Re: fission question (Why no China Syndrome with Daghlian and Slotin??)

From: Norman Yarvin (norman.yarvin_at_snet.net)
Date: 07/11/04 

Date: 11 Jul 2004 01:53:26 GMT

In article <79cf0a8.0407081742.42abafe0@posting.google.com>,
Steve Harris sbharris@ROMAN9.netcom.com <sbharris@ix.netcom.com> wrote:
>Norman Yarvin <norman.yarvin@snet.net> wrote in message news:<cchosl010h7@news2.newsguy.com>...
>> In article <79cf0a8.0407071059.1390bf5d@posting.google.com>,
>> Steve Harris sbharris@ROMAN9.netcom.com <sbharris@ix.netcom.com> wrote:
>> >Norman Yarvin <norman.yarvin@snet.net> wrote in message news:<ccfg6102e3u@news1.newsguy.com>...
>> >> In article <79cf0a8.0407041402.163437c7@posting.google.com>,
>> >> Steve Harris sbharris@ROMAN9.netcom.com <sbharris@ix.netcom.com> wrote:
>> >>
>> >> >Now, having said that, the second interesting thing about the Slotin
>> >> >and Daghlian incidents is what DIDN'T happen. The cores didn't melt
>> >> >and give a mini-China syndrome, burning globs of liquid plutonium into
>> >> >the floor. I've seen a picture of the core after the Daghlian
>> >> >accident, and it's perfectly intact.
>> >> >
>> >> >So why should it have been? IF you do the simple math with no
>> >> >assumptions, once you get over critical surface/volume/reflection
>> >> >configuration, then the reaction should increase exponentially at the
>> >> >intrinsic reaction doubling rate, which time is on the order of
>> >> >dimension/fast neutron velocity. There is no intrinsically stable
>> >> >region. It goes up and up, very fast, until energy production is so
>> >> >large the mass melts and/or blows apart.
>> >> >
>> >> >Now, obviously, that didn't happen in either of these accidents. From
>> >> >discriptions, it sounds as though the reaction went up to some ungodly
>> >> >high power output very fast, but then quit increasing. And didn't go
>> >> >past the limit where things melted or vaporized. So where was the
>> >> >brake. Was it a TRIGA type thing where neutrons coming back from
>> >> >heated tungsten-hydride moderator/reflectors were now so hot that they
>> >> >weren't doing their job?
>> >>
>> >> One candidate for the "brake" is thermal expansion. Just as implosion
>> >> can make a subcritical mass critical, thermal expansion can make a
>> >> barely-critical mass subcritical.
>> >
>> >
>> >COMMENT:
>> >
>> >If that happened, the reaction could have been a "huff and puff" sort,
>> >with blast of prompt-criticality followed by thermal shut-off,
>> >followed by cooling and then criticality again. That does happen in
>> >TRIGA type reactors.
>>
>> I'm pretty sure it would have just heated up and stayed hot, on the edge
>> of criticality. The heating mechanism is very fast; cooling is not at
>> all fast. Very little heat would need to be generated on an ongoing
>> basis, to keep it hot. (That is, very little heat compared to what would
>> be required to heat it up in the first place.)
>>
>> To get oscillations, there needs to be delay of some sort in the feedback
>> loop -- inertia, if you will. It needs to smell like a second-order (or
>> higher) differential equation, and this smells to me like a first-order
>> one. That's because the cooling is so slow that it doesn't really enter
>> into the dynamics. In a TRIGA reactor, the neutrons are much slower, and
>> the cooling is much faster (since it's water doing the cooling, whereas
>> this is just a sphere of plutonium in the open air.)
>
>
>COMMENT:
>
>You're right, of course. Assuming the Pu heated up right to melting
>point at around 900 K the biggest cooling factor is of course IR
>radiation, not air convection, but it's still not enough. Giving us
>the benefit of all doubts on IR cooling and assuming 100% viewfactor
>(off I'm sure by 75%, since only the top of this gismo was open), you
>get less than 700 watts of IR cooling from this little 8.4 cm diameter
>sphere. And since that much Pu has a heat capacity of around 800 J/K,
>that gives you less than 1 C/sec cooling rate max, which isn't enough
>to do squat (you have to use the entire heat capacity of the sphere,
>because with Pu's diffusivity of 0.026 cm^2/sec and only a 4.2 cm
>radius sphere, you don't get big enough thermal internal thermal
>gradients to affect the cooling time scale range, even with very high
>heat removal rates in the hundreds to thousands of watt range).
>
>Even if you assume the Pu liquified and went up to the melting temp of
>the nickel plating, radiation cooling goes up only by a factor of 15
>or so, and 15 C/sec is still no big deal when you're at 1500 K.
>
>But I don't have a good alternative. The bricks were actually 4 inch
>thick (radial to the reaction) WC, tungsten carbide, with the C used
>as the moderator. There wasn't time enough for more than their
>surfaces to warm, and the fast neutrons from the fission would have
>been penetrating and bouncing back from much deeper regions of the
>bricks, that hadn't warmed at all. No no change there. Neutrons inside
>the sphere that scattered off Pu atoms would have encountered hotter
>atoms, but since Pu is so massive it doesn't provide significant
>moderation anyway, so no effect THERE.
>
>So my best present guess is that in both accidents the mini-reactor
>just went up so some really high power level, and stuck there, for
>reasons I have yet to figure out. Maybe there exist a whole succession
>of shorter and shorter neutron-producing isotopes produced by fission,
>and in both cases the opperators were "lucky" enough NOT to go into a
>prompt critical range so high as to no longer depended on ANY of
>these. So perhaps they were still in the rate-doubling regime measured
>in seconds or fractions of a second, rather than the natural <
>microsecond range that characterizes a fission bomb fizzle.
>
>But I don't believe it. There's some really basic negative feedback
>mechanism here that I'm still missing.

Yeah, and I've been trying to tell you what it is. :-) The thermal
expansion of the plutonium, just by itself, lowers the level of
criticality. This is the reverse of what happens in an implosion
bomb, where compressing a sphere of plutonium changes a barely
subcritical mass into a supercritical one. Here the sphere expands
from heat, and a critical mass becomes subcritical. The essence of the
mechanism is that with more space between nuclei, an emitted neutron
is less likely to hit one. I'm not sure whether this mechanism is
sufficient to explain why those criticality accidents weren't worse,
but it seems like a good candiate.

Another candidate, since there was carbon acting as a moderator, would
be that the reaction never went prompt critical. Slow neutrons are
literally slow; in the case of thermal neutrons, their speeds are
something like the speeds of hydrogen molecules at the same
temperature, whereas with fast neutrons, the speeds are healthy
fractions of the speed of light. That makes a few orders of magnitude
difference in the doubling time. If the assembly were only very
slightly supercritical to begin with, the doubling time could come
down to human timescales. 

-- 
Norman Yarvin						http://yarchive.net

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