Sometimes it is useful to discuss the rate of change of reactor power in terms similar to those used in radioactive decay calculations. Doubling or halving time are terms that relate to the amount of time it takes reactor power to double or be reduced to one-half the initial power level. If the stable reactor period is known, doubling time can be determined as follows.

Doubling time (DT) = (In 2)

where:

When the doubling time is known, the power level change from P_o is given by the following equation.

where:

t = time interval of transient

DT = doubling time

The following example problems reinforce the concepts of period and startup rate.

Example 1:

A reactor has a of 0.10 sec^-1 and an effective delayed neutron fraction of 0.0070. If kerf is equal to 1.0025, what is the stable reactor period and the SUR?

Solution:

Step 1:First solve for reactivity using Equation (3-5).

Step 2:Use this value of reactivity in Equation (4-9) to calculate reactor period.

Step 3:The startup rate can be calculated from the reactor period using Equation (4-11).

Example 2:

130 pcm of negative reactivity is added to a reactor that is initially critical at a power of 100 watts. for the reactor is 0.05 sec^-1 and the effective delayed neutron fraction is 0.0068. Calculate the steady state period and startup rate. Also calculate the power level 2 minutes after the reactivity insertion.

Solution:

Step 1:Use Equation (4-9) to calculate the reactor period.

Step 2:The startup rate can be calculated from the reactor period using Equation (4-11).

Step 3:Use either Equation (4-1) or Equation (4-10) to calculate the reactor power two minutes after the reactivity insertion.

Example 3:

A reactor has a power level of 1000 watts and a doubling time of 2 minutes. What is the reactor power level 10 minutes later?

Solution:

Use Equation (4-12) to calculate the final power level.

Summary

The important information in this chapter is summarized below.

Reactor Kinetics Summary

Reactor period is the time required for reactor power to change by a factor of e (2.718).

Doubling time is the time required for reactor power to double.

Reactor startup rate is the number of factors of ten that reactor power changes in one minute.

The delayed neutron fraction () is the fraction of all fission neutrons that are born as delayed neutrons for a particular type of fuel (that is, uranium-235 and plutonium-239).

The average delayed neutron fraction () is the weighted average of the total delayed neutron fractions of the different types of fuel used in a particular reactor.

The effective delayed neutron fraction () is the average delayed neutron fraction multiplied by an Importance Factor which accounts for the fact that delayed neutrons are born at lower average energies than fast neutrons.

The reactor period equation is stated below.

where:

Equations (4-9) and (4-11) can be used to calculate the stable reactor period and startup rate.

The concept of doubling time can be used in a similar manner to reactor period to calculate changes in reactor power using Equation (4-12).

The reactor period or the startup rate can be used to determine the reactor power using Equations (4-6) and (4-10).

Prompt jump is the small, immediate power increase that follows a positive reactivity insertion related to an increase in the prompt neutron population.

Prompt drop is the small, immediate power decrease that follows a negative reactivity insertion related to a decrease in the prompt neutron population.

Prompt critical is the condition when the reactor is critical on prompt neutrons alone.

When a reactor is prompt critical, the neutron population, and hence power, can increase as quickly as the prompt neutron generation time allows.

Measuring reactivity in units of dollars is useful when determining if a reactor is prompt critical. A reactor that contains one dollar of positive reactivity is prompt critical since one dollar of reactivity is equivalent to .