- 31 -


and


x = 2(E - E0)/r, y   2 (Er - E]}/r, e = FA, A = (41EOkT/MN)1/2 (2.22)

        Doppler broadened resonance absorption cross section in solid fuel reactors are computed using (2.20), with T(e,x) evaluated from tabulated values based on the resonance parameters F and E0, and the fuel temperature T.

        Doppler broadening in a plasma core reactor is expected to differ quantitatively from the solid core reactor, due to the larger kinetic energy of the plasma core fuel nuclei. The following treatment of the Doppler effect in a plasma reactor is based on the assumption that the single level Breit-Wigner formula (2.12) accurately describes resonance absorption cross sections. The relative kinetic energy of the neutron-nucleus collision is again given by equation (2.14). From the same arguments used in the investigation of the Doppler effect in solid core reactors, the third term of (2.14) will have a significant effect on the relative energy in the plasma fuel reactor also. For fuel nuclei at a temperature of 100,0000K and a neutron at the energy of the first uranium resonance, the ratio of the second to the first term is 0.04, or forty times larger than the corresponding ratio for the solid core reactor. Thus, the second term of (2.14) can result in