Shape factors of non-critical small fast assemblies and their use in ksub(eff) calculations

Distortion of shape of the core of a hard spectrum small fast assembly from a spherical to a non-spherical geometry results in decrease of reactivity following an increase in net neutron leakage from the core both in bare and reflected systems. If the original reactivity is to be restored the overall core dimensions (or density) have to be increased. The paper points out that to a good approximation the criteria for preserving reactivity consequent on distortion of core shape of bare systems may be taken as constancy of mean chord length of core measured in units of neutron mean free path or the mass per unit surface area (delta) of the core. It is demonstrated that shape factor curves of constant density cores are almost independent of the system ksub(eff) in the range 0.7 < ksub(eff) < 1.3 for bare and reflected small fast assemblies which are not too highly distorted away from spherical. The flatter shape factor curves of reflected systems are deduced from an extension of the Los Alamos Density Exponent Formula. The paper concludes by illustrating how the ksub(eff) of non-critical non-spherical small fast assemblies both bare and reflected may be computed using the relation. ksub(eff) = k sub(α)sup(*)(1-exp(-THETA(Msub(x)/Ssub(fx) x Msub(spx))sup(1/3))) where Msub(x) is the core mass of the test assembly whose ksub(eff) is desired, Msub(spx) = critical mass of equivalent spherical system and Ssub(fx) = appropriate shape factor. The limitation and regions of validity of these concepts are examined by comparing with multigroup two dimensional transport theory calculations. (orig.)