Re: fission question

From: Carey Sublette (careysub_at_earthling.net)
Date: 07/27/04 

Date: Tue, 27 Jul 2004 05:15:12 GMT

"John Schilling" <schillin@spock.usc.edu> wrote in message
news:ce3lcn$53b$1@spock.usc.edu...
> sharp@cadence.com (Steven Sharp) writes:
>
> >Here are some back-of-the-envelope calculations based on the
> >information I have available from 2000 revision of the report
> >of historical criticality accidents compiled by Los Alamos,
> >and Carey Sublette's NWFAQ.
>
> >The reactivity in the Slotin accident was estimated at 10 "cents"
> >above prompt critical. For Pu-239, 0.25% of the neutrons emitted
> >are delayed neutrons. So I will assume that 10 "cents" gives us
> >an excess of about 0.00025 neutrons per fission, or a neutron
> >multiplication factor of 1.00025 per generation. I will further
> >assume a time between generations of 10ns, which is typical.
>
> >With those numbers, in 100 microseconds an initial neutron would
> >only have increased to 1.00025**10000, or 12.18 neutrons. That
> >means a growth of only one order of magnitude every 100 usec.
> >In 1 msec, there would still only be 7.0E9 neutrons, which would
> >correspond to a fission rate of 7.0E17 fissions/sec. That is
> >roughly in the same timescale as the graph in the report.
>
> >With this timescale, the small size of the core, and the speed of
> >sound in the core, there is presumably enough time for thermal
> >expansion to occur and propagate without any shock waves, quenching
> >the reaction without any core damage. The excess reactivity is
> >so small that only a modest expansion of the core would be needed
> >to eliminate it.
>
> >Now for the bad news. I went looking for the thermal coefficient
> >of expansion for plutonium. I found out that in the delta phase,
> >like this core, it actually has a small negative coefficient,
> >getting denser with increased temperature. Oops. The Pu would have
> >been alloyed with 3-3.5% gallium to stabilize it in the delta phase.
> >The NWFAQ said that the alloy has an "almost zero" expansion
> >coefficient. I am guessing that it must be slightly positive, or
> >the accidents would have been much worse.
>
> For real materials, the coefficient of thermal expansion is itself
> a function of temperature, and usually increases with temperature.
> Delta-phase Pu has a negative coefficient of thermal expansion *at
> room temperature*, and the gallium-stabilized alloy pretty close to
> zero, but that may not be true a few hundred degrees hotter.
>
>
> >Thermal expansion still seems like the only reasonable non-destructive
> >quenching mechanism. The Los Alamos report does not state the quenching
> >mechanism for these two accidents, but it is the only one that makes
> >sense from what it describes.

I was going to make an informed estimate about how large a density decrease
would be required to drive a multiplication factor of 1.00025 below 1, but
haven't had the time.

But since this is only very slightly above critical mass, and the critical
mass is proportional to the inverse square density, and the density is
proportional to the cube of linear dimension, this is going to be tiny (it
makes the critical mass a sixth power of the linear dimension). This
proprotionate increase in going to be a one, a decimal point, and a bunch of
zeros before you come to the first significant digit after that.

Carey Sublette

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