Effects of Design Variables on Viscous Rayleigh-Taylor Growth to Study Plasma Viscosity

In attempts to make Inertial Fusion Energy (IFE) a more practical solution to the fusion energy concept, studying the growth of hydrodynamic instabilities in high-energy-density (HED) plasmas at extreme conditions during laser compression can provide information about the transport properties of IFE-relevant materials. In this work an analytical model for viscous linear Rayleigh-Taylor growth is employed to study the behavior of hydrodynamic instability growth of viscous of HED plasmas under high temperature and pressure. Through this model, a parameterization study can be conducted to find ideal values of amplitude, wavelength, material densities, and laser acceleration for experimental design. The growth of hydrodynamic instabilities in HED plasmas can be modelled using RTI, which is dependent on the viscosity and density of various materials. In this work, an in-house MATLAB code that solves viscous RTI was used to find the ideal materials and values of governing variables, that leads to the largest sensitivity between different material kinematic viscosities for experimental design. The primary challenge associated with this approach is establishing reasonable bounds of each variable given limitations of laser facilities, such as the National Ignition Facility. These limitations include diagnostic resolutions, small experimental timescales, and laser power limitations. This study examines the sensitivity of RTI growth to key governing variables. Results show that the most pronounced viscosity-dependent separation occurs when the lowdensity material is zero, reducing the system to a single high-density material rather than a two-material interface. Additionally, increasing laser-induced acceleration leads to exponential separation in final amplitudes. These findings suggest that further exploration in the nonlinear regime could refine experimental conditions for probing viscosity in HED plasmas. Further investigation into viscosity effects within the non-linear regime should be pursued using in-house hydrodynamic simulations and existing visualization tools.The objective of these simulations is to map the effects of viscosity on RTI growth in the nonlinear regime such that experiments may be designed with sufficient sensitivity to amplitude evolution to infer plasma viscosity