- 27 -


shifts the energy at which neutrons are absorbed to higher or lower values, depending on the direction of the target nuclei with respect to that of the incident neutron. This energy shift is referred to as Doppler broadening (.18) of the resonance cross section, since the neutron "sees" a cross section which is spread over an increasingly wider energy range as the nuclear motion increases. Doppler broadening strongly affects neutron absorption since the neutron density is a rapidly varying function in the neighborhood of a resonance. At the comparatively low temperatures of solid core reactors, the Doppler effect is very important in determining reactor criticality and stability. The kinetic energy of an absorbing nuclei in a plasma core reactor will correspond to temperatures in the 50,0000K to 100,0001K range, as compared to a maximum of about 30000K for a solid core reactor. At such high fuel temperatures, the effects of Doppler broadening in a plasma core reactor are expected to be much larger than the corresponding effects in a solid core reactor. In order to compare the Doppler broadening equations in the plasma and solid core reactors, the approximations used in treating the Doppler effect in a solid core reactor will be examined briefly.

        In a solid core reactor operating at any appreciable power level, the fuel nuclei will have sufficient thermal