Consistent P₁ Criticality Calculations

A “consistent P₁” four-factor formula is derived. This formula, which contains an additional term not found in the usual four-factor formula, introduces a change in k_eff ∼ D²B² where D is the thermal diffusion coefficient. The term is negative for hydrogen and positive for other moderators. The correction will be at most 1% Δk for a practical system. Since the four-factor formula is not expected to be accurate to 1%, it is proposed that this term be used mainly as a criterion for determining whether consistent P₁ multigroup calculations are required, or whether simple group diffusion methods will suffice. By using the consistent P₁ equations when the term D²B² is of the order 1%, one will avoid the introduction of a consistent error into his reactor calculations. Finally, the consistent P₁ multigroup equations are displayed, and it is seen that the procedure for their solution is not a great deal more difficult than for solving the usual multigroup equations.