The Effect of Anomalous Resistivity on the Electrothermal Instability
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.