¯eff¯effeff0¯effeffREACTOR KINETICSDOE-HDBK-1019/2-93Reactor Theory (Reactor Operations)NP-04Rev. 0Page 16In this case, the production of prompt neutrons alone is enough to balance neutron losses andincrease 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 allowsis known as prompt critical. The prompt critical condition does not signal a dramatic changein neutron behavior. The reactor period changes in a regular manner between reactivities aboveand below this reference. Prompt critical is, however, a convenient condition for marking thetransition from delayed neutron to prompt neutron time scales. A reactor whose reactivity evenapproaches prompt critical is likely to suffer damage due to the rapid rise in power to a veryhigh level. For example, a reactor which has gone prompt critical could experience a severalthousand percent power increase in less than one second.Because the prompt critical condition is so important, a specific unit of reactivity has beendefined that relates to it. The unit of reactivity is the dollar ($), where one dollar of reactivityis equivalent to the effective delayed neutron fraction . A reactivity unit related to thedollar is the cent, where one cent is one-hundredth of a dollar. If the reactivity of the core is onedollar, the reactor is prompt critical. Because the effective delayed neutron fraction isdependent upon the nuclides used as fuel, the value of the dollar is also dependent on thenuclides used as fuel.StablePeriodEquationFor normal reactor operating conditions, the value of positive reactivity in the reactor is neverpermitted to approach the effective delayed neutron fraction, and the reactor period equation isnormally written as follows.(4-8)Equation (4-8) is referred to as the transient period equationsince it incorporates the termto account for the changing amount of reactivity in the core. The */ term (prompt period) isnormally 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 reactorperiod is unchanging, Equation (4-8) can be simplified further to Equation (4-9) which is knownas the stable period equation.(4-9)