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
percent mille (pcm)
The reactivity unit is one-thousandth of a percent %ΔK/K (equal to 10-2x10-3 = 10-5 of keff). The unit of pcm is used at many LWRs because reactivity insertion values are generally quite small, and units of pcm allow reactivity to be written in whole numbers. The operational changes such as control rods movement usually cause reactivity insertion of the order of units of pcm per one step. The fact that the effective delayed neutron fraction changes with the fuel burnup have an important consequence. Due to the difference in βeff a response of a reactor on the same reactivity insertion (in units of pcm) is different at the beginning (BOC) and the end (EOC) of the cycle.
For example, one step of control rods causes a greater response at EOC than at BOC. Even though we assume that one step causes the same reactivity insertion (e.g.,, +10pcm) in both cases, this assumption is not always correct because the control rod’s worth increases with fuel burnup.
(10 pcm = 1.43 cents for βeff = 0.007; 10 pcm = 2.00 cents for βeff = 0.005)
keff = 0.99 ρ = (keff – 1) / keff = -0.01 ρ = -0.01 * 105 = -1000 pcm