Perturbations, Mass, and Critical Mass

Rigorous transport relations between mass, critical mass, and arbitrary perturbations are developed for nonuniform reactors. It is shown that reactivity is equal to the difference between the fractional increase of mass and critical mass, multiplied by the fractional destruction rate of total importance by moderator or by leakage. Sufficient conditions for an increase or decrease of critical mass in nonuniform reactors are obtained, and it is shown that burnup always increases the critical mass of thermal reactors.