Reactor Kinetics/Neutron Sources

Question 1

Purpose of Source Neutrons

Answer 1

Ensure neutron population is high enough during shutdown to provide source range NI indication.
Used to confirm operability and monitor n population changes.

Question 2

Types of intrinsic neutron sources

Answer 2

Spontaneous fission
Photo-neutron reactions
Alpha-neutron reactions

Question 3

Describe Spontaneous Fission source neutrons

Answer 3

Heavy nuclei that will spontaneously fission without absorbing a neutron.
U235/238, Cm242/244.
Also Pu239, but not as prevalent.

Question 4

Describe Photo Neutron reaction source neutrons

Answer 4

High energy Gammas produced from fission (power) interact with Deuterium to crap out a neutron.
Dies off quickly after shutdown to to no more high energy gammas from power.

Question 5

Describe Alpha Neutron reaction source neutrons.

Answer 5

Alpha particles interact with various isotopes in the core and poop out neutrons.
These alpha particles come from decay of heavy elements in the fuel.
Alphas interact primarily with O18 and B11.
Alphas also interact with transuranic elements to produce neutrons.

Question 6

Intrinsic Source Neutrons over Core Life.

Answer 6

Make PSA announcement upon initial startup.
After that go relax at the SPA.
When it’s all over go get a bathroom PAS.
While you are pooing be careful not to get bit in the arse by an ASP.

Question 7

Why do we have installed neutron sources.

Answer 7

Give visible count rate
Provide operability of SRNIs
Help monitor approach to criticality.

Question 8

Examples of Installed Neutron Sources

Answer 8

Primary: Californium-252. Hi cost/short half life.
Secondary: Beryllium Sources;
1: Antimony-Beryllium; absorbs neutron and decays to give off hi energy gamma to interact w/Be
2: Photo-Neutron; Gamma interacts w/installed Be source
3: Alpha-Neutron; alpha particle emitter reacts w/installed Be source.

Question 9

What is subcritical multiplication?

Answer 9

Process where Source Neutrons add to the neutrons available (from fission) to sustain the chain reaction when keff<1.

Note: Majority of neutron population is from fission neutrons, but source neutrons pick up the slack.

Question 10

Equation for Subcritical Multiplication

Answer 10

CR=S(o)[1/(1-keff)]n

S(o)= source strength (cps)
CR= neutron count rate (cps)
n= detector efficiency.

Note: NRC equation sheet combines N=CR/n which is total neutron population.

Question 11

What is Subcritical Multiplication Factor (M)?

Answer 11

Factor source neutrons are multiplied by to get neutron population.

M=1/(1-keff)

Substitute M into subcritical multiplication formula and get;

CR=S(o)•M•n

Question 12

Use formula for subcritical multiplication factor and solve for keff.

Answer 12

keff=1-(1/M)

Basis for 1/M plots. As 1/M gets closer to 0-> keff gets closer to 1 (criticality).
Note:
5-7 1/M plots leads to criticality.

Question 13

How do changes in keff change Count Rate in a subcritical reactor?

Answer 13

CR(1)[1-keff(1)]=CR(2)[1-keff(2)]
Also,
CR(1)•p(1)•[1-p(2)]=CR(2)•p(2)•[1-p(1)]
If keff is ~1, then;
CR(2)/CR(1)~p(1)/p(2)

Question 14

Describe Subcritical Multiplication response on Rx Startup.

Answer 14

Initially when withdrawing rods, time to reach equilibrium is dominated by delayed neutron precursors with shorter mean life-> 5 mean lives is shorter.
Then longer lived precursors take over causing the 5 mean lives to be longer and longer.
As keff approaches 1, each rod pull increases count rate more significantly and takes longer to reach equilibrium.

Question 15

Subcritical Reactor Reactivity Rules of Thumb.

Answer 15

1: Double count rate= keff halfway from starting point to keff=1.
2: If the amount of reactivity that was added to double the count rate is added again-> Rx will be critical.
3: With each doubling, distance to criticality is halved.
4: 5-7 doublings during S/U should reach criticality.

Question 16

Why are Delayed Neutrons important?

Answer 16

They increase the neutron generation times, resulting in more controlled power increases with reactivity additions.

Question 17

What is Delayed Neutron Fraction (beta)?

Answer 17

Ratio of delayed neutrons to all neutrons born (prompt and delayed) for a particular fuel isotope.

Question 18

Examples of various Delayed Neutron Fractions that we care about.

Answer 18

U235: beta=0.0064
U238: beta=0.0148
Pu239: beta=0.0021
Pu241: beta=0.0054

Note: beta is constant for each particular isotope. Also when considering U235, if 0.64% neutrons are delayed (0.0064), then 99.36% are prompt.

Question 19

What is Average Delayed Neutron Fraction (beta bar)?

Answer 19

Weighted average of all the isotopes In the core that produce delayed neutrons. Changes over core life because the composition of the fuel changes over core life.

Question 20

How does Beta Bar change over core life in a Clean Core (1st cycle)?

Answer 20

BOL: U235@93%, U238@7%
EOL: U235@42%, U238@8%, Pu239@45%, and Pu241@5%.

Beta for Pu239 is significantly smaller than uranium-> Beta Bar lowers over core life.

Question 21

What is Average “Effective” Delayed Neutron Fraction (Beta Bar Effective)?

Answer 21

Fraction of fissions induced by delayed neutrons over all fissions.
Measure of effectiveness of a delayed neutron to cause fission.
Compares 1 prompt and 1 delayed n.

Question 22

Describe Importance Factor (I) as it relates to Beta Bar Effective

Answer 22

Delayed neutrons are born at lower energy-> higher resonance escape probability and lower fast fission factor. The importance factor takes these into account.
In larger, lower enriched cores (commercial cores), the loss in fast fission factor dominates the rise in resonance escape probability-> I<1.
Beta Bar Effective=Beta Bar•I

Question 23

Calculate Average Generation Time when taking both prompt and delayed neutrons into account.

Answer 23

Tave=Tprompt(1-Beta)+Tdelayed(Beta)
Prompt n generation time=10^-4 sec
Delayed n generation time=12.7 sec

Tave=10^-4sec•(1-0.9934)+12.7sec(0.0064)
Tave=0.08 seconds when taking delayed neutrons into account

Question 24

Values of Beta Bar Effective over core life.

Answer 24

Cycle 1: BOL: 0.007; EOL: 0.0054

Cycle 3 on: BOL: 0.006; EOL: 0.005

Assume Cycle 1 unless stated otherwise in stem of question.

Question 25

How does Beta Bar Effective over core life change reactor period and SUR?

Answer 25

As Beta Bar Effective lowers over core life, for a given amount of reactivity added, this causes period to be lower and SUR to be higher.

Question 26

Describe Reactor Period (Tao) and terms

Answer 26

Tao=(l*/p)+(Beta Bar Eff-p)/(Lambda Eff•p+delta p).

l*=prompt neutron generation time (10^-4 sec)
p=reactivity
Lambda Eff=effective delayed neutron precursor decay constant
delta p=rate of change of reactivity

NRC equation sheet omits prompt portion as it only adds 0.1 sec.

Question 27

What is Effective Delayed Neutron Precursor Decay Constant (Lambda Eff)?

Answer 27

Adjusts for balance of short, medium and long lived delayed neutron precursors.
Changes based on power changes large and small.
Reciprocal of mean life (Tao)- which is how long, on average, a delayed neutron precursor will exist before decaying.

Question 28

Values typically used for Lambda Eff

Answer 28

0.08 Steady State
0.1 on the run (power increase)
0.05 on the dive (power decrease)
0.0124 on the floor (Rx trip)

NRC uses 0.1 for small positive reactivity additions.

Question 29

Power equation using Period

Answer 29

P(f)=P(o)•e^(t/Tao)

Time in seconds

Question 30

What is Prompt Jump?

Answer 30

Immediate effect of positive reactivity on neutron population (due to 10^-4 n generation time).

Question 31

What is Prompt Drop?

Answer 31

Immediate drop in power due to prompt neutron production immediately lowering.

Question 32

How is Prompt Neutron population affected following Rx trip?

Answer 32

Prompt neutrons gone immediately.
Delayed neutron precursors remain.
Short lived decay first while longest lived take longer.
Longest lived account for -80 second period after trip (-1/3 DPM) until fully decayed to subcritical multiplication.

Question 33

What is Prompt Critical?

Answer 33

Achieving criticality without contribution from delayed neutrons.

Happens when reactivity added is > Beta Bar Effective (removes delayed neutron component from period equation leaving only prompt neutron component. Bad Ju Ju!)

Question 34

What aspect of Control Rods affects the amount of “prompt jump” change during rod movement?

Answer 34

Differential Rod Worth.

Question 35

How does Beta Bar Effective effect Source Count Rate?

Answer 35

CR is independent of Beta Bar Effective. Only based on keff.

CR(1)•[1-keff(1)]=CR(2)•[1-keff(2)]

Gotcha!

Therefore stable neutron counts are the same after reactivity additions both at BOL and EOL, but it takes longer to stabilize at BOL due to smaller SUR.

Question 36

How does Fast Nonleakage Probability affect Effective Delayed Neutron Fraction?

Answer 36

If Fast Nonleakage Probability decreases, more fast neutrons leak out of the core. Since prompt neutrons are born at higher energy than delayed neutrons, more collisions are required to thermalize them and therefore a higher percentage of them will leak out vs delayed n’s. As a result the Importance Factor for Beta Bar Eff rises which causes Beta Bar Eff to rise.