Discussion:
fission question
(too old to reply)
eric adam
2004-07-03 00:09:17 UTC
Permalink
im not a scientist. i was reading about cerenkov radiation and
neutrinos. it said that the amount of blue glow produced is tantamount
to the amount of fission that occurs. isnt fission an incredibly
energetic process? i guess the question is what is the difference
between the fission that produces big nuclear explosions and the
fission that produces little blue glows in labs?
j***@specsol-spam-sux.com
2004-07-03 00:19:52 UTC
Permalink
Post by eric adam
im not a scientist. i was reading about cerenkov radiation and
neutrinos. it said that the amount of blue glow produced is tantamount
to the amount of fission that occurs. isnt fission an incredibly
energetic process? i guess the question is what is the difference
between the fission that produces big nuclear explosions and the
fission that produces little blue glows in labs?
A lot of noise, heat, radiation, a mushroom cloud, and a big hole in the
ground.

Other than that, not much.
--
Jim Pennino

Remove -spam-sux to reply.
Gregory L. Hansen
2004-07-03 02:38:42 UTC
Permalink
Post by eric adam
im not a scientist. i was reading about cerenkov radiation and
neutrinos. it said that the amount of blue glow produced is tantamount
to the amount of fission that occurs. isnt fission an incredibly
energetic process? i guess the question is what is the difference
between the fission that produces big nuclear explosions and the
fission that produces little blue glows in labs?
To make a big nuclear explosion, you need a whole bunch of fissions in
rapid succession. But they can come a lot slower and still make a little
blue glow.

One of the problems in designing the nuclear bomb was the tendency for the
nuclear material to blow itself apart before much of the fuel was
consumed. With uranium, a gun-type device was good enough, which
separated two sub-critical hemispheres in a barrel and used a chemical
explosion to drive them together. Plutonium goes faster, and that's why
implosion devices are used for that. A rather complicated shell of
chemical explosives and detonators surround a shell of plutonium,
and scrunch it into a little ball.

You don't get a bona fide nuclear explosion by accident. But any lump of
fissile material can make a little blue glow.
--
"Beer is living proof that God loves us and wants us to be happy."
-- Benjamin Franklin
Steve Harris
2004-07-03 06:22:52 UTC
Permalink
Post by Gregory L. Hansen
You don't get a bona fide nuclear explosion by accident. But any lump of
fissile material can make a little blue glow.
Well, not any lump. It has to be a big enough lump to generate a lot
of fission products, which means critical or over. The blue glow of
swimming pool reactors is Cherenkov radiation from betas from beta
decay of neutron rich fission products. Alphas and gammas and neutrons
don't do it. You need of course a critical mass of fissile material to
see the glow from a swimming pool reactor.

There's a question as to where the glow comes from in prompt critical
nuke accidents, as happened twice as Los Alamos with 6.2 kg Pu-239
bomb cores, going prompt critical when surrounded by shielding and
assembled. I doubt that was Cherenkov glow, because betas in air don't
really go fast enough for that (the speed of light in air is too close
to what it is in vacuum). Not too many people have ever seen the glow
from an air prompt-critical accident, and many of those that have,
didn't live. One can speculate it was purple glow from nitrogen
ionization from a hell of a lot of betas (neutrons are not good
ionizers, but there are so many fast ones in this kind of accident
that maybe even they show). Or maybe fission fragments making it out
of the nickel shell of a Pu-239 core.
Eric Gisse
2004-07-03 11:11:29 UTC
Permalink
***@ix.netcom.com (Steve Harris ***@ROMAN9.netcom.com) wrote in message news:<***@posting.google.com>...
[snip]
Post by Steve Harris
There's a question as to where the glow comes from in prompt critical
nuke accidents, as happened twice as Los Alamos with 6.2 kg Pu-239
bomb cores, going prompt critical when surrounded by shielding and
assembled. I doubt that was Cherenkov glow, because betas in air don't
really go fast enough for that (the speed of light in air is too close
to what it is in vacuum). Not too many people have ever seen the glow
from an air prompt-critical accident, and many of those that have,
didn't live. One can speculate it was purple glow from nitrogen
ionization from a hell of a lot of betas (neutrons are not good
ionizers, but there are so many fast ones in this kind of accident
that maybe even they show). Or maybe fission fragments making it out
of the nickel shell of a Pu-239 core.
2?

The first one that I know of was in the Manhattan project days, killed
one scientist too. That was the one where he slipped the tool holding
the hemispheres apart and they merged, and he moved them apart with
this hands.

When was the second?
Steve Harris
2004-07-03 23:02:02 UTC
Permalink
Post by Eric Gisse
[snip]
Post by Steve Harris
There's a question as to where the glow comes from in prompt critical
nuke accidents, as happened twice as Los Alamos with 6.2 kg Pu-239
bomb cores, going prompt critical when surrounded by shielding and
assembled. I doubt that was Cherenkov glow, because betas in air don't
really go fast enough for that (the speed of light in air is too close
to what it is in vacuum). Not too many people have ever seen the glow
from an air prompt-critical accident, and many of those that have,
didn't live. One can speculate it was purple glow from nitrogen
ionization from a hell of a lot of betas (neutrons are not good
ionizers, but there are so many fast ones in this kind of accident
that maybe even they show). Or maybe fission fragments making it out
of the nickel shell of a Pu-239 core.
2?
The first one that I know of was in the Manhattan project days, killed
one scientist too. That was the one where he slipped the tool holding
the hemispheres apart and they merged, and he moved them apart with
this hands.
When was the second?
That *was* the second: the Slotin case in May 46. Many people have
assumed it was first, a misconception fostered by it being featured in
the movie "Fat Man and Little Boy" as happening even before the
Trinity test. Slotin was with 6 other people, but he was the only one
getting enough radiation to die (a week later)

The first incident was in late Aug 1945, just 2 weeks after the end of
the war. I suspect it used the same core that would otherwise have
gone into the 3rd Japanese nuke. Daghlian, working alone, fatally
radiated himself with it by dropping a neutron moderator/reflector
brick onto a nearly assembled mini-nuclear reactor made from the
Pu-239 bomb core. He died 3 weeks later.

http://www.campusprogram.com/reference/en/wikipedia/l/li/list_of_nuclear_accidents.html


There is one more case involving a prompt critical accident with loss
of life from radiation per se (not just poisoninng or explosians in
reactors), which happpened in the late 50's when a vat of plutonium
solution got to critical and went FOOF. This radiation dose eventually
killed the crane opperator.

All three accidents mentioned above each killed one person from
radiation.

SBH
Steve Harris
2004-07-03 06:23:23 UTC
Permalink
Post by Gregory L. Hansen
You don't get a bona fide nuclear explosion by accident. But any lump of
fissile material can make a little blue glow.
Well, not any lump. It has to be a big enough lump to generate a lot
of fission products, which means critical or over. The blue glow of
swimming pool reactors is Cherenkov radiation from betas from beta
decay of neutron rich fission products. Alphas and gammas and neutrons
don't do it. You need of course a critical mass of fissile material to
see the glow from a swimming pool reactor.

There's a question as to where the glow comes from in prompt critical
nuke accidents, as happened twice as Los Alamos with 6.2 kg Pu-239
bomb cores, going prompt critical when surrounded by shielding and
assembled. I doubt that was Cherenkov glow, because betas in air don't
really go fast enough for that (the speed of light in air is too close
to what it is in vacuum). Not too many people have ever seen the glow
from an air prompt-critical accident, and many of those that have,
didn't live. One can speculate it was purple glow from nitrogen
ionization from a hell of a lot of betas (neutrons are not good
ionizers, but there are so many fast ones in this kind of accident
that maybe even they show). Or maybe fission fragments making it out
of the nickel shell of a Pu-239 core.
Steve Harris
2004-07-03 23:08:58 UTC
Permalink
Post by Gregory L. Hansen
Post by eric adam
im not a scientist. i was reading about cerenkov radiation and
neutrinos. it said that the amount of blue glow produced is tantamount
to the amount of fission that occurs. isnt fission an incredibly
energetic process? i guess the question is what is the difference
between the fission that produces big nuclear explosions and the
fission that produces little blue glows in labs?
To make a big nuclear explosion, you need a whole bunch of fissions in
rapid succession. But they can come a lot slower and still make a little
blue glow.
One should mention the blue glow that surrounds really strong alpha
emitters like radium and especially polonium. But that's certainly
due to nitrogen ionization from alphas. I suppose you could consider
alpha emission a sort of spontaneous fission.

But I know of no things that glow from less than crtical mass nuclear
neutron initiated type fission. That's very hard to control. You've
either got too little to see anything, or so much that with just an
air shield, you're going to get enough rads in a few seconds to
(eventually) kill you.

SBH
x
2004-07-03 16:17:36 UTC
Permalink
The fission reaction in a nuclear explosion is a controlled out-of-control
fission reaction. That is, the two fissile masses are slamed together at
high velocity with a trmendous amount of heat applied at the critical time
to force a out-of-control chain reaction. The reaction is the production of
an enormous amount of neutrons which are forced or deflected back into the
fissile mass creating more heat and more neutrons and the reaction is then
considered to be out of control and the heavy nuclei of the fissile
material rips apart releasing the energy that kept it intact. The energy
involved is the strong nuclear force. In a lab, the fissile material is not
allowed to over heat. The amount of neutrons that are allowed to escape is
controlled by graphite rods that absorb any excess amount of neutrons. So
the lab fissile material never reaches a temperature that would cause it to
go into critical mass and 'out of control'.
Post by eric adam
im not a scientist. i was reading about cerenkov radiation and
neutrinos. it said that the amount of blue glow produced is tantamount
to the amount of fission that occurs. isnt fission an incredibly
energetic process? i guess the question is what is the difference
between the fission that produces big nuclear explosions and the
fission that produces little blue glows in labs?
--
Using M2, Opera's revolutionary e-mail client: http://www.opera.com/m2/
m***@cars3.uchicago.edu
2004-07-04 07:42:49 UTC
Permalink
Post by x
The fission reaction in a nuclear explosion is a controlled out-of-control
fission reaction. That is, the two fissile masses are slamed together at
high velocity with a trmendous amount of heat applied at the critical time
to force a out-of-control chain reaction. The reaction is the production of
an enormous amount of neutrons which are forced or deflected back into the
fissile mass creating more heat and more neutrons and the reaction is then
considered to be out of control and the heavy nuclei of the fissile
material rips apart releasing the energy that kept it intact. The energy
involved is the strong nuclear force. In a lab, the fissile material is not
allowed to over heat. The amount of neutrons that are allowed to escape is
controlled by graphite rods that absorb any excess amount of neutrons. So
the lab fissile material never reaches a temperature that would cause it to
go into critical mass and 'out of control'.
Temperature has nothing to do with it.

Mati Meron | "When you argue with a fool,
***@cars.uchicago.edu | chances are he is doing just the same"
Steve Harris
2004-07-04 22:02:53 UTC
Permalink
Post by m***@cars3.uchicago.edu
Post by x
The fission reaction in a nuclear explosion is a controlled out-of-control
fission reaction. That is, the two fissile masses are slamed together at
high velocity with a trmendous amount of heat applied at the critical time
to force a out-of-control chain reaction. The reaction is the production of
an enormous amount of neutrons which are forced or deflected back into the
fissile mass creating more heat and more neutrons and the reaction is then
considered to be out of control and the heavy nuclei of the fissile
material rips apart releasing the energy that kept it intact. The energy
involved is the strong nuclear force. In a lab, the fissile material is not
allowed to over heat. The amount of neutrons that are allowed to escape is
controlled by graphite rods that absorb any excess amount of neutrons. So
the lab fissile material never reaches a temperature that would cause it to
go into critical mass and 'out of control'.
Temperature has nothing to do with it.
Mati Meron | "When you argue with a fool,
COMMENT:

Indeed. Guys like Daghlian and Slotin fried themselves from an
absolutely cold start.

Now, the interesting thing is why Daghlian and Slotin friend
themselves and Fermi with the first reactor in Chicago didn't. And
the answer is that Fermi's carbon-block moderated reactor was so huge
that he could add or subtract fractional extra moderator so slowly
that he had a chance to get the machine into the "barely critical"
realm where criticality depends on the decay of neutron-producing
fission products with half-lifes of a couple of minutes, and those
half-lives determine the doubling time of the fission rate and the
radiation in that region. So you have time to watch it go up, and shut
it down.

Whereas, if you screw up like Daghlian and Slotin and change the
configuration a whole lot all at once, you can go right on through the
controllable-critical region into the prompt-critical region, and then
your radiation doubling time is so small that you have chance for
control, and go right up to lethal reaction powers, immediately. The
neutrons from that, fry you.

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?

Inquiring minds want to know. I wonder if they had the balls to repeat
these accidents under control "dragon" type conditions, just to see
what really DID happen? I'll bet not. If they did, it's still
classified.

Steve
m***@cars3.uchicago.edu
2004-07-05 05:20:11 UTC
Permalink
Post by Steve Harris
Post by m***@cars3.uchicago.edu
Post by x
The fission reaction in a nuclear explosion is a controlled out-of-control
fission reaction. That is, the two fissile masses are slamed together at
high velocity with a trmendous amount of heat applied at the critical time
to force a out-of-control chain reaction. The reaction is the production of
an enormous amount of neutrons which are forced or deflected back into the
fissile mass creating more heat and more neutrons and the reaction is then
considered to be out of control and the heavy nuclei of the fissile
material rips apart releasing the energy that kept it intact. The energy
involved is the strong nuclear force. In a lab, the fissile material is not
allowed to over heat. The amount of neutrons that are allowed to escape is
controlled by graphite rods that absorb any excess amount of neutrons. So
the lab fissile material never reaches a temperature that would cause it to
go into critical mass and 'out of control'.
Temperature has nothing to do with it.
Mati Meron | "When you argue with a fool,
Indeed. Guys like Daghlian and Slotin fried themselves from an
absolutely cold start.
Now, the interesting thing is why Daghlian and Slotin friend
themselves and Fermi with the first reactor in Chicago didn't. And
the answer is that Fermi's carbon-block moderated reactor was so huge
that he could add or subtract fractional extra moderator so slowly
that he had a chance to get the machine into the "barely critical"
realm where criticality depends on the decay of neutron-producing
fission products with half-lifes of a couple of minutes, and those
half-lives determine the doubling time of the fission rate and the
radiation in that region. So you have time to watch it go up, and shut
it down.
Whereas, if you screw up like Daghlian and Slotin and change the
configuration a whole lot all at once, you can go right on through the
controllable-critical region into the prompt-critical region, and then
your radiation doubling time is so small that you have chance for
control, and go right up to lethal reaction powers, immediately. The
neutrons from that, fry you.
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?
Inquiring minds want to know. I wonder if they had the balls to repeat
these accidents under control "dragon" type conditions, just to see
what really DID happen? I'll bet not. If they did, it's still
classified.
Hmm, interesting point...

Mati Meron | "When you argue with a fool,
***@cars.uchicago.edu | chances are he is doing just the same"
Norman Yarvin
2004-07-07 00:29:53 UTC
Permalink
Post by Steve Harris
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.
--
Norman Yarvin http://yarchive.net
Steve Harris
2004-07-07 18:59:18 UTC
Permalink
Post by Norman Yarvin
Post by Steve Harris
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. We all have the picture of it going on and
staying on until the WH brick was knocked away, but I doubt if the
people observing were following closely enough to note if the power
might have been decreasing near the end. Indeed, the fact that in both
cases Slotin and Daghlian went in vaguely suggests that maybe the
initial flair cooled a bit, or at least didn't keep going up and up.

Any nuke reactor that runs at constant power must be running in some
regime where there is a negative feedback loop of some kind-- usually
partly an active one (which is why those reactor control rooms are so
frigging complicated). Something which is outside the mechanics of the
simple nuclear fission reaction per se, which is inherrently unstable
and exponential, like any chain reaction process. Fission reactions,
like fires in large masses of mixed fuel/oxidizer, or thermal
decomposition in large masses of TNT, are not inherrently stable and
smooth.

For there to be a quiet burn, as there apparently was (albeit a high
power one), that HAD to have been happening in both the Daghlian and
Slotin accidents, because there was no full fizzle-meltdown of the
kind that is supposed to happen in bombs when you assemble them but
don't do it exactly right, or do it without inertial confinement. The
Daghlian and Slotin criticality conditins went on for seconds, which
is an *eternity* in nuclear fission physics. We just don't think of it
that way.

Both the Slotin and Daghlian accidents remind me of the old Twain
story of the man who dropped a cigar at the black powder factory, and
"burnt up near half a bushel before he could get it put out." That's
a funny story if you know black powder. And the Slotin and Daghlian
accidents I think should be just as funny-peculiar to the average
person reading them who has had any experience with reactor control.
So I wonder what I'm missing.

SBH
Norman Yarvin
2004-07-07 21:10:45 UTC
Permalink
Post by Steve Harris
Post by Norman Yarvin
Post by Steve Harris
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.
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.)
--
Norman Yarvin http://yarchive.net
Steve Harris
2004-07-09 01:42:25 UTC
Permalink
Post by Norman Yarvin
Post by Steve Harris
Post by Norman Yarvin
Post by Steve Harris
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.
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.

Come on, you real physicists reading this. Any ideas?

SBH
Norman Yarvin
2004-07-11 01:53:26 UTC
Permalink
Post by Steve Harris
Post by Norman Yarvin
Post by Steve Harris
Post by Norman Yarvin
Post by Steve Harris
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.
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.)
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
Steven Sharp
2004-07-19 21:05:42 UTC
Permalink
Post by Norman Yarvin
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.
Post by Norman Yarvin
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.
Post by Norman Yarvin
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.
Post by Norman Yarvin
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.
Harry Conover
2004-07-29 03:31:44 UTC
Permalink
Post by Steven Sharp
Post by Norman Yarvin
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.
Out of where did you learn this remarkable tidbit of information?

It doesn't seem to appear on my table of neutron capture
cross-sections, so maybe I'm missing something.

Please elaborate.

Harry C.
Steven Sharp
2004-07-29 23:15:06 UTC
Permalink
Post by Harry Conover
Post by Steven Sharp
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.
Out of where did you learn this remarkable tidbit of information?
It doesn't seem to appear on my table of neutron capture
cross-sections, so maybe I'm missing something.
Please elaborate.
I believe that you have misunderstood the statement. It was not saying
that the fission cross-sections of different isotopes, and therefore the
critical mass of different isotopes, is related in this way to the density
of the isotope.

It is saying that once you pick a specific fissile isotope, the total mass
required for criticality is related to the density of the mass. If the
density is changed by temperature, pressure, phase changes, voids in the
material, concentration in a solution, etc., then the critical mass
changes.

You may be thinking of the critical mass as a property of an isotope
from a databook, given for a bare solid sphere in a certain phase at
laboratory temperatures and pressures, and listed along with its cross-sections.

On the other hand, we are talking about how the critical mass of that
same material changes as we move away from those standard conditions:
adding neutron reflectors or changing the temperature. And anything
that changes the density of the material, such as thermal expansion,
changes the critical mass in inverse proportion to the square of the
density.
Harry Conover
2004-07-31 02:36:32 UTC
Permalink
Post by Steven Sharp
Post by Harry Conover
Post by Steven Sharp
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.
Out of where did you learn this remarkable tidbit of information?
It doesn't seem to appear on my table of neutron capture
cross-sections, so maybe I'm missing something.
Please elaborate.
I believe that you have misunderstood the statement. It was not saying
that the fission cross-sections of different isotopes, and therefore the
critical mass of different isotopes, is related in this way to the density
of the isotope.
It is saying that once you pick a specific fissile isotope, the total mass
required for criticality is related to the density of the mass. If the
density is changed by temperature, pressure, phase changes, voids in the
material, concentration in a solution, etc., then the critical mass
changes.
Well obviously this is true, and is the very basis for the plutonium
bombs that are triggered simultanously by explosive compression and
the injection of neutrons.

Still, this does not make your question any clearer. What sort of
UNCLASSIFED information are you seeking and what is your purpose for
needing sensitive defense information of this type.

You should realize that information of this type is not completely
analytical, which is precisely why experiments called "Tickling the
Dragon's Tail" are conducted, and why the first implosion type bomb
was tested in New Mexico prior to its sister design being dropped on
Japan.

If you want this type of parametric information on fissionable
material that goes well beyond what is printed in textbooks, then you
better have a damn good justification for needing it! Beyond that,
you simply going to have to live with the fact that for fast fission
(as in an atomic bomb), critical mass decreases as fissionable
material density increases. Reflectors also come into play, but these
are not classified so you can read about these in most nuclear physics
textbooks.


Harry C.
Michael Moroney
2004-08-09 14:16:15 UTC
Permalink
What exactly happened during that accident in Japan, where they apparently
accidentally made a "nuclear reactor in a bucket" by putting too much
enriched fuel in a bucket in 1999 in a fuel reprocessing plant? A few
people were killed.
--
-Mike
Steven Sharp
2004-08-11 00:01:22 UTC
Permalink
Post by Michael Moroney
What exactly happened during that accident in Japan, where they apparently
accidentally made a "nuclear reactor in a bucket" by putting too much
enriched fuel in a bucket in 1999 in a fuel reprocessing plant? A few
people were killed.
It was fairly typical of criticality accidents during processing. The
major difference was that the plant was in the middle of a highly
populated area, and that they were completely unprepared for such an
accident, which the company had decided was not a possibility. Two of
the workers died within months, and the other received a heavy dose.
Radiation readings at the border of the site were high enough that
residents within 350 meters were advised to evacuate.

The company was processing a uranyl nitrate solution. They deviated from
the prescribed procedures in order to speed up processing. They were
supposed to transfer the solution to a container consisting of vertical
columns. Apparently these were awkward to work with, so they used a
different container that was shorter and larger around. An amount of
solution that would not have been critical in the columns was critical
in the more compact shape of the container they used. The reaction
continued for around 20 hours until they were able to remotely drain
the water from a cooling jacket around the container, which reduced the
reactivity (by reducing neutron reflection and moderation).
ZZBunker
2004-08-09 19:14:25 UTC
Permalink
Post by Harry Conover
Post by Steven Sharp
Post by Harry Conover
Post by Steven Sharp
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.
Out of where did you learn this remarkable tidbit of information?
It doesn't seem to appear on my table of neutron capture
cross-sections, so maybe I'm missing something.
Please elaborate.
I believe that you have misunderstood the statement. It was not saying
that the fission cross-sections of different isotopes, and therefore the
critical mass of different isotopes, is related in this way to the density
of the isotope.
It is saying that once you pick a specific fissile isotope, the total mass
required for criticality is related to the density of the mass. If the
density is changed by temperature, pressure, phase changes, voids in the
material, concentration in a solution, etc., then the critical mass
changes.
Well obviously this is true, and is the very basis for the plutonium
bombs that are triggered simultanously by explosive compression and
the injection of neutrons.
Still, this does not make your question any clearer. What sort of
UNCLASSIFED information are you seeking and what is your purpose for
needing sensitive defense information of this type.
You should realize that information of this type is not completely
analytical, which is precisely why experiments called "Tickling the
Dragon's Tail" are conducted, and why the first implosion type bomb
was tested in New Mexico prior to its sister design being dropped on
Japan.
If you want this type of parametric information on fissionable
material that goes well beyond what is printed in textbooks, then you
better have a damn good justification for needing it! Beyond that,
you simply going to have to live with the fact that for fast fission
(as in an atomic bomb), critical mass decreases as fissionable
material density increases. Reflectors also come into play, but these
are not classified so you can read about these in most nuclear physics
textbooks.
The negative feedback in nuclear reactor control rooms
is IDENTICAL to the negative feedback in conventional
power plant control rooms, regardless of the
power output of the plant, from 100 Watts to
1000 MW. So it is actually brain-dead simple.

It is a sign that says:

UNAUTHORIZED PERSONNEL, particularly chemists,
NOT ALLOWED IN THE CONTROL ROOM.
Post by Harry Conover
Harry C.
Steven Sharp
2004-08-10 23:47:43 UTC
Permalink
Post by Harry Conover
Still, this does not make your question any clearer. What sort of
UNCLASSIFED information are you seeking and what is your purpose for
needing sensitive defense information of this type.
The only information needed to check the current hypothesis is the
thermal expansion coefficient of the plutonium-gallium alloy being
used in the bomb core. My statement about the relationship between
density and critical mass was not a question, as you appear to be
the only one questioning it.

The purpose of the information should be clear from the title of
the posting, as well as earlier posts in the thread. Steve Harris
is trying to reconcile the events of these two early criticality
accidents with what he understands of the physics involved. It
is a matter of intellectual and scientific curiosity.
Post by Harry Conover
You should realize that information of this type is not completely
analytical, which is precisely why experiments called "Tickling the
Dragon's Tail" are conducted, and why the first implosion type bomb
was tested in New Mexico prior to its sister design being dropped on
Japan.
Critical mass values are indeed difficult to determine analytically,
especially with the limited computing resources available during the
Manhattan Project. The fact that fission neutrons come in a spectrum
of possible energies, which can change further during scattering, and
that the neutron cross-sections depend on the energy, make this very
complex to analyze.
Post by Harry Conover
If you want this type of parametric information on fissionable
material that goes well beyond what is printed in textbooks, then you
better have a damn good justification for needing it! Beyond that,
you simply going to have to live with the fact that for fast fission
(as in an atomic bomb), critical mass decreases as fissionable
material density increases. Reflectors also come into play, but these
are not classified so you can read about these in most nuclear physics
textbooks.
While the actual critical mass values are difficult to determine
analytically, the relationship between density and critical mass
appears to be quite easy to analyze. A straightforward argument
reveals that critical mass is inversely proportional to the square
of the density.

I also think that you are underestimating the amount of information
on weapon physics and engineering that is readily available or can
be derived.
Steve Harris
2004-08-10 01:01:41 UTC
Permalink
Post by Norman Yarvin
Post by Steve Harris
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.
It's just hard to believe. How much is a plutonium sphere going to
expand as you heat it 400 C? Not bloody much. So it's amazing the
whole assembly didn't go POOF in a semi-explosive fizzle.

Think of it semi-quantitatively this way. If you drop a WC brick on a
Pu sphere which is just critical with 20 bricks around it already, you
block and reflect neurons from some large % of its remaining surface.
So the effective ratio of "loss-surface" to volume goes down hugely.
By 10's of %'s, I imagine. With only the top surface exposed, you
might block 20% of the remainder. How much does the sphere have to
expand to make up for that? I would think a heck of a lot.
Post by Norman Yarvin
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.
Not that healthy. 6% or 7%.
Post by Norman Yarvin
That makes a few orders of magnitude
difference in the doubling time.
Yes, but it only goes from nanoseconds to microseconds. Thermal
neutrons of course go 41% faster than hydrogen molecules. So you get 2
* speed of sound * SQRT 30 = 3.8 km/sec. Vs. fission neutrons going
5000 times faster. So doubling times are 2 ns vs 10 microseconds or
something.
Post by Norman Yarvin
If the assembly were only very
slightly supercritical to begin with, the doubling time could come
down to human timescales.
I can't think of any way it can be at human time-scales unless it's in
the sub-prompt region where we're relying on short lived
neutron-emitting isotope decay. Anything over that fries you either
instantly, or instantly-instantly.

The Los Alamos paper pretty much confirms this. Thermal expansion
stops the first power spike which is gigantic and more or less
instant. After that, the thing was cooking along pretty much at near
equilibrium power output on the edge of prompt/super criticality. I
guess all thermal stuff is what provides the feedback in this region.

SBH
Norman Yarvin
2004-08-10 22:20:38 UTC
Permalink
Post by Steve Harris
Think of it semi-quantitatively this way. If you drop a WC brick on a
Pu sphere which is just critical with 20 bricks around it already, you
block and reflect neutrons from some large % of its remaining surface.
So the effective ratio of "loss-surface" to volume goes down hugely.
By 10's of %'s, I imagine. With only the top surface exposed, you
might block 20% of the remainder. How much does the sphere have to
expand to make up for that? I would think a heck of a lot.
That argument is fair, but its consequence is that the arrangement must
have been significantly subcritical, instead of "just critical", before
the last brick was added, so that the last brick brought it just above
criticality.
--
Norman Yarvin http://yarchive.net
Steven Sharp
2004-08-12 00:51:57 UTC
Permalink
Post by Steve Harris
It's just hard to believe. How much is a plutonium sphere going to
expand as you heat it 400 C? Not bloody much. So it's amazing the
whole assembly didn't go POOF in a semi-explosive fizzle.
So let's do some math to check the plausibility. I don't have the
thermal expansion coefficient for the plutonium, just some indication
that it is very small but positive. So I'll start with a similar
situation with uranium, just to establish the credibility of thermal
expansion of a core as a quenching mechanism. I will not take into
account the fact that the reflector is not heating up nearly as fast
as the core and thus not expanding as much.

Assume a reactivity increase to 15 cents over prompt critical, which
would be 1.15 dollars over delayed critical. In uranium, the difference
between delayed and prompt critical mass is 2.4%, so assume an increase
to 2.8% above delayed critical mass. Since critical mass is inversely
proportional to the square of density, that would be canceled by a
volume increase of 1.4%. That requires a linear expansion of 0.46%.
The thermal expansion coefficient of uranium is 1.39e-5/K, which gives
us a required temperature increase of 330K.

So a uranium core could be quenched by thermal expansion from this
reactivity to sub-delayed-critical by less than a 400C increase.

Plutonium has a lower thermal expansion coefficient. However, it
only has a difference between delayed and prompt critical mass of
0.8%, so a dollar of reactivity is less for it. It only requires
a linear expansion of 0.15% to quench a 1.15 dollar reactivity
increase. And to get below prompt critical only requires a 0.02%
expansion, which only requires a tiny expansion coefficient.

If you want to understand this, there is no substitute for doing
the math.
Steven Sharp
2004-08-14 02:58:20 UTC
Permalink
Post by Steve Harris
Think of it semi-quantitatively this way. If you drop a WC brick on a
Pu sphere which is just critical with 20 bricks around it already, you
block and reflect neurons from some large % of its remaining surface.
So the effective ratio of "loss-surface" to volume goes down hugely.
By 10's of %'s, I imagine. With only the top surface exposed, you
might block 20% of the remainder. How much does the sphere have to
expand to make up for that? I would think a heck of a lot.
I think this makes some incorrect assumptions about the configuration
of the reflector. I had a similar mental picture of bricks stacked
around the sides of the core with the top still exposed. With further
consideration, I think this may be incorrect. I think it is much more
likely that the top had already been covered, and the last brick was
completing or nearly completing a rough cube around the core.

The photo in the Los Alamos report shows the core sitting in a hemi-
spherical hollow in a reflector block, with bricks stacked up about
even with the top of that block. The text describes this as having
about half of the blocks in place. That implies that the full
configuration had another hollowed-out block sitting on the top of
the core, with bricks built up on the sides, and another layer of
bricks on the top.

The bricks are described as 4.4 kg, and the total reflector weight
as 236 kg. So it isn't adding one brick to 20 bricks, it is adding
one brick to the equivalent of over 50 bricks. Each brick looks
like it is 2x1x1 in shape, with the reflector having a length of 5
on a side (2 brick-lengths plus a brick-width). A cube-shaped
reflector would be 5x5x5 and require the equivalent of 62.5 bricks.
That would be around 275 kg minus 7kg for the core hollow giving
268 kg, which is close to the total reflector weight. Without the
top layer of bricks, it would be only 220 kg, which is too low.
Without the close-fitting block over the core, the mass wouldn't be
anywhere close to right. So the core must have been completely
covered already, and that last brick was part of the top layer.

There is another reason to believe that the core must have been
thoroughly covered already. This was a Fatman bomb core. It had
to be significantly subcritical when inside the bomb, where it was
surrounded by a 7 cm thick natural uranium reflector. Based on
the figures above, if this tungsten carbide reflector was cubical,
it would have been around 8 cm thick from the core to the center
of a cube face. Tungsten carbide is only slightly better than
uranium as a reflector. For this assembly to be critical, the
core must have been fully covered.

Based on all this, the last brick increased the reflector mass
by less than 2%. The brick was not directly against the core,
but was at least 3 cm away. That is more than one neutron mean
free path away, where the reflector effectiveness has dropped
off. This would not have increased the reactivity by a large
amount.

At any rate, we already have a good estimate of the reactivity
of the assembly from the Los Alamos report, so this is moot. The
assembly was barely prompt critical.
Post by Steve Harris
Post by Norman Yarvin
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.
Yes, but it only goes from nanoseconds to microseconds. Thermal
neutrons of course go 41% faster than hydrogen molecules. So you get 2
* speed of sound * SQRT 30 = 3.8 km/sec. Vs. fission neutrons going
5000 times faster. So doubling times are 2 ns vs 10 microseconds or
something.
There wouldn't have been all that much moderation anyway. By the time
a neutron has scattered enough times in the reflector to slow down much,
the odds of it getting back to the core rather than escaping are low.
You get a small slowdown for a small fraction of the neutrons.
Post by Steve Harris
I can't think of any way it can be at human time-scales unless it's in
the sub-prompt region where we're relying on short lived
neutron-emitting isotope decay. Anything over that fries you either
instantly, or instantly-instantly.
The Los Alamos paper pretty much confirms this. Thermal expansion
stops the first power spike which is gigantic and more or less
instant. After that, the thing was cooking along pretty much at near
equilibrium power output on the edge of prompt/super criticality. I
guess all thermal stuff is what provides the feedback in this region.
Not quite on the edge of prompt. From the appendix on quenching
mechanisms, the reactivity "reflects" around prompt critical, i.e.
it goes as much below prompt critical as it initially went above.
This makes sense because it has to cut down the neutron flux, which
requires a neutron multiplication below 1, before the power output
drops and isn't reducing reactivity so fast.

So being barely prompt critical slowed the time scales down to
microseconds, which allowed time for thermal expansion to reduce
the core to sub-prompt critical. It was still delayed critical,
which might have been beyond the ability of thermal expansion to
quench before melting, but was slow enough for human time scales.
Steven Sharp
2004-08-14 22:41:34 UTC
Permalink
Post by Steven Sharp
The bricks are described as 4.4 kg, and the total reflector weight
as 236 kg. ... Each brick looks
like it is 2x1x1 in shape, with the reflector having a length of 5
on a side (2 brick-lengths plus a brick-width). A cube-shaped
reflector would be 5x5x5 and require the equivalent of 62.5 bricks.
I now have a better theory for the full assembly. The top and bottom
layers were only 4x4 instead of 5x5, making the shape a little more
spherical. With the middle 3 layers that are 5x5 (including the 3x3x3
for the form-fitting blocks), that is the equivalent of 53.5 bricks
or 235.4 kg. That is dead-on the total reflector mass. They didn't
subtract out the spherical cavity for the core in this total. This
also resolves the issue that you couldn't build a top or bottom 5x5
layer out of an integer number of 2x1 bricks, but you _can_ build
a 4x4 layer. It also explains why the picture shows the bottom layer
in some kind of frame, with tape or strapping around the bottom of the
second layer bricks. The 5x5 layer would have hung out over the lower
4x4 layer and needed support to keep the bricks from falling off.

This configuration matches the available information very well. As a
result, we know that there was already at least 3 cm of reflector
between the core and the last brick. It would probably have been one
of the 4 outermost bricks of the top layer. Even if it fell perfectly
into its intended position (which is the closest it could get) it
would have been 4.5 cm away at its closest corner.

Steven Sharp
2004-07-22 00:02:00 UTC
Permalink
Post by Steve Harris
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.
That should be "core", not "cores", since both accidents involved the
exact same core. Both times the nickel canning was still intact. The
estimated yields were 10**16 and 3*10**15 fissions. For comparison, that
corresponds to the energy of an ounce or two of high explosives (though
the fission energy would mostly be released as heat, not kinetic energy).
Post by Steve Harris
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.
As noted elsewhere, the dominant quenching mechanism was thermal
expansion of the core itself.
Post by Steve Harris
Inquiring minds want to know. I wonder if they had the balls to repeat
these accidents under control "dragon" type conditions, just to see
what really DID happen? I'll bet not. If they did, it's still
classified.
Well, the unclassified document that I have has a footnote that says:

"The Los Alamos National Laboratory archives include some data and comments
about a rerun performed 2 October 1945 to determine the radiation dose
received in the accident of 21 August 1945. The yield of the rerun was
about 6x10**15 fissions, but the prompt critical state was not reached.
The maximum reactivity of the system during this experiment was about
60 cents above delayed criticality."
Steven Sharp
2004-07-22 19:56:01 UTC
Permalink
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.

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.
John Schilling
2004-07-26 19:17:43 UTC
Permalink
Post by Steven Sharp
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.
Post by Steven Sharp
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.
And I'd wager it is the one at work in that case. Most of the other
candidates would not be effective for prompt, fast fission.
--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
*White Elephant Research, LLC * "There is no substitute *
****@spock.usc.edu * for success" *
*661-718-0955 or 661-275-6795 * -58th Rule of Acquisition *
Carey Sublette
2004-07-27 05:15:12 UTC
Permalink
Post by John Schilling
Post by Steven Sharp
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.
Post by Steven Sharp
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
Steven Sharp
2004-07-27 19:32:41 UTC
Permalink
Post by Carey Sublette
Post by Steven Sharp
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.
BTW, I slipped up on the decimal point here. In 1 msec, there would
be 7.1E10 neutrons, and a fission rate of 7.1E18 fissions/sec. It
doesn't affect the timescale much, but I didn't want somebody else to
catch it before me.
Post by Carey Sublette
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.
Another BTW: I think the multiplication factor was probably a little higher
than this. I found another reference to a reactivity increase in "cents"
with a corresponding multiplication factor that was slightly higher than
my estimate would have given. This one was for Uranium, so I can't apply
it directly. My guess is that the difference is because I just used the
fraction of neutrons that are delayed, but these delayed neutrons probably
have a lower energy, for which there is a higher fission cross-section.
The difference was less than 10%, so I am assuming I was close.
Post by Carey Sublette
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.
Agreed. However, the density still only has a linear dependence on the
temperature increase, not the cube of it. The coefficient for volume is
3 times the linear expansion coefficient, but still close to linear, i.e.
(1+delta)**3 is approximately 1+3*delta. That still leaves the critical
mass depending on the inverse square of the temperature change.

To get any further, we need the thermal coefficient value. And as John
Schilling points out, when it is this close to zero, trying to treat it
as constant is probably invalid.
Steven Sharp
2004-08-05 22:36:23 UTC
Permalink
Post by Steven Sharp
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.
OK, I managed to track down some papers online that provided more
metallurgical data on plutonium and plutonium alloyed with gallium.
One of them stated that the expansion coefficent was up to zero
with 2% (molar) gallium. This would make it positive with 3% or
more. Another showed a graph of the expansion over a temperature
range. For a 2% alloy, it started positive and then leveled off to
flat or a tiny bit negative. The line for a 6% alloy was quite positive
and close to linear. Interpolating for a 3% alloy would clearly
indicate a positive coefficient.

So that seems to confirm thermal expansion as a viable quenching
mechanism for the core. The papers also commented on the extremely
high specific heat of the alloy. In fact, delta phase plutonium has
the highest specific heat of any pure element at "low" temperatures.
That would affect the temperature increase.
Steve Harris
2004-07-22 23:04:24 UTC
Permalink
Post by Steven Sharp
Post by Steve Harris
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.
That should be "core", not "cores", since both accidents involved the
exact same core.
Fascinating. Didn't know that.


Both times the nickel canning was still intact. The
Post by Steven Sharp
estimated yields were 10**16 and 3*10**15 fissions. For comparison, that
corresponds to the energy of an ounce or two of high explosives (though
the fission energy would mostly be released as heat, not kinetic energy).
Very good info, and I check your figures. Yes, 1e10^16 fissions at
3.2e-11 J/fission is 320 kJ. At 4.4 kJ per gram of HE, that's 73 grams
of HE, which is a couple of ounces.

But take a look at the energy production rate. We can't figure the
first release lasted longer than maybe 5 seconds, so you're running
those 320 kJ out in 5 seconds, for a power of 64 kilowatts. That's
enough to melt the core if you let it keep up. The equalibrium temp is
the one at which the core loses that much in IR radiation from its
surface area of 0.022 m^2. So you need 2.9 megawatts/m^2, and
Stefan-Bolzmann gives you 2676 K for that, way above the melting point
of nickel. With outputs of 10's of kw, this is a meltdown situation at
equilibrium.

I figured the total heat capacity of the sphere at around 800 J/K, so
at a power output of 64 kw you're getting a temp increase of 80 C/sec,
which is only +400 C over the course of the event, in worst case. Not
*quite* enough to melt the plutonium, but getting very close (within
another few seconds). I figure only 2 or 3 times the total energy of
this though WOULD have melted the sphere, nickel can and all, which
means that in both cases the prompt attentions of the operators
probably did prevent meltdowns.
Post by Steven Sharp
Post by Steve Harris
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.
As noted elsewhere, the dominant quenching mechanism was thermal
expansion of the core itself.
I suppose. But that doesn't mean the situation wasn't headed for a
meltdown at the energies you post. It only explains why the power
levels didn't go to megawatts or gigawatts immediately, and blow the
thing apart before anybody could get to it.
Post by Steven Sharp
Post by Steve Harris
Inquiring minds want to know. I wonder if they had the balls to repeat
these accidents under control "dragon" type conditions, just to see
what really DID happen? I'll bet not. If they did, it's still
classified.
"The Los Alamos National Laboratory archives include some data and comments
about a rerun performed 2 October 1945 to determine the radiation dose
received in the accident of 21 August 1945. The yield of the rerun was
about 6x10**15 fissions, but the prompt critical state was not reached.
The maximum reactivity of the system during this experiment was about
60 cents above delayed criticality."
Wow, that's cheap. :) Read, of course, the modern "percent" for
"cents".


Now that you have given us the fission number it's interesting to
divide the total atoms in the sphere (1.55e25) by the fission rate
(figure 2e15/sec). You get something like 250 years. So if you could
have kept the sphere together there was enough Pu-239 to run it at the
power of the accident for centuries. Though of course it would have
gone subcritical from dilution long before.

Steve
Steven Sharp
2004-07-23 21:55:31 UTC
Permalink
Post by Steve Harris
But take a look at the energy production rate. We can't figure the
first release lasted longer than maybe 5 seconds, so you're running
those 320 kJ out in 5 seconds, for a power of 64 kilowatts.
A lot of the power is produced in an initial spike, followed by a lower
plateau. However, looking at the graph of the plateau, 64 kilowatts
is pretty close to the graph at 1 second elapsed time.
Post by Steve Harris
That's
enough to melt the core if you let it keep up. The equalibrium temp is
the one at which the core loses that much in IR radiation from its
surface area of 0.022 m^2. So you need 2.9 megawatts/m^2, and
Stefan-Bolzmann gives you 2676 K for that, way above the melting point
of nickel. With outputs of 10's of kw, this is a meltdown situation at
equilibrium.
Are you sure that radiation is the dominant heat loss mechanism from
the core in that timeframe? These cores were sitting inside
hemispherical hollows in metal reflectors. The thermal contact may not
have been great, but there would be some conduction into that larger
metallic mass, delaying meltdown.

In another posting I mentioned a Soviet accident that did reach
thermal equilibrium, lasting 6.5 days before being disassembled.
This involved a uranium core with copper reflector, stabilizing at
around 865 C and 480 watts. Those figures certainly support your
prediction of eventual meltdown for 10s of kw in a smaller core.
Post by Steve Harris
I figured the total heat capacity of the sphere at around 800 J/K, so
at a power output of 64 kw you're getting a temp increase of 80 C/sec,
which is only +400 C over the course of the event, in worst case. Not
*quite* enough to melt the plutonium, but getting very close (within
another few seconds). I figure only 2 or 3 times the total energy of
this though WOULD have melted the sphere, nickel can and all, which
means that in both cases the prompt attentions of the operators
probably did prevent meltdowns.
The nickel canning was only 5 mils thick, so it wouldn't have provided
much structural support.

Before melting, the plutonium would presumably have transitioned from
the delta to the epsilon phase. The NWFAQ says that the gallium alloy
is stabilized in delta phase up to at least 475 C. Normally the epsilon
phase is denser than the delta phase (which would have made the assembly
more reactive), but it's not clear to me what effect the gallium alloying
would have on this. The epsilon phase does have a significant positive
coefficient of expansion, which would tend to slow things down again
with further temperature increase. However, upon melting, liquid
plutonium is denser than solid plutonium. So the situation could have
gotten quite messy.

As an aside, Daghlian may have made the situation worse in the short
term by moving back in, since his body would have provided additional
neutron reflection and moderation.
Post by Steve Harris
Post by Steven Sharp
"The Los Alamos National Laboratory archives include some data and comments
about a rerun performed 2 October 1945 to determine the radiation dose
received in the accident of 21 August 1945. The yield of the rerun was
about 6x10**15 fissions, but the prompt critical state was not reached.
The maximum reactivity of the system during this experiment was about
60 cents above delayed criticality."
Wow, that's cheap. :) Read, of course, the modern "percent" for
"cents".
Actually, the "cent" is defined as "A unit of reactivity equal to
one-hundredth of the increment between delayed criticality and prompt
criticality (a dollar)." So yes, a percent, but of a particular change
in reactivity. So that was 60% of the way between delayed and prompt
criticality. The accidents themselves were estimated as 15 cents and
10 cents above prompt criticality (or 1.15 dollars and 1.10 dollars
above delayed criticality).

If you are interested in reading the Los Alamos report yourself, I
can send it to you. It is a 4M PDF file.
Steve Harris
2004-07-26 05:22:55 UTC
Permalink
Post by Steve Harris
But take a look at the energy production rate. We can't figure the
first release lasted longer than maybe 5 seconds, so you're running
those 320 kJ out in 5 seconds, for a power of 64 kilowatts.
A lot of the power is produced in an initial spike, followed by a lower
plateau. However, looking at the graph of the plateau, 64 kilowatts
is pretty close to the graph at 1 second elapsed time.
That's
enough to melt the core if you let it keep up. The equalibrium temp is
the one at which the core loses that much in IR radiation from its
surface area of 0.022 m^2. So you need 2.9 megawatts/m^2, and
Stefan-Bolzmann gives you 2676 K for that, way above the melting point
of nickel. With outputs of 10's of kw, this is a meltdown situation at
equilibrium.
Are you sure that radiation is the dominant heat loss mechanism from
the core in that timeframe? These cores were sitting inside
hemispherical hollows in metal reflectors. The thermal contact may not
have been great, but there would be some conduction into that larger
metallic mass, delaying meltdown.
COMMENT:

At 2.9 MW/m^2 and 2676 K you're getting 64 kw out by IR, and to get
more out by conduction your surface total "heat transfer coefficient"
would have to be greater than 2.9 MJ/sec/m^2 divided by 2676 K = about
1084 watts/m^2/degree K of deltaT. This is a pretty high number. A
well-stirred water bath can go up to heat transfer coefficients of
5000 watts/m^2/degree K, but I doubt you could do this with simple
physical contact with most solid materials, and certainly not with a
non-metal. So yes, at these temps, radiation cools better than just
about anything but running water.

Now, this doesn't mean radiation was the dominant mode of cooling
through the temp range of the two prompt-critical Los Alamos
accidents, which I'm guessing was 300 K up to . For one thing, with
only the top of the assembly open, at best, the view factor for heat
radiation leak into the room would have to be less than 1/6th of
theoretical (think of basically only one open side of a cube, in this
case the top). There's no way of easily calculating heat leak across a
small air gap into WC bricks—-- or at least I know of none (my guess
is that IR would quickly heat the surface of the reflector to sphere
surface temp, and then the heat sinking limit would be diffusivity of
a large amount of tungsten carbide from limited 0.02 m^2 contact
point, which I'm not going to be masochistic enough to attempt. And
finally the temp reached in the real accident was a lot lower if you
figure 320 kJ into an 800 J/K heat capacity Pu-239 sphere = +400 C. If
it got up to only 300 K room temp + 400 K for heating = 700 K, now
your max IR loss for an uncovered sphere is only 300 watts. And a
sixth of that is 50 watts. So yes, no doubt at *that* point, free air
convection and conduction through the bottom of the sphere into the
cradle is winning. But the temp is still going up fast.

The point is the sphere is generating 64 kw = almost 3 MW/m^2 and you
have to get rid of that somehow. Even with a stirred water bath and
its 5000 watt/K/m^2 heat transfer coefficient, you're going to get
calculated surface temp deltas of 2.9MW/5000 = 580 K. Which when
added to liquid water temp of at least 273 K gives you a minimum
sphere surface temp of 853 K, which of course is 580 C. Plutonium
melts around that temp, so if it's going to melt even in a running
water bath at ice temp, it's CERTAINLY going to melt at equilibrium
power output with the much worse conduction/convection conditions in
the Daghlian and Slotin accidents. Even if you subtract IR radiation
losses at 850 K (650 watts with viewfactor of 1/6 = 100 watts), you
still need to get rid of 2.8 MW, which gives a delta of 560 K between
the sphere and the "best" conductive bath you can imagine (which in
this case we didn't have), and that's still too close to Pu melting
point. So in the real world, it would have soon melted.

It's interesting what a little physics can tell you, eh?
Post by Steve Harris
Post by Steven Sharp
In another posting I mentioned a Soviet accident that did reach
thermal equilibrium, lasting 6.5 days before being disassembled.
This involved a uranium core with copper reflector, stabilizing at
around 865 C and 480 watts. Those figures certainly support your
prediction of eventual meltdown for 10s of kw in a smaller core.<<

COMMENT:
Yes, indeed, and those number, imply a fairly insulated sphere, with
IR cooling very much surpressed. If we figure a critical mass U-235
uranium sphere has to be at least 20 kg, then the surface area is 0.05
m^2 or so. Theoretical max IR cooling at 865 C = 1138 k and this area
is 4754 watts, which is 10 times what you say was actually getting
out. If the sphere is enclosed sphere in a copper reflector, then the
whole thing heats up, and you have an even bigger surface area
somewhere at 1138 K trying to cool by radiation. You shouldn't be able
to get that hot. The only way to do this is a big temp gap between
sphere and reflector. The implied "heat transfer coefficient" for such
a sphere and whatever bath is cooling it, is 9.6 kW/m^2 divided by 845
C delta or so = 11 watts/m^2/K. That's lousy—- about what you'd
expect from free air convection. So there must have been a bad air gap
between sphere and reflector, insulating it. If you had good thermal
contact between sphere and a piece of copper, then you'd see only a
small sphere-refelector temp gap, and equilibrium temp would be
limited by the radiation+convection contact resistance of this copper
reflector and the cool space around it, at equilibrium, and things
couldn't have gotten this hot. BTW, this implies the temp above has to
be the core temp-—it can't be the copper reflector temp unless they
have somehow insulated the reflector, too.
Post by Steve Harris
I figured the total heat capacity of the sphere at around 800 J/K, so
at a power output of 64 kw you're getting a temp increase of 80 C/sec,
which is only +400 C over the course of the event, in worst case. Not
*quite* enough to melt the plutonium, but getting very close (within
another few seconds). I figure only 2 or 3 times the total energy of
this though WOULD have melted the sphere, nickel can and all, which
means that in both cases the prompt attentions of the operators
probably did prevent meltdowns.
The nickel canning was only 5 mils thick, so it wouldn't have
provided
Post by Steve Harris
much structural support.
COMMENT:
Interesting. So no doubt meltdowns were very narrowly averted by just
seconds, in both cases.
Post by Steve Harris
Post by Steven Sharp
As an aside, Daghlian may have made the situation worse in the short
term by moving back in, since his body would have provided additional
neutron reflection and moderation.<<

COMMENT:
Yeah, but if he had run away, look what this would have become. Melted
plutonium running like mercury through the gaps in the WC bricks
pilled around the assembly, and then in globs and splatters,
mercury-style, all over the floor. It least it would have killed the
reaction. Thank goodness OSHA, the EPA and Hazmat didn't exist. Can
you imagine...?

If Slotin historically used Daglian's intact core, as you say, then
that means if Daghlian had run like hell instead of pilling out the
brick, he would (perhaps) have saved not only himself, but later
Slotin too. It would have been such a mess after Daghlian with all
those plutonium splatters all over hell that probably nobody else
would have done that ever again.

Sharp
Post by Steve Harris
If you are interested in reading the Los Alamos report yourself, I
can send it to you. It is a 4M PDF file.<

Yes, mail it to the "ix" address above. Thanks!!


Steve Harris
Steven Sharp
2004-07-26 22:05:42 UTC
Permalink
Post by Steve Harris
It's interesting what a little physics can tell you, eh?
Enough to convince me that a meltdown was on its way.
Post by Steve Harris
So there must have been a bad air gap
between sphere and reflector, insulating it. If you had good thermal
contact between sphere and a piece of copper, then you'd see only a
small sphere-refelector temp gap, and equilibrium temp would be
limited by the radiation+convection contact resistance of this copper
reflector and the cool space around it, at equilibrium, and things
couldn't have gotten this hot.
The core and reflector were made up of nested hemi-shells, so there
were multiple air gaps within the core, and within the bottom half of
the reflector. Adding a single hemi-shell of reflector to the top made
it go critical, so there were fewer gaps there.
Post by Steve Harris
BTW, this implies the temp above has to
be the core temp-?it can't be the copper reflector temp unless they
have somehow insulated the reflector, too.
Yes, this was explicitly stated to be the core temp.
Post by Steve Harris
Interesting. So no doubt meltdowns were very narrowly averted by just
seconds, in both cases.
Sure seems like it.

I see an error in my thinking that was causing me to believe that it
wouldn't happen. I was looking at the feedback mechanism (presumably
thermal expansion) that was quenching the reaction. Since it reduced
the reactivity below prompt critical in milliseconds, I assumed
everything would be okay. I assumed there would be an equilibrium at
the edge of prompt criticality, where power output would equal heat loss,
with the negative feedback keeping the core at that temperature.

But the graph in the report shows continued high power production after
the initial spike, in the tens of kilowatts. The reason for that should
have been obvious to me: the system is still delayed critical. It needs
to lose several times as much reactivity as it has already lost, before
the reaction can die down. It looks like it will melt before then.
Post by Steve Harris
Yeah, but if he had run away, look what this would have become. Melted
plutonium running like mercury through the gaps in the WC bricks
pilled around the assembly, and then in globs and splatters,
mercury-style, all over the floor.
I don't know how far it would have gotten in a simple melting before
solidifying on the cooler bricks. And it wouldn't take much deformation
of the core to take it subcritical. In the picture of the assembly, the
lower half of the core seems to be in a hollow without any crevices, which
would help contain it.
Post by Steve Harris
It least it would have killed the
reaction.
Unless the plutonium-gallium alloy contracted during melting by enough
to go prompt critical again before there was enough deformation to offset
it. Then the power growth rate would be much faster than any disassembly
by gravity-driven flow. I'm guessing that thermally driven shock waves
would be the next disassembly mechanism to kick in.
Post by Steve Harris
If Slotin historically used Daglian's intact core, as you say, then
that means if Daghlian had run like hell instead of pilling out the
brick, he would (perhaps) have saved not only himself, but later
Slotin too.
I don't think he could have saved himself. There was a lot of energy in
that initial prompt spike, which only took a few milliseconds. His
dosage would have been somewhat lower, but probably still lethal.
p***@hotmail.com
2004-07-26 14:11:38 UTC
Permalink
***@cadence.com (Steven Sharp) wrote in message news:<***@posting.google.com>...
[snip]
Post by Steven Sharp
Are you sure that radiation is the dominant heat loss mechanism from
the core in that timeframe? These cores were sitting inside
hemispherical hollows in metal reflectors. The thermal contact may not
have been great, but there would be some conduction into that larger
metallic mass, delaying meltdown.
Horseback feeling from experience with commercial nuclear fuel:
A core such as this, in five seconds, would be fairly accurately
treated as adiabatic. That is, practically speaking no energy
would conduct out thermally in that time. I certainly have not
run any numbers on it. Certainly a power pulse in the 10's of
kilowatts range would be very little affected by conduction during
the first few seconds.

Probably thermal radiation during the first few seconds would be
nearly negligable as well. Just not time for the heat to move around
very much.

I'm thinking, though, that a significant fraction of the energy
would have gone away as neutrons that didn't interact with the
core. The fact that this thing is just barely over prompt would
tend to say that there are still a goodly fraction going away,
winding up in lab gear, lab personnel, etc. So, the lack of a
melt may not be all that surprising, as long as the event is
terminated in a few seconds. The lab equipment probably got warm
(thermally as well as by induced radiation) fairly quickly.
Socks
Steve Harris
2004-07-26 20:00:34 UTC
Permalink
Post by Eric Gisse
[snip]
Post by Steven Sharp
Are you sure that radiation is the dominant heat loss mechanism from
the core in that timeframe? These cores were sitting inside
hemispherical hollows in metal reflectors. The thermal contact may not
have been great, but there would be some conduction into that larger
metallic mass, delaying meltdown.
A core such as this, in five seconds, would be fairly accurately
treated as adiabatic. That is, practically speaking no energy
would conduct out thermally in that time. I certainly have not
run any numbers on it. Certainly a power pulse in the 10's of
kilowatts range would be very little affected by conduction during
the first few seconds.
COMMENT:

Agreed. This is a little 2 inch ball of metal into which we're dumping
60 kw. It doesn't matter what solid it's in contact with-- it's gunno
go over 500 C and melt.
Post by Eric Gisse
Probably thermal radiation during the first few seconds would be
nearly negligable as well. Just not time for the heat to move around
very much.
Well, the heat doesn't have to move inside the metal because it's
generated uniformly in place. The interior will certainly melt. IR at
best would keep an external shell intact, which would depend on a thin
rind of solid Pu-239 cooled by radiative surface loss. However, we
calculated that at the melting point of Pu, and it's less than 300
watts at the melting point, so no help there.
Post by Eric Gisse
I'm thinking, though, that a significant fraction of the energy
would have gone away as neutrons that didn't interact with the
core. The fact that this thing is just barely over prompt would
tend to say that there are still a goodly fraction going away,
winding up in lab gear, lab personnel, etc. So, the lack of a
melt may not be all that surprising, as long as the event is
terminated in a few seconds. The lab equipment probably got warm
(thermally as well as by induced radiation) fairly quickly.
Socks
Nah, you're wrong there. Fission neutrons have a median (most
probably) energy of maybe 0.7 Mev and average maybe 2 Mev. We use the
average. Figure 2.5 neutrons per fission and you get 5 MeV in neutrons
per 200 MeV fission. That's only 2.5% of the energy in neutrons.
Sorry. 97% or more of fission thermal power comes from fission
fragments smacking into surroundings. And most don't get far.

SBH
p***@hotmail.com
2004-07-27 14:09:33 UTC
Permalink
Both Stevens took me to task for saying a significant fraction of
energy would leak out as neutrons. Of course, I was wrong as they
said. And, had I actually thought carefully about it, I'd have
known this. It's what I know from commercial reactors as well.
The bulk of the heat is generated in the fuel, and only a small
portion in the support structure of the reactor.

I hang my head and "mea culpa."
Socks
Steven Sharp
2004-07-26 22:29:55 UTC
Permalink
Post by p***@hotmail.com
A core such as this, in five seconds, would be fairly accurately
treated as adiabatic.
Certainly the models in the Los Alamos report assumed this.
Post by p***@hotmail.com
I'm thinking, though, that a significant fraction of the energy
would have gone away as neutrons that didn't interact with the
core.
With plutonium, you get 2 spare neutrons from each fission. A typical
fission neutron has around 2 MeV. Fission releases around 180 MeV.
So only around 2% of the fission energy could be carried away by neutrons.
p***@hotmail.com
2004-07-22 18:36:29 UTC
Permalink
***@ix.netcom.com (Steve Harris ***@ROMAN9.netcom.com) wrote in message news:<***@posting.google.com>...
[snip]
Post by Steve Harris
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?
As somebody else mentioned, thermal expansion of the core
probably had a big part in it. There's probably some temperature
effect on the reflector and moderator as well. I can't tell you
what they are just off, but I know that most commercial reactors
have to take such effects into account.
Post by Steve Harris
Inquiring minds want to know. I wonder if they had the balls to repeat
these accidents under control "dragon" type conditions, just to see
what really DID happen? I'll bet not. If they did, it's still
classified.
They had a few fizzles, and a few cases where they intended to
be sub-critical but went just over. So, they may not have done the
repeat with just that design of core. But they did similar cases
(some by not by intention) with other core designs.
Socks
x
2004-07-05 21:57:27 UTC
Permalink
Post by m***@cars3.uchicago.edu
Post by x
The fission reaction in a nuclear explosion is a controlled out-of-
control fission reaction. That is, the two fissile masses are slamed
together at high velocity with a trmendous amount of heat applied at the
critical time to force a out-of-control chain reaction. The reaction is
the production of an enormous amount of neutrons which are forced or
deflected back into the fissile mass creating more heat and more
neutrons and the reaction is then considered to be out of control and
the heavy nuclei of the fissile material rips apart releasing the energy
that kept it intact. The energy involved is the strong nuclear force. In
a lab, the fissile material is not allowed to over heat. The amount of
neutrons that are allowed to escape is controlled by graphite rods that
absorb any excess amount of neutrons. So the lab fissile material never
reaches a temperature that would cause it to go into critical mass and
'out of control'.
Temperature has nothing to do with it.
Mati Meron | "When you argue with a fool,
Depends on your 'distance' of vision of the reaction taking place. The
whole point of it all is to disassemble all of the available nuclei. I
suppose one might get 100% of the fissile material being fissioned by
submersing the fuel in a cryostat and using a metal spring to gently bring
the subcritical masses together.
--
Using M2, Opera's revolutionary e-mail client: http://www.opera.com/m2/
m***@cars3.uchicago.edu
2004-07-05 23:48:12 UTC
Permalink
Post by x
Post by m***@cars3.uchicago.edu
Post by x
The fission reaction in a nuclear explosion is a controlled out-of-
control fission reaction. That is, the two fissile masses are slamed
together at high velocity with a trmendous amount of heat applied at the
critical time to force a out-of-control chain reaction. The reaction is
the production of an enormous amount of neutrons which are forced or
deflected back into the fissile mass creating more heat and more
neutrons and the reaction is then considered to be out of control and
the heavy nuclei of the fissile material rips apart releasing the energy
that kept it intact. The energy involved is the strong nuclear force. In
a lab, the fissile material is not allowed to over heat. The amount of
neutrons that are allowed to escape is controlled by graphite rods that
absorb any excess amount of neutrons. So the lab fissile material never
reaches a temperature that would cause it to go into critical mass and
'out of control'.
Temperature has nothing to do with it.
Mati Meron | "When you argue with a fool,
Depends on your 'distance' of vision of the reaction taking place. The
whole point of it all is to disassemble all of the available nuclei.
The whole point of this is to set a chain reaction going and keep the
mass in place long enough not to let disassembly to take place. So
you need a critical mass (which is a function of cross section and
density) and you need containment (kinematical containment, in the
case of a bomb. Again, temperature doesn't enter into this.
Post by x
I suppose one might get 100% of the fissile material being fissioned by
submersing the fuel in a cryostat and using a metal spring to gently bring
the subcritical masses together.
You'll better have a goddamn powerful spring to keep them from flying
apart when the reaction starts. But that's a technicality, would
you've a spring powerful enough, you could do it. What you do in
practical application, is send the pieces flying inwards, fast, and
rely on inertia to keep them from reversing direction for the
microsecond or so that is required.

Mati Meron | "When you argue with a fool,
***@cars.uchicago.edu | chances are he is doing just the same"
Paul Cardinale
2004-07-06 18:54:49 UTC
Permalink
Post by eric adam
im not a scientist. i was reading about cerenkov radiation and
neutrinos. it said that the amount of blue glow produced is tantamount
to the amount of fission that occurs. isnt fission an incredibly
energetic process? i guess the question is what is the difference
between the fission that produces big nuclear explosions and the
fission that produces little blue glows in labs?
The short answer is that fission, like other processes can happen
either quickly or slowly. When it happens quickly, you get an
explosion.

Paul Cardinale
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