Reactor Kinetics/Neutron Sources Flashcards
Purpose of Source Neutrons
Ensure neutron population is high enough during shutdown to provide source range NI indication.
Used to confirm operability and monitor n population changes.
Types of intrinsic neutron sources
Spontaneous fission
Photo-neutron reactions
Alpha-neutron reactions
Describe Spontaneous Fission source neutrons
Heavy nuclei that will spontaneously fission without absorbing a neutron.
U235/238, Cm242/244.
Also Pu239, but not as prevalent.
Describe Photo Neutron reaction source neutrons
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.
Describe Alpha Neutron reaction source neutrons.
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.
Intrinsic Source Neutrons over Core Life.
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.
Why do we have installed neutron sources.
Give visible count rate
Provide operability of SRNIs
Help monitor approach to criticality.
Examples of Installed Neutron Sources
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.
What is subcritical multiplication?
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.
Equation for Subcritical Multiplication
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.
What is Subcritical Multiplication Factor (M)?
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
Use formula for subcritical multiplication factor and solve for keff.
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.
How do changes in keff change Count Rate in a subcritical reactor?
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)
Describe Subcritical Multiplication response on Rx Startup.
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.
Subcritical Reactor Reactivity Rules of Thumb.
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.
Why are Delayed Neutrons important?
They increase the neutron generation times, resulting in more controlled power increases with reactivity additions.
What is Delayed Neutron Fraction (beta)?
Ratio of delayed neutrons to all neutrons born (prompt and delayed) for a particular fuel isotope.
Examples of various Delayed Neutron Fractions that we care about.
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.
What is Average Delayed Neutron Fraction (beta bar)?
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.
How does Beta Bar change over core life in a Clean Core (1st cycle)?
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.
What is Average “Effective” Delayed Neutron Fraction (Beta Bar Effective)?
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.
Describe Importance Factor (I) as it relates to Beta Bar Effective
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
Calculate Average Generation Time when taking both prompt and delayed neutrons into account.
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
Values of Beta Bar Effective over core life.
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.
