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REACTOR KINETICS
DOE-HDBK-1019/2-93
Reactor Theory (Reactor Operations)
NP-04
Rev. 0
Page 16
In this case, the production of prompt neutrons alone is enough to balance neutron losses and
increase the neutron population. The condition where the reactor is critical on prompt neutrons,
and the neutron population increases as rapidly as the prompt neutron generation lifetime allows
is known as prompt critical. The prompt critical condition does not signal a dramatic change
in neutron behavior. The reactor period changes in a regular manner between reactivities above
and below this reference. Prompt critical is, however, a convenient condition for marking the
transition from delayed neutron to prompt neutron time scales. A reactor whose reactivity even
approaches prompt critical is likely to suffer damage due to the rapid rise in power to a very
high level. For example, a reactor which has gone prompt critical could experience a several
thousand percent power increase in less than one second.
Because the prompt critical condition is so important, a specific unit of reactivity has been
defined that relates to it. The unit of reactivity is the dollar ($), where one dollar of reactivity
is equivalent to the effective delayed neutron fraction
. A reactivity unit related to the
dollar is the cent, where one cent is one-hundredth of a dollar. If the reactivity of the core is one
dollar, the reactor is prompt critical. Because the effective delayed neutron fraction is
dependent upon the nuclides used as fuel, the value of the dollar is also dependent on the
nuclides used as fuel.
Stable Period Equation
For normal reactor operating conditions, the value of positive reactivity in the reactor is never
permitted to approach the effective delayed neutron fraction, and the reactor period equation is
normally written as follows.
(4-8)
Equation (4-8) is referred to as the transient period equation since it incorporates the term
to account for the changing amount of reactivity in the core. The */ term (prompt period) is
normally negligible with respect to the remainder of the equation and is often not included.
For conditions when the amount of reactivity in the core is constant (
), and the reactor
period is unchanging, Equation (4-8) can be simplified further to Equation (4-9) which is known
as the stable period equation.
(4-9)
