The Advanced Test Reactor (ATR) is a high power density test reactor designed primarily for accelerated irradiation of nuclear fuels and materials irradiation under controlled environmental conditions. For more than 45 years, the ATR has operated primarily in support of the Office of Naval Reactors (NR) but the mission has gradually expanded to cater to other customers, such as the DOE Office of Nuclear Energy (NE), private industry, and universities. . Featuring nine large flux traps that can accommodate independently-cooled high-pressure In-Pile Tubes (IPTs), ATR is still reliable and effective but increasingly expensive to maintain and operate every year. The sophisticated test hardware and experiments required of recent fuel and materials irradiation campaigns are limited by the safety limits and operating envelope of this aging facility, which are becoming harder to meet as equipment reliability is diminished. Furthermore, the fabrication and transport of its highly enriched uranium (HEU) fuel is deemed a proliferation concern. Under the Global Threat Reduction Initiative (GTRI), ATR and the other high flux test reactors in the US fleet must eventually be converted to low enriched uranium (LEU) in order to continue operating. Studies are underway to assess the costs and technical viability of this fuel conversion. One foreseeable outcome is that the cost of upgrades, fuel conversion, and more frequent LEU fuel loadings needed to keep ATR viable will exceed those of building and operating a replacement reactor. In anticipation of this scenario, work was commenced under the Laboratory Directed Research and Development (LDRD) program to investigate test reactor concepts that could satisfy the current missions of the ATR. Naturally, the needs of other value-adding missions were considered as part of the initial design study.This work build upon a project from the 1990's called the Broad Application Test Reactor (BATR). In FY 2012, a survey of anticipated customer needs was performed, followed by analysis of the original BATR concepts with fuel changed to low-enriched uranium. Departing from these original BATR designs, four concepts were identified for further analysis in FY2013. The project informally adopted the acronym MATRIX (Multiple-Application Thermal Reactor for Irradiation eXperiments). This report discusses analysis of the four MATRIX concepts along with a number of variations on these main concepts. Designs were evaluated based on their satisfaction of anticipated customer requirements and the "Cylindrical" variant was selected for further analysis of options. This downselection should be considered preliminary and the backup alternatives should include the other three main designs.The analysis described within indicates that the baseline Cylindrical MATRIX design can achieve a higher burnup than the ATR (or longer cycle length given a particular batch scheme). The volume of test space in IPTs is larger in MATRIX than in ATR with comparable magnitude of neutron flux. In addition to the IPTs, ...