Publications

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We explore the use of reduced physics models for efficient kinetic particle simulations of space charge limited (SCL) emission in inner magnetically insulated transmission lines (inner MITLs), with application to Sandia National Laboratories' Z machine. We propose a drift kinetic (guiding center) model of electron motion in place of a fully kinetic model and electrostatic-magnetostatic fields in place of electromagnetic fields. The validity of these approximations is suggested by the operational parameters of the Z machine, namely, current pulse lengths of order 100 ns compared with Larmor periods typically smaller than 10-11 s, typical Larmor radii of a few (tens) of microns (magnetic fields of tens to hundreds of Tesla) compared with MITL dimensions of a few centimeters, and transient time of light waves along the inner MITL of order a fraction of a nanosecond. Guiding center orbits eliminate the fast electron gyromotion, which enables the use of tens to hundreds of times larger time steps in the numerical particle advance. Electrostatic-magnetostatic fields eliminate the Courant-Friedrichs-Lewy (CFL) numerical stability limit on the time step and allow the use of higher grid resolutions or, alternatively, larger time steps in the fields advance. Overall, potential computational cost savings of tens to hundreds of times exists. The applicability of the reduced physics models is examined on two problems. First, in the simulation of space charge limited emission of electrons from the cathode surface due to high electric fields in a radial inner MITL geometry with a short load. In particular, it is shown that a drift kinetic-based particle-in-cell (PIC) model with electrostatic-magnetostatic fields is able to accurately reproduce well-known physics of electron vortex formation, spatially and temporally. Second, deeper understanding is gained of the mechanism behind vortex formation in this MITL geometry by considering an exemplar problem of an electron block of charge. This simpler setup reveals that the main mechanism of vortex formation can be attributed to pure drift motion of the electrons, that is, the (fully kinetic) gyromotion of the electrons is inessential to the process. This exemplar problem also suggests a correlation of the spatial dimensions of vortices to the thickness of the electron layer, as observed in SCL simulations. It also confirms that the electromagnetic nature of the fields does not play an essential role. Finally, an improved hybrid fully kinetic and drift kinetic model for electron motion is proposed, as means of capturing finite Larmor radius (FLR) effects; the particular FLR physics that is missed by the drift kinetic model is the particle-wall interaction. By initializing SCL emitted electrons as fully kinetic and later transitioning them to drift kinetic, according to simple criteria, the accuracy of SCL simulations can be improved, while preserving the potential for computational efficiency.

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This project explores the idea of performing kinetic numerical simulations in the Z inner magnetically insulated transmission line (inner MITL) by reduced physics models such as a guiding center drift kinetic approximation for particles and electrostatic and magnetostatic approximation for the fields. The basic problem explored herein is the generation, formation, and evolution of vortices by electron space charge limited (SCL) emission. The results indicate that for relevant to Z values of peak current and pulse length, these approximations are excellent, while also providing tens to hundreds of times reduction in the computational load. The benefits could be enormous: Implementation of these reduced physics models in present particle-in-cell (PIC) codes could enable them to be routinely used for experimental design while still capturing essential non-thermal (kinetic) physics.

In this article, we derive the vacuum electric fields within specific cylindrically symmetric magnetically insulated transmission lines (MITLs) in the limit of an infinite speed of light for an arbitrary time-dependent current. We focus our attention on two types of MITLs: the radial MITL and a spherically curved MITL. We then simulate the motion of charged particles, such as electrons, present in these MITLs due to the vacuum fields. In general, the motion of charged particles due to the vacuum fields is highly nonlinear since the fields are nonlinear functions of spatial coordinates and depend on an arbitrary time-dependent current drive. Using guiding center theory, however, one can describe the gross particle kinetics using a combination of $\textbf {E} \times \textbf {B}$ and $\nabla B$ drifts. In addition, we compare our approximate inner MITL field models and particle kinetics with those from a fully electromagnetic simulation code. We find that the agreement between the approximate model and the electromagnetic simulations is excellent.

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In this study, we examine the effects of the radiation reaction force on electrons in a radial magnetically insulated transmission line (MITL) near a load with peak currents of 60+ MA. More specifically, we study the differences in electron motion and kinetic energy with or without radiation reaction physics using a novel guiding center drift approach that incorporates E $\times$ B and ∇B drifts. A key finding of this study is that an electron's magnetic moment, which would be conserved when radiation reaction physics is not incorporated, can be significantly reduced in magnetic fields on the order of 10,000's T when radiation reaction is included. The reduction of magnetic moment gives rise to a significant reduction in cycloidal kinetic energy as well as a reduction in the electron's ∇B drift.

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A challenge for the TW-class accelerators driving Z-pinch experiments, such as Sandia National Laboratories’ Z machine, is to efficiently couple power from multiple storage banks into a single multi-MA transmission line. The physical processes that lead to current loss are identified in new large-scale, multidimensional simulations of the Z machine. Kinetic models follow the range of physics occurring during a pulse, from vacuum pulse propagation to charged-particle emission and magnetically-insulated current flow to electrode plasma expansion. Simulations demonstrate that current is diverted from the load through a combination of standard transport (uninsulated charged-particle flows) and anomalous transport. Standard transport occurs in regions where the electrode current density is a few 10⁴–10⁵ A/cm² and current is diverted from the load via transport without magnetic insulation. In regions with electrode current density >10⁶ A/cm², electrode surface plasmas develop velocity-shear instabilities and a Hall-field-related transport which scales with electron density and may, therefore, lead to increased current loss.

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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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We report that a critical component of the magnetically driven implosion experiments at Sandia National Laboratories is the delivery of high-current, 10s of MA, from the Z pulsed power facility to a target. In order to assess the performance of the experiment, it is necessary to measure the current delivered to the target. Recent Magnetized Liner Inertial Fusion (MagLIF) experiments have included velocimetry diagnostics, such as PDV (Photonic Doppler Velocimetry) or Velocity Interferometer System for Any Reflector, in the final power feed section in order to infer the load current as a function of time. However, due to the nonlinear volumetrically distributed magnetic force within a velocimetry flyer, a complete time-dependent load current unfold is typically a time-intensive process and the uncertainties in the unfold can be difficult to assess. In this paper, we discuss how a PDV diagnostic can be simplified to obtain a peak current by sufficiently increasing the thickness of the flyer. This effectively keeps the magnetic force localized to the flyer surface, resulting in fast and highly accurate measurements of the peak load current. Additionally, we show the results of experimental peak load current measurements from the PDV diagnostic in recent MagLIF experiments.

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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