility of predictions at higher drive currents.

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Absolute calibration of streaked visible spectroscopy systems has been performed at Z-machine at Sandia National Labs in order to determine temperatures of electrode surfaces during the current pulse. The ability to calibrate the full system, including all fiber optic runs and probes is crucial to understanding errors in the calibration process. The calibration procedure involves imaging a blackbody light source, with a known spectral radiance which is coupled to an integrating sphere. This source is streaked slowly over a few ns using Sydor streak cameras. The slow sweep is converted to a 100-500ns sweep by imaging a bright light source on both sweep rates, and obtaining wavelength and time dependent correction curves. Any broadband light source or several laser lines of differing wavelengths can be used for this correction. This technique has yielded temperature estimates of several eV in the Z convolute.

The results presented here were obtained with a self-magnetic pinch (SMP) diode mounted at the front high voltage end of the RITS accelerator. RITS is a Self-Magnetically Insulated Transmission Line (MITL) voltage adder that adds the voltage pulse of six 1.3 MV inductively insulated cavities. The RITS driver together with the SMP diode has produced x-ray spots of the order of 1 mm in diameter and doses adequate for the radiographic imaging of high area density objects. Although, through the years, a number of different types of radiographic electron diodes have been utilized with SABER, HERMES III and RITS accelerators, the SMP diode appears to be the most successful and simplest diode for the radiographic investigation of various objects. Our experiments had two objectives: first to measure the contribution of the back-streaming ion currents emitted from the anode target and second to try to evaluate the energy of those ions and hence the Anode-Cathode (A-K) gap actual voltage. In any very high voltage inductive voltage adder utilizing MITLs to transmit the power to the diode load, the precise knowledge of the accelerating voltage applied on the A-K gap is problematic. This is even more difficult in an SMP diode where the A-K gap is very small (∼1 cm) and the diode region very hostile. The accelerating voltage quoted in the literature is from estimates based on the measurements of the anode and cathode currents of the MITL far upstream from the diode and utilizing the para-potential flow theories and inductive corrections. Thus, it would be interesting to have another independent measurement to evaluate the A-K voltage. The diode's anode is made of a number of high-Z metals in order to produce copious and energetic flash x-rays. It was established experimentally that the back-streaming ion currents are a strong function of the anode materials and their stage of cleanness. We have measured the back-streaming ion currents emitted from the anode and propagating through a hollow cathode tip for various diode configurations and different techniques of target cleaning treatment: namely, heating at very high temperatures with DC and pulsed current, with RF plasma cleaning, and with both plasma cleaning and heating. We have also evaluated the A-K gap voltage by energy filtering technique. Experimental results in comparison with LSP simulations are presented.

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%.

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This LDRD investigated plasma formation, field strength, and current loss in pulsed power diodes. In particular the Self-Magnetic Pinch (SMP) e-beam diode was studied on the RITS-6 accelerator. Magnetic fields of a few Tesla and electric fields of several MV/cm were measured using visible spectroscopy techniques. The magnetic field measurements were then used to determine the current distribution in the diode. This distribution showed that significant beam current extends radially beyond the few millimeter x-ray focal spot diameter. Additionally, shielding of the magnetic field due to dense electrode surface plasmas was observed, quantified, and found to be consistent with the calculated Spitzer resistivity. In addition to the work on RITS, measurements were also made on the Z-machine looking to quantify plasmas within the power flow regions. Measurements were taken in the post-hole convolute and final feed gap regions on Z. Dopants were applied to power flow surfaces and measured spectroscopically. These measurements gave species and density/temperature estimates. Preliminary B-field measurements in the load region were attempted as well. Finally, simulation work using the EMPHASIS, electromagnetic particle in cell code, was conducted using the Z MITL conditions. The purpose of these simulations was to investigate several surface plasma generations models under Z conditions for comparison with experimental data.