Collaboration by some of the world's brightest minds of the 21st Century pinpointed fourteen Grand Engineering Challenges that face humankind today. At the top of this list is "Provide Energy from Fusion"; a requirement deemed crucial for humankind to thrive flourish. Scientists from all over the globe have risen to this challenge in many ways; most recognizably by attempting to succeed at performing inertial confinement fusion (ICF). However, ICF currently remains unsuccessful at providing net-positive energy production, largely due to hydrodynamic instabilities, such as the shock-driven Richtmyer-Meshkov instability (RMI), which occur within the fusion reaction process, creating detrimental mixing. Applying magnetohydrodynamic approaches however, can mitigate these instabilities and reduce fluid mixing. It is precisely this problem that necessitates the research on magnetohydrodynamic instabilities presented in this dissertation to aid in solving the challenge to "Provide Energy from Fusion"; specifically the development of an experiment for investigating the magnetohydrodynamic Richtmyer-Meshkov instability (MHD-RMI). ... By developing and performing the computational and experimental efforts at the Missouri Fluid Mixing and Shock Tube Laboratory (FMSTL), the author has laid the groundwork to observe the suppression of the MHD-RMI in future shock tube experiments.