An important step toward the advent of nuclear fusion as a future power source is the development of plasma-facing materials that can function as designed for a long period of time. While ITER and other devices including Wendelstein 7-X and the Joint European Torus will provide insight into divertor and first wall performance, a dedicated device to advance the understanding of material performance in the representative plasma environments is needed. The Material Plasma Exposure eXperiment has been proposed as a linear plasma device to generate and to direct fusion reactor-like plasma energy and particle flux at the target materials with electron temperatures of 1-15 eV and electron densities of <inline-formula> <tex-math notation="LaTeX">10^{20} </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">10^{21}\,\,\text{m}^{-3} </tex-math></inline-formula>. Given that the requirements for radio frequency (RF) heating on-axis field are no greater than 2.5 T and the warm bore diameters must be between 60 cm and 1.5 m, the conceptual design was developed for the experiments on a set of superconducting magnets carried out using commercially available NbTi superconductors. This conceptual design evaluated the cryogenic heat loads, mechanical loads, and quench protection to ensure that the current design is compatible with current technologies. In addition, an alternative evaluation of this design relative to ReBCO high-temperature superconducting magnets determined the conditions under which these technologies could be advantageous.