Kinetics With Delayed Neutrons. B. Rouben McMaster University EP 4P03/6P03 2008 Jan-Apr. Point-Kinetics Equations.
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Using the values of 1 and 2 from Eqs. (14) & (13)
The 2nd term decays away very quickly (typically in 1 s), therefore the neutron density (or flux/power) experiences a prompt jump or drop by a factor /(-) [this is good as long as is not too large with respect to ]
The point-kinetics equations apply even in steady state, with =0.
The relationship between the precursor concentrations and the neutron density can be obtained by setting the time derivatives to 0 in the point-kinetics equations. For G precursor groups at steady state (subscript ss):
From Eq. (21) we get
[Note: This relationship holds also at all points in the reactor.]
Summing Eq. (22) over all g yields back Eq. (21), since
This means that in this case, even if we ignore the delayed neutrons ( ), keff will be = or >1, i.e., the reactor is critical on prompt neutrons alone. This isprompt criticality.
The delayed neutrons then no longer play a crucial role, and when increases beyond (prompt supercriticality),very very short reactor periods (< 1 s, or even much smaller, depending on the magnitude of ) develop.
Thus, it is advisable to avoid prompt criticality.