The Reactor Accelerator Coupling Experiments (RACE) are a set of neutron source driven subcritical experiments under temperature feedback conditions. These experiments will involve coupling an accelerator driven neutron source to a TRIGA reactor system in a subcritical configuration. The accelerator source will consist of a 40 MeV electron linear accelerator (LINAC) and a heavy metal target. The electrons from the accelerator produce bremsstrahlung radiation in the target which in turn produces a source of neutrons via photonuclear reactions. The available core at the The University of Texas at Austin (UT) with standard TRIGA fuel will be used to carry out these studies. The primary objective of this thesis was to study the feasibility of RACE especially with respect to the heat generation rates capable of placing the reactor in a temperature feedback regime. First, the accelerator target (or neutron source) was optimized for size, shape, and type of material to be used. Analyses were then performed for several arrangements of this target in the UT TRIGA reactor. One of these arrangements was found to provide heat generation rates well into the temperature feedback regime of the fuel. Lastly, a multi-target system [named the Texas Transmutation System (TTS)] was designed to allow for more detailed accelerator driven systems (ADS) studies. It was shown that this system would allow for operation over a wide-range of subcriticalities and with a wide-range of heat loads. Thus, the feasibility for these experiments has been proven, and it is recommended that continued study and implementation of these experiments be performed.