Reactor Kinetics and Neutron Sources

Question 1

Explain the necessity for installed neutron sources in a reactor core

Answer 1

Important in monitoring reactor during shutdown and startup by providing a statistically valid count rate on the Source Range Instruments.

Question 2

What are the two classifications of source neutrons and their definitions?

Answer 2

1. Intrinsic Neutrons: They come into existence because the core and its materials are there, i.e. fission products.
2. Installed Neutrons: A special device is installed into the core to generate free neutrons. Installed neutrons are further classified as primary (produces neutrons without any activation - made of transuranic nuclides, often Californium) and secondary (does not produce neutrons immediately and must be activated in an operating core before they produce any neutrons).

Question 3

What is subcritical multiplication?

Answer 3

It is the process of utilizing source neutrons and fuel to maintain a constant neutron population with k_eff less than 1.0.

The neutron population is maintained above the source strength as a result of source neutrons in a reactor with k_eff less than 1.0.

Maximum neutron population for a known Keff and source strength.

Nt = So( 1 / 1 - Keff)

Question 4

True of False

The closer the reactor is to being critical, the larger the subcritical multiplication factor (1/1-k_eff).

Answer 4

TRUE

The closer to critical, the larger the M-factor.

When positive reactivity is added to a subcritical reactor (while the reactor remains
subcritical), neutron population increases as a result of decreased losses per generation and thus increased fission neutron production.

Neutron population increases at a decreasing rate until an equilibrium value is reached - fission neutron losses equal source neutron strength.

The next positive reactivity addition results in a corresponding increase in neutron population. Once again, count rate increases at a decreasing rate until an equilibrium value is reached.

It takes longer to achieve this new value because the fraction of fission neutrons lost in each generation is less as k_eff approaches unity.

Question 5

True or False

“HALVING the DISTANCE to CRITICALITY DOUBLES the COUNTS”

Answer 5

TRUE

When reactivity is added to a subcritical reactor in an amount equal to the amount associated with 1/2 (1-k_eff ), the count rate will double.

Going from 0.90 K_eff and 100 cps to 200 cps results in a K_eff of 0.95. [0.5(1-0.90)]

CR₁(1-K_eff1) = CR₂(1-K_eff2)

Question 6

True or False

“CRITICALITY in 5 to 7 DOUBLINGS”

Answer 6

TRUE

When the initial count rate at the beginning of a startup has doubled 5-7 times, the reactor will be at or near critical.

Question 7

True or False

When enough reactivity is added to the reactor to double the count rate, if the same reactivity is added to the reactor again, the reactor will be supercritical.

Answer 7

TRUE

“FIXED REACTIVITY ADDITIONS versus COUNT RATE DOUBLING”

Question 8

Describe the production of delayed neutrons.

Answer 8

On fission, a number of daughter products could be produced. These are grouped with their decay rates averaged. Those that decay via neutron emmission are called delayed neutron precursors.

Question 9

Immediately following one operating cycle of a new or refueled reactor, what is the largest contributor of intrinsic sources to the core.

Answer 9

The photo-neutron reaction

Photo-neutron reactions occur when a gamma causes the dissociation of deuterium.

Question 10

Define delayed neutron fraction

Answer 10

The delayed neutron fraction is the fraction of neutrons that are born delayed.

It is a ratio of the number of neutrons born delayed to the total number of neutrons born from fission of a particular nuclide. For U-235 it is 0.0064. Meaning 64 of every 10,000 neutrons from U-235 fission is a delayed neutron.

The delayed neutron fraction (β) represents the fraction of neutrons born delayed from fission of a particular nuclide.

Question 11

Define the effective delayed neutron fraction.

Answer 11

The effective delayed neutron fraction β_eff is the fraction of neutron induced fissions caused by delayed neutrons averaged over the entire core (and all the fissioning nuclides).

Decreases over core life due to depletion of U-235 and build up of P-239.

Question 12

State the reasons for variation in delayed neutron fraction and effective delayed neutron fraction.

Answer 12

Time in core life (fuel cycle) and the fission yield (or fission fraction) for each fuel must be considered. The fission fraction (γ) is defined as the percentage of fissions that occur in the reactor for each particular fuel type present.

The delayed neutron fraction remains constant for a nuclide. However the fission yield can change with core life. U-238 is contstant over core life at 7%. U-235 goes from 93% at BOL to 55% at EOL. P-239 goes from 0% at BOL to 38% at EOL.

Question 13

Define the power equation

Answer 13

P = P₀e^t/T

P = final power (time t)
Po = initial power (time to)
t = time interval in seconds
τ = reactor period in seconds

Question 14

Define doubling time and calculate it using the power equation.

Answer 14

It is the time required for power to double. The relationship between doubling time and reactor period is τ =1.44DT

Where:
DT = doubling time in seconds
τ = reactor period in seconds

Question 15

Explain the effect of delayed neutrons on reactor control.

Answer 15

When reactor power increases, the delayed neutrons being produced come from precursors that were formed at the previous, lower power level.

As a result, the effective delayed neutron fraction is lower. For example, if reactor power were to instantly change from 10% to 20%, the delayed neutrons present would be from precursors that were formed at 10% power.

Thus, the delayed neutrons make up a smaller fraction of the neutron population during power increases. This condition exists as long as power is changing and will last until an equilibrium precursor concentration is achieved at the higher power level.

The effect of delayed neutrons is in slowing down the reactor power changes.

Question 16

Explain prompt critical

Answer 16

Prompt criticality occurs when the reactivity added is greater than or equal to the core average delayed neutron fraction causing the reactor to go critical on prompt neutrons alone.

Because β_eff (effective delayed neutron fraction) decreases over core life, the amount of reactivity required to achieve prompt criticality also decreases during the core life.

Question 17

Explain prompt jump, and prompt drop.

Answer 17

Prompt jump is the rapid, almost instantaneous rise in power when reactivity is added in step fashion

Prompt drop is when a large amount of negative reactivity is inserted into a critical reactor, the power initially drops quickly prior to reaching a stable period.

Question 18

Define startup rate.

Answer 18

It is the number of decades that power changes in a minute (Decades per minute).

A decade is a factor of 10. Thus, if SUR is 1.0 DPM, reactor power will increase by a factor of 10 times its original value in one minute. The relationship between SUR and power is given in the following equation:

SUR( t )
P = P₀ 10^SUR(t)
Where: P = reactor power at any time t
Po = reactor power at time to
t = time interval t=t-to (min)
SUR = startup (DPM)

Question 19

Describe the factors affecting startup rate.

Answer 19

reactivity changes

Question 20

What is the average neutron generation time and what happens to it over core life? What does this mean for the operator?

Answer 20

BOL it is 0.0875 seconds, EOL it is 0.0676 seconds. Meaning the cycle of neutron generations is faster which means the response to reactivity changes will be faster at the end of core life.