What is the expression for discharge burnup B in an M-batch operation?

In an M-batch operation, the expression for discharge burnup ( B ) can be derived based on the relationship between various parameters influencing fuel utilization and depletion in a nuclear reactor. The correct expression, ( B = \frac{2\alpha MT}{M + 1} ), arises from the interplay of factors like fuel composition, burnable poisons, and the residence time of fuel in the reactor.

To understand why this expression is valid, consider the terms involved:

• ( \alpha ) represents a parameter related to the specific burnup rate of the fuel, which quantifies how much energy is produced per unit mass of fuel over time.

• ( M ) denotes the number of batches, which reflects how the reactor operates with a staggered loading of fuel to maintain a continuous output while managing fission products and neutron economy.

• ( T ) indicates the total time during which the fuel undergoes fission reactions in the reactor.

The numerator ( 2\alpha MT ) captures the total energy produced from the fuel across multiple batches and time. The factor of 2 in the numerator typically arises from the fact that each batch experiences a certain amount of burnup over its operational period, and contributions from all (