What does B_m^2 equal for criticality in a reactor core?

In the context of nuclear reactor theory, particularly when discussing the criticality of a reactor core, the term ( B_m^2 ) refers to the multiplication factor known as the fast fission factor, whereas ( B_g^2 ) signifies the thermal fission factor. Criticality in a reactor core occurs when the number of neutrons produced by fissions equals the number of neutrons lost due to absorption and leakage.

For a reactor to be at criticality, it is essential that the fast and thermal components of the fission process balance each other appropriately. When ( B_m^2 = B_g^2 ), it indicates that the multiplication of neutrons from fast fissions is equal to that from thermal fissions. This balance is crucial for maintaining the sustained chain reaction necessary for stable reactor operation.

In a critical reactor, it is anticipated that both fast and thermal reactions contribute equally to the overall fission process, which is why this equation holds true at criticality. Understanding this relation is key in reactor design and safety assessments, ensuring that the reactor operates within desired parameters.