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

From: Steven Sharp (sharp_at_cadence.com)
Date: 07/19/04 

Date: 19 Jul 2004 14:05:42 -0700

Norman Yarvin <norman.yarvin@snet.net> wrote in message news:<ccq6im09e0@news4.newsguy.com>...
>
> 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.

Or another way to view it, the surface area of the mass through which
neutrons can escape has increased, while the reactive mass has remained
constant. Critical mass is inversely proportional to the square of the
density of the material.

> 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.

Sure. The assemblies were barely supercritical, so it didn't take much
expansion to bring them back down.
 
> 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.

Here you seem to be confusing delayed versus prompt criticality with
moderated versus unmoderated reactions. Reactors generally use delayed
criticality with a lot of moderation, while bombs use prompt criticality
with minimal moderation. However, it is possible to have a moderated
prompt critical reaction, or an unmoderated delayed critical reaction.
Both factors do affect the time constants.

Delayed criticality means that the reaction is only critical when the
contribution of delayed neutrons emitted from fission fragments are taken
into account, which happens over a period of seconds after the fission
itself. This is different from moderation, which you described.

The accidents in question apparently went prompt critical. There was
some neutron reflection and moderation involved.

> If the assembly were only very
> slightly supercritical to begin with, the doubling time could come
> down to human timescales.

Yes, or more importantly, to thermal expansion timescales. I have
a report from Los Alamos on historical criticality accidents
including these two early incidents. The reactivities are estimated
to be 15 "cents" and 10 "cents" above prompt critical, where a "cent"
is 1% of the difference in reactivity between delayed and prompt
critical. The estimated times for the excursions is several seconds
for the first accident and half a second for the second one.

The calculated fission rate for the first incident at a 15 cent
reactivity climbs to a peak of 10**19 fissions per second after a
couple of milliseconds, then drops to less than 10**16 fissions per
second well before .01 seconds, declining slowly after that. This
dropoff is presumably due to thermal expansion from the power spike.
Before one second has elapsed, the power output closely matches an
exactly prompt critical assembly, indicating that the system is
back to the edge of criticality. Total fission yield was estimated
at 10**16 fissions.

The report describes other accidents, both US and Soviet. Some of
them did melt parts of the core. There was an interesting Soviet
one that reached steady state at around 480 Watts of power output
with a uranium core at around 865 degrees C. It went through some
slow power oscillations at 40 minute intervals on its way to
equilibrium. It had to be disassembled by remote control.

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