Thermonuclear fusion reactors have not yet achieved breakeven; high plasma temperatures are required to obtain high reaction rates. Accompanying the high plasma temperatures are high bremsstrahlung radiation losses, plasma instabilities, first wall problems and large amounts of energy for plasma containment. To reduce the detrimental effects and maintain high reaction rates, a two component target plasma system was proposed with one of the fuel species acting as a target plasma magnetically confined at a relatively low temperature. The second fuel species is then injected at high energy into the target plasma to interact with the confined plasma as it slows down, depositing energy and undergoing fusion reactions. The reactor confinement scheme chosen to contain the target plasma was the multipoled Octahedrally Symmetric MAgnetiC well (OSMAC) which has been studied previously at Iowa State University;The energy balance calculations performed for the two component reactor configuration included a newly modeled asymptotic slowing down number density and plasma temperature effects through Doppler broadening of the fusion cross section. The new slowing down number density was compared with models from Fokker-Planck and Boltzmann collision term approaches. This new model allows the relatively easy introduction of finite geometry effects. A numerical comparison of relaxation rate formulae was accomplished. Both D-('3)He and D-T fuel cycles were considered;As a result of this work it becomes evident that D-('3)He and D-T fueled two component reactors operating according to the assumptions made and equations used herein is incapable of achieving breakeven conditions. It is implied that the operating conditions used herein require the reassessment and redevelopment of the physics model of fast ions slowing down in a cold plasma. A new slowing down number density model presented herein has been found comparable with existing models. Included in this dissertation is a computer program for finding Doppler broadened cross sections.