ConsistentP1Criticality Calculations

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Abstract
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 keff ∼ 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.

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