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PostPosted: Mar 08, 2011 5:31 pm 
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I am in a limited way I have been trying to better understand what might happen in a fast MSR if there was a significant reactivity insertion than occurs very quickly (if it happens much slower than 0.01s, not a lot seems to happen according to Elsa Merle-Lucott's thesis). To that end I have built a little stepwise model looking at reactivity, salt expansion and the time required for a change in salt volume to be signalled to the core outlet at the speed of sound increasing the outlet flow compared to the inlet flow (if we assume that remains fixed) after some notional delay.

I can see how Doppler shift works almost immediately and salt expansion, while somewhat slower is still reasonably fast.

One aspect that troubles me and could be quite significant, in the event that the reactivity insertion is sufficient to make one part or the entire core prompt critical, the power increases exponentially and very quickly (prompt neutrons have approximately 1 million generations per second in a fast reactor according to the DOE Nuclear Handbook H1019).

So with this massive increase in power, albeit temporarily, what is happening to the spectrum?

If the spectrum is hardening further in an already hard spectrum do we encounter real problems of increased reactivity of fissionable fertile materials like U238 with an increased population higher energy neutrons? After all for a U/Pu or Th/U Breeder, there are usually massive quantities of fertile material present, if it became significantly more reactive the overall reactivity change could be catastrophic.

I suspect the answer is a Nuclear Reactions 101 answer, but I don't know what it is.

See attached for an indication of changes in fissionability WRT neutron energy.
Attachment:
Ottewitte Thesis 1982 Page 30.pdf [52.33 KiB]
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PostPosted: Mar 08, 2011 5:45 pm 
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If the spectrum gets faster the cross-section of the fission and fertile goes down very fast so I really doubt that a faster spectrum could do anything but go down in reactivity. More so if there is thorium as the fertile.


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PostPosted: Mar 08, 2011 6:05 pm 
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Lindsay wrote:
....do we encounter real problems of increased reactivity of fissionable fertile materials like U238 with an increased population higher energy neutrons?

Yes, slightly increased.
But U238 & Th232 cannnot sustain a chain reaction, due to their small fission x-section......


Attachments:
Pu238,239,240,241,242,243_U238_Th232_(n,f)_fast.gif
Pu238,239,240,241,242,243_U238_Th232_(n,f)_fast.gif [ 14.99 KiB | Viewed 3784 times ]
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PostPosted: Mar 08, 2011 7:13 pm 
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Thanks Jaro and Lars. The Jaro plot looks far less threatening that the Ottewitte one.

Looking at the U238 trace a shift from 6 MeV to 7 - 8 almost doubles the fission cross section, that might do something in U/Pu machine, interestingly on a ratio basis Th232 isn't that much different, I expected that Th232 would have to be pushed much harder to the right hand side before doing anything interesting.

Given the reduction in cross section for other isotopes and at other energy levels perhaps the overall effect is far more muted than the Ottewitte figure might lead one to think. Once again, another situation where proper simulation codes would no doubt give us a precise answer.


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PostPosted: Mar 08, 2011 7:52 pm 
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I don't think there are many neutrons that hit 6-7 MeV even right out of fission. Hit one lithium or fluoride nucleus and you drop out of that speed range immediately. Check out the macro-cross section of the lithium and fluoride in the reactor versus the uranium and I think you'll find that this is nothing to worry about - double check sure but very unlikely to be an issue.

http://neutron.kth.se/courses/transmuta ... ectra.html shows the spectrum right after fission.


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PostPosted: Mar 08, 2011 7:55 pm 
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Lindsay wrote:
The Jaro plot looks far less threatening that the Ottewitte one...
That's because the latter plots the RATIO of fission to capture -- which can be quite high, even at insignificant fission x-section (ie. below ~1.3MeV)

Lindsay wrote:
Looking at the U238 trace a shift from 6 MeV to 7 - 8 almost doubles the fission cross section, that might do something in U/Pu machine....
There are very few fission neutrons born with > 6MeV energy -- I would just ignore those, unless you've got a supply of 14MeV neutrons, as in a fusion-boosted fission weapon.


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PostPosted: Mar 08, 2011 8:09 pm 
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Lars wrote:
I don't think there are many neutrons that hit 6-7 MeV even right out of fission. Hit one lithium or fluoride nucleus and you drop out of that speed range immediately. Check out the macro-cross section of the lithium and fluoride in the reactor versus the uranium and I think you'll find that this is nothing to worry about - double check sure but very unlikely to be an issue.

http://neutron.kth.se/courses/transmuta ... ectra.html shows the spectrum right after fission.

jaro wrote:
There are very few fission neutrons born with > 6MeV energy

Thanks guys, I think that is the key piece of information that I was missing, from a physics point of view, there just aren't that many neutrons operating at that energy level, therefore the contribution is minor at best. Excellent, time for me to get back to my MCFR project in the garage :shock:.


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PostPosted: Mar 08, 2011 8:12 pm 
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Lars wrote:
I don't think there are many neutrons that hit 6-7 MeV even right out of fission. Hit one lithium or fluoride nucleus and you drop out of that speed range immediately.
Not exactly.
Neutrons between 3 to 6 MeV could do a couple of hits and still be above the U238 fission threshold of ~1.3MeV
But its true that if maximizing U238 fission is desired, Li, F, O or Na atoms must be kept to a minimum.
U metal is best in that regard.
Next best is UO2, then UF3/UF4.


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PostPosted: Oct 06, 2011 3:11 pm 
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One of the French papers has a very interesting discussion of the different reactivity strengths in different spectrums.

http://hal.in2p3.fr/docs/00/03/09/52/PDF/TMSR.pdf

Quote:
The Doppler coefficient is linked to the 233U fission resonance
and the 232Th capture resonance (and, to a lesser degree,
to the 234U capture resonance). These two elements have
opposite effects on the feedback coefficient: 233U worsens it
whereas 232Th improves it. The thermal agitation of the salt nuclei
induces a widening of these resonances so that their influence
is increased. The value of the Doppler coefficient depends
on how intense the flux is at these resonance values. When
the spectrum hardens, the flux is more intense for high energies
and less so for low energies, the thoriumresonances are favored
(main resonance located at 22 eV while that of 233U is at 2 eV).
The Doppler coefficient then becomes more negative. Beyond
a certain degree of spectrum hardening, the large resonances
of both thorium and uranium lie in a zone where the flux has a low intensity and their importance is reduced. This explains
the worsening of the Doppler coefficient for large radii.
The density coefficient is related to the expansion of the salt
which pushes a fraction of the fuel outside of the moderated
zone. The consequence is spectrum softening because the proportion
of graphite to salt is larger, thus increasing the fission
rate. The effect is small for small radii where thermalization
is already very efficient and where it is counterbalanced by
captures in the graphite. For large radii, the thermal part of
the spectrum contributes practically nothing in the neutron balance
and the effects of neutron escape are felt more strongly.
The density coefficient can become negative when the effects
of captures in the graphite (small radius, large proportion of
graphite) or of neutron escapes (large radius, fast neutron spectrum)
dominate over the effects of thermalization.
The graphite coefficient comes from an energy shift of the
thermal part of the neutron spectrum (around 0.2 eV), due to
heating of the moderator. This shift increases the fission rate
because of a small low energy (0.3 eV) resonance in the fission
cross section of 233U [4]. Its impact on the stability decreases
as the amount of graphite in the core decreases and as the influence
of the thermal portion of the spectrum weakens.


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PostPosted: Oct 06, 2011 3:25 pm 
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What is really interesting is that in the French design, the salt density coefficient is negative for very thermal and fast spectra, but actually positive for intermediate spectra. Doppler is always negative in fluoride spectra, but it wants to shoot up beyond that as you can see from figure 4. So very fast reactors can't rely on doppler alone; too few neutrons are near the moderated resonance range. So fast reactors rely on really good density coefficients, causing increased leakage rather than thermalization. Choosing a salt that expands greatly upon heating becomes an important safety goal for really fast molten salt reactors. For very well moderated spectra increased thermalization does not occur because the neutrons are already well thermalized.

While generalizing by specific reactor configurations is tricky, this raises an important question about highly heterogeneous designs such as Jaro's HW-MSR. That reactor has a lot of well thermalized neutrons, where the density coefficient should be negative, and a bunch of quite fast neutrons, where the density coefficient is also negative. On the other hand these fast neutrons will tend to not leak from the core but be thermalized by the heavy water, leading to positive density coefficients for that part of the spectrum. How much fast fission bonus can we have while retaining a negative global coefficient for such a reactor?


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