The Effect of Anomalous Resistivity on the Electrothermal Instability
Masti, Robert Leo
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The current driven electrothermal instability (ETI) forms when the material resistivity is temperature dependent, occurring in nearly all Z-pinch-like high energy density platforms. ETI growth for high-mass density materials is predominantly striation form which corresponds to magnetically perpendicular mode growth. The striation form is caused by a resistivity that increases with temperature, which is often the case for high-mass density materials. In contrast, low-density ETI growth is mainly filamentation form, magnetically aligned modes, because the resistivity tends to decrease with temperature. Simulating ETI is challenging due to the coupling of magnetic field transport to equation of state over a large region of state space spanning solids to plasmas. This dissertation presents a code-code verification study to effectively model the ETI. Specifically, this study provides verification cases which ensure the unit physics components essential to modeling ETI are accurate. This provides a way for fluid-based codes to simulate linear and nonlinear ETI. Additionally, the study provides a sensitivity analysis of nonlinear ETI to equation of state, vacuum resistivity, and vacuum density. Simulations of ETI typically use a collisional form of the resistivity as provided, e.g., in a Lee-More Desjarlais conductivity table. In regions of low-mass density, collision-less transport needs to be incorporated to properly simulate the filamentation form of ETI growth. Anomalous resistivity (AR) is an avenue by which these collision-less micro-turbulent effects can be incorporated into a collisional resistivity. AR directly changes the resistivity which will directly modify the linear growth rate of ETI, so a new linear growth rate is derived which includes AR's added dependency on current density. This linear growth rate is verified through a filamentation ETI simulation using an ion acoustic based AR model. Kinetically based simulations of vacuum contaminant plasmas provide a physical platform to study the use of AR models in pulsed-power platforms. Using parameters from the Z-machine pulsed-power device, the incorporation of AR can increase a collisional-based resistivity by upwards of four orders of magnitude. The presence of current-carrying vacuum contaminant plasmas can indirectly affect nonlinear ETI growth through modification of the magnetic diffusion wave. The impact of AR on nonlinear ETI is explored through pulsed-power simulations of a dielectrically coated solid metallic liner surrounded by a low-density vacuum contaminant plasma.
General Audience Abstract
High-energy-density physics (HEDP) is the study of materials with pressures that exceed 1Mbar, and is difficult to reach here on Earth. Inertial confinement fusion concepts and experiments are the primary source for achieving these pressures in the laboratory. Inertial confinement fusion (ICF) is a nuclear fusion concept that relies on the inertia of imploding materials to compress a light fuel (often deuterium and tritium) to high densities and temperatures to achieve fusion reactions. The imploding materials in ICF are driven in many ways, but this dissertation focuses on ICF implosions driven by pulsed-power devices. Pulsed-power involves delivering large amounts of capacitive energy in the form of electrical current over very short time scales (nanosecond timescale). The largest pulsed-power driver is the Z-machine at Sandia National Laboratory (SNL) which is capable of delivering upwards of 30 MA in 130 ns approximately. During an ICF implosion there exists instabilities that disrupt the integrity of the implosion causing non-ideal lower density and temperature yields. One such instability is the Rayleigh-Taylor instability where a light fluid supports a heavy fluid under the influence of gravity. The Rayleigh-Taylor is one of the most detrimental instabilities toward achieving ignition and was one of the main research topics in the early stages of this Ph.D. The study of this instability provided a nice intro for modeling in the HEDP regime, specifically, in the uses of tabulated equations-of-state and tabulated transport coefficients (e.g., resistivity and thermal conductivity). The magneto Rayleigh-Taylor instability occurs in pulsed-power fusion platforms where the heavy fluid is now supported by a magnetic field instead of a light fluid. The magneto Rayleigh-Taylor instability is the most destructive instability in many pulsed-power fusion platforms, so understanding seeding mechanisms is critical in mitigating its impact. Magnetized liner inertial fusion (MagLIF) is a pulsed-power fusion concept that involves imploding a solid cylindrical metal annulus on laser-induced pre-magnetized fuel. The solid metal liners have imperfections and defects littered throughout the surface. The imperfections on the surface create a perturbation during the initial phases of the implosion when the solid metal liner is undergoing ohmic heating. Because a solid metal has a resistivity that increases with temperature, as the metal heats the resistivity increases causing more heating which creates a positive feedback loop. This positive feedback loop is similar to the heating process in a nichrome wire in a toaster, and is the fundamental bases of the main instability studied in this dissertation, the electrothermal instability (ETI). ETI is present in all pulsed-power fusion platforms where a current-carrying material has a resistivity that changes with temperature. In MagLIF, ETI is dominant in the early stages of a current pulse where the resistivity of the metal increases with temperature. An increasing resistivity with temperature is connected to the axially growing modes of ETI which is denoted as the striation form of ETI. Contrary to the striation form of ETI, the filamentation form of ETI occurs when resistivity decreases with temperature and is associated with the azimuthally growing modes of ETI. Chapter 2 in this dissertation details a study of how to simulate striaiton ETI for a MagLIF-like configuration across different resistive magnetohydrodynamics (MHD) codes. Resistivity that decreases with temperature typically occurs in low-density materials which are often in a gaseous or plasma state. Low density plasmas are nearly collision-less and have resistivity definitions that often overestimate the conductivity of a plasma in certain experiments. Anomalous resistivity (AR) addresses this overestimation by increasing a collisional resistivity through micro-turbulence driven plasma phenomenon that mimic collisional behavior. The creation of AR involves reduced-modeling of micro-turbulence driven plasma phenomenon, such as the lower hybrid drift instability, to construct an effective collision frequency based on drift speeds. Because AR directly modifies a collisional resistivity for certain conditions, it will directly alter the growth of ETI which is the topic of Chapter 3. The current on the Z-machine is driven by the capacitor bank through the post-hole convolute, the magnetically insulated transmission lines, and then into the chamber. Magnetically insulated transmission lines have been shown to create low-density plasma through desorption processes in the vacuum leading to a load surrounded by a low-density plasma referred to as a vacuum contaminant plasmas (VCP). VCP can divert current from the load by causing a short between the vacuum anode and cathode gap. In simulations, this plasma would be highly conducting when represented by a collisionally-based resistivity model resulting in non-physical vacuum heating that is not observed in experiments. VCP are current-carrying low-density and high-temperature plasmas which make them ideal candidates to study the role of AR as described in Chapter 4. Chapter 4 investigates the role AR in a VCP would have on striation ETI for a MagLIF-like load.
- Doctoral Dissertations