In recent, high intensity laser pulse interaction with solid density matter has been studied in several laboratory and facilities. Multi-MeV proton and ion beams from plasma produced by this interaction is one important application research area of HEDP. In this thesis, the basic theory of hot electron generation associated with proton acceleration will be introduced. A basic proton acceleration mechanism called TNSA will be introduced with supplemental free plasma expansion model. To investigate proton acceleration at the Texas Petawatt Facility, the experimental set up and target alignmen will be introduced in the chapter 5. While the analysis of data acquired from this experiment is still unfinished, a brief result with RCF image will be introduced in chapter 6. / text

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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. / Doctor of Philosophy / 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.

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Recent concepts for controlled magneto-inertial fusion (MIF), such as magnetized liner inertial fusion (MagLIF), have suffered from magnetohydrodynamic (MHD) instabilities that lead to degradations in fusion yield. High levels of azimuthally-correlated MHD instability structures have been observed on cylindrical liner experiments without a pre-imposed axial magnetic field (Bz=0) elsewhere in the literature and are believed to be seeded from surface machining roughness. This dissertation uses highly resolved (0.5 μm and less resolution) 1D and 2D resistive magnetohydrodynamics (MHD) arbitrary-Lagrangian-Eulerian (ALE) simulations of electrical wire explosions (EWEs) and liner implosions to show that micrometer-scale surface roughness seeds the electrothermal instability (ETI), which induces early melting in pockets across the conductor and leads to millimeter-scale instability growth. The relationship between the ETI and the MRTI in liner implosions is also described in this dissertation, which shows that the traditional growth rates associated with these modes are coupled together and are not linearly independent. This dissertation also describes the preliminary implementation of a Koopman neural network architecture for learning the nonlinear dynamics of a high energy density (HED) exploding or imploding electrical conductor. / Doctor of Philosophy / Researchers have been working on controlling nuclear fusion and harnessing it as a power source since the discovery that nuclear fusion powers stars. In many of these controlled nuclear fusion concepts the aim is to heat the fuel until it forms a high-temperature plasma state of matter and then compress it to the point that the atoms are close enough and at high enough speeds that they collide fuse together. In the magnetized liner inertial fusion (MagLIF) concept these temperatures, densities, and pressures are achieved by surrounding the fusion fuel with a cylindrical piece of metal called a liner and using magnetic fields to implode the liner inward. Experiments have shown, however, that these liner implosions do not occur smoothly and that the system becomes unstable and can mix liner material into the fuel, which disrupts the fusion process. This dissertation investigates the stability of liner implosions and electrical wire explosions. In particular, this dissertation shows that surface roughness imparted on the surface of a solid fusion target by a machining process can grow into a millimeter-scale perturbation. It also describes the relationship between two common types of instabilities found in current-driven nuclear fusion: the magneto-Rayleigh-Taylor instability and the electrothermal instability. Finally, it looks at using neural networks to better understand the dynamics of electrical wire explosions.

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Diagnosing the temperatures and densities of plasmas is critical to the understanding of a wide variety of phenomena. Everything from equations of state for warm dense matter (WDM) found in Jovian planets and inertial confinement fusion (ICF) to turbulent and dissipative processes in laser-produced plasmas, rely on accurate and precise measurements of temperature and density. This work presents improvements on two distinct techniques for measuring temperatures and densities in plasmas: x-ray Thomson scattering (XRTS), and Langmuir probes (LPs). At the OMEGA laser facility, experiments on warm dense matter were performed by firing lasers at an ablator foil and driving a planar shock into cryogenically cooled liquid deuterium. XRTS in the collective scattering regime was implemented to probe the matter, measuring densities of n_e ~ 4.3 x 10²³ cm^-3, temperatures of T_e ~ 12 eV and ionizations of Z ~ 1.0. Through an extension to XRTS theory for inhomogeneous systems, it was possible to extract an additional parameter, the length scale of the shock, whose value of ? ~ 1.33 nm was consistent with the predicted mean free path, and therefore the thickness of the shock. A unique triple Langmuir probe prototype was designed and tested at the Gregori group's lab at the University of Oxford. This probe was designed for a high temporal resolution of ~ 200 MHz for probing laser-produced shocks. The probes were used to measure the shock formed from ablating carbon rods in an argon gas fill. The probe yielded plasma parameters of n_e ~ 1.0 x 10¹⁷ cm^-3 , and T^e ~ 1.5 eV, consistent with measurements from interferometry and emission spectroscopy.

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Les simulations hydrodynamiques pour la physique de haute densité d'énergie ainsi que pour la fusion par confinement inertiel exigent une description détaillée de flux d'énergie. Le mécanisme principal est le transport électronique, qui peut être un phénoméne non local qui doit être décrit avec des modèles de Fokker-Planck, stationnaires et simplifiés dans les codes hydrodynamiques à grande échelle. Mon travail thèse est consacré au développement d'un nouveau modèle de transport non local basé sur l'utilisation d'une méthode de fermeture entropique pour la résolution des premiers moments de l'équation de Fokker-Planck agrémentée d'un opérateur de collision dédié. Une telle fermeture permet une bonne résolution des fortes anisotropies de la fonction de distribution électronique dans les régimes où le développement d'instabilités électrostatiques à petite échelle le requiert. Ce modèle aux moments (M1) est comparé avec succès au modèle de Schurtz, Nicolaï et Busquet (SNB), référent dans le domaine du transport électronique non local. Ce modèle, basé sur l'hypothèse d'une faible anisotropie de la fonction de distribution sous-jacente induisant une relation de fermeture polynomiale (P1), utilise un opérateur de collision simplifié dont nous avons proposé une amélioration. Après avoir considéré plusieurs configurations typiques de transport de chaleur, nous avons montré que le modèle M1 ultidimensionnel peut prendre naturellement en compte des effets d'un plasmas magnétisés sur le transport électronique. De plus, ce modèle permet de calculer des fonctions de distribution utiles aux études cinétiques comme la stabilité du plasma dans la zone de transport. Nous confirmons avec notre modèle que le transport d'énergie électronique peut fortement modifier l'amortissement des ondes de Langmuir et des ondes acoustiques ; contrairement aux modèles non locaux simplifiés, M1 décrit les modifications de la fonction de distribution et l'amortissement des ondes du plasma. La structure du modèle permet également de prendre en compte naturellement des champs magnétiques autogénérés, qui jouent un rôle crucial dans des simulations multidimensionnelles. Ces champs magnétiques pourraient également être étudiés pour concentrer l'énergie dans les schémas d'ignition. Enfin, nous montrons que le modèle M1 reproduit les résultats de la théorie locale élaborée par Braginskii pour tous les niveau de magnétisation et propose de nouveaux résultats pour le régime non local. Ce travail constitue une première validation de l'utilisation des fermetures entropiques, dans les régimes de faibles anisotropies, qui va s'ajouter aux tests dans les régimes fortement anisotropes. / Hydrodynamic simulations in high-energy-density physics and inertial con nement fusion require a detailed description of energy uxes. The leading mechanism is the electron transport, which can be a nonlocal phenomenon that needs to be described with quasistationary and simplified Fokker-Planck models in large scale hydrodynamic codes. My thesis is dedicated to the development of a new nonlocal transport model based on a fast-moving-particles collision operator and on a first moment Fokker-Planck equation, simplified with an entropic closure relation. Such a closure enables a better description of the electron distribution function in the limit of high anisotropies, where small scale electrostatic instabilities could be excited. This new model, so called M1, is successfully compared with the well known nonlocal electron transport model proposed by Schurtz, Nicolaï and Busquet, using different collision operators, and with the reduced Fokker-Planck model, based on a small-anisotropies polynomial closure relation (P1). Several typical configurations of heat transport are considered. We show that the M1 entropic model may operate in two and three dimensions and is able to account for electron transport modifications in external magnetic fields. Moreover, our model enables to compute realistic electron distribution functions, which can be used for kinetic studies, as for the plasma stability in the transport zone. It is demonstrated that the electron energy transport may strongly modify damping of Langmuir and ion acoustic waves, while the simplified nonlocal transport models are not able to describe accurately the modifications of the distribution function and plasma wave damping. The structure of the M1 model allows to naturally take into account self-generated magnetic fields, which play a crucial role in multidimensional simulations. Moreover, magnetic fields could also be used for the focusing of energetic particles in alternative ignition schemes. The M1 model reproduces the results of the local transport theory in plasma, developed by Braginskii, in a broad range of degrees of magnetization and predicts new results in the nonlocal regime. This work constitutes a first validation of the entropic closure assumption in the weakly-anisotropic regime. It can be added to the existing tests, in the strongly-anisotropic regimes.