Units of Reactivity
Mathematically, reactivity is a dimensionless number, but various units can express it. The most common units for research reactors are units normalized to the delayed neutron fraction (e.g.,, cents and dollars) because they exactly express a departure from prompt criticality conditions.
The most common units for power reactors are units of pcm or %ΔK/K. The reason is simple. Units of dollars are difficult to use because the normalization factor, the effectively delayed neutron fraction, significantly changes with the fuel burnup. In LWRs, the delayed neutron fraction decreases with fuel burnup (e.g.,, from βeff = 0.007 at the beginning of the cycle up to βeff = 0.005 at the end of the cycle). This is due to isotopic changes in the fuel. It is simple. Fresh uranium fuel contains only 235U as the fissile material. Meanwhile, during fuel burnup, the importance of fission of 239Pu increases (in some cases up to 50%). Since 239Pu produces significantly fewer delayed neutrons (0.0021 for thermal fission), the resultant core delayed neutron fraction of a multiplying system decreases (the weighted average of the constituent delayed neutron fractions).
βcore= ∑ Pi.βi
The unit of reactivity has been normalized to the delayed neutron fraction. Reactivity in dollars = ρ / βeff. The cent is 1/100 of a dollar. This is a very useful unit because the reactivity in dollars (rather in cents) determines exactly the response of the reactor on the reactivity insertion. Conversion of dollars to pcm depends on βeff. For reactor core with βeff = 0.006 (0.6%) one dollar is equal to about 600 pcm. It is a substantial amount of reactivity because if the core’s reactivity is one dollar, the reactor is prompt critical.
BOC and βeff = 0.006
keff = 0.99 ρ = (keff – 1) / keff = -0.01 ρ = -0.01 / 0.006 = -1.67 $ = -167 cents
EOC and βeff = 0.005
keff = 0.99 ρ = (keff – 1) / keff = -0.01 ρ = -0.01 / 0.005 = -2.00 $ = -200 cents