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Jim,
Congratulations, a very good description of the paper. The
only subtle point that I would add is that U-235 and Pu-239 fission very well
with fast neutrons, so there is no need at all to moderate the neutrons in order
for this to work. Their only difference from U-238 in this regard is that
the fission cross-section in U-238 has a threshold at ~1 MeV,
but U-235 or Pu-239 do not. That is also why the authors discuss
Th-232, because if it were included then you would also have production of
U-233, which fissions as well if not better than U-235.
In
fact, given the lack of low-z or hydrogenous material, and
the resonance capture effect in U-238 at intermediate neutron
energies, this system probably had a fairly hard fission
spectrum. That would also tend to reduce the effectiveness of the
fission-product poisins, since most of their cross-sections are inversely
proportional to the neutron energy. This would keep the system running
longer before they shut it down.
Since
neutron flux would be low, the reactivity changes due to poisins would be very
slow. The temperature would be the main reactivity feedback
mechanism. Since the system would be well insulated, it would achieve a
very stable equilibrium operating regime and power level. Should be fairly
easy to calculate.
It's
an interesting hypothesis. I'm like you - I would never have thought of
it, but once I see it on paper it makes a great deal of sense. Maybe I'll
put my nuclear engineer hat on for a while and run some calculations
:-)
Doug
Minnema, PhD, CHP
NNSA,
US DOE
Those who followed the citation Jaro provided would discover the PNAS
paper, Deep-Earth reactor: Nuclear fission, helium, and the geomagnetic field,
by D.F. Hollenback and J.M. Herndon, PNAS, v. 98, no. 20, 25 Sept 2001.
The paper answers many of the questions being asked. Herndon has been
interested for a number of years in what might be providing the energy for the
Earth's magnetic field, with the puzzle being the relatively frequent (in
geological terms) flips in the polarity of the field.
Herndon hypothesizes that the flips result from a nuclear reactor that
operates for a period of time, then shuts down because of accumulating fission
product neutron "poisons". Later, as the fission products diffuse out of
the uranium/plutonium/other_actinides core, the reactor starts up
again.
When
I first saw media reports of this hypothesis a few weeks ago, I thought. "Of
course, how obvious". The key is the large size of the
reactor. In general, the neutron production will be proportional to
volume = (4/3)*pi*r^3. Neutron leakage out of the reactor will be
proportional to surface area = 4*pi*r^2. Thus the leakage fraction will
be proportional to 4*pi*r^2/(4/3)*pi*r^3 = 3/(pi*r), which is inversely
proportional to the radius of the reactor. The hypothesized 5 mile
diameter ball of uranium is HUGE. Neutron leakage would be
negligible. Hollenbach and Herndon describe the reactor as a fast
neutron reactor, but, in fact, with the reactor that big, the only thing that
would prevent a neutron from slowing down to speeds that will cause fissions
in U-235 or Pu-239 would be either causing a fast fission of one of the many
actinides or being captured by U-238, with the eventual creation of an atom of
Pu-239.
Hollenback and Herndon use one of the standard reactor code systems,
SCALE, to investigate the evolution of a roughly five mile ball of U-235 and
U-238 from 4.5 billion years ago to the present. The code calculates the
value of k-effective, the parameter that determines whether an assembly of
fissile material and other materials will be critical.. They treat two
cases: 1) at each time step, fission product poisons are simply removed from
the system, and 2) fission product poisons accumulate in the system. In
the first case, k-eff begins around 1.8, drops steadily, and settles into a
steady state around 1.02 about 2.5 billion years ago. In the second
case, k-eff drops below 1.0 at around 2.7 billion years ago. The two
cases probably bound the behavior of the real system. The authors
hypothesize, but do not yet support with calculation, that poisons will shut
the reactor down, then would diffuse/float out of the system over a relatively
short time, after which the reactor would start up again. They posit the
on/off oscillations as the source of the magnetic field
flips.
Table 2 of the paper summarizes the quanties of actinides present at
different times. Beginning 4.5 billion years ago with approximately 40%
U-235 and 60% U-238, by 3 billion years ago, there are a wide variety of
actinides present, dominated by Th-230, Th-232, U-233 (fissile), U-235
(fissile), U-236, U-238, Np-237, and Pu-239 (fissile), with the quanties of
Th-232, U-235, and U-238 being 2-4 orders of magnitude greater than the
others.
They
argue is some detail, that this hypothesis is consistent with the observed
ratio of He-3 to He-4 in the deep mantle (as evidenced by the ratio in magma
from some volcanoes).
The
paper is extremely interesting and is available online from www.nas.edu.
Best
regards.
Jim
Dukelow
Pacific Northwest National Laboratory
Richland, WA
These comments are mine and have not been reviewed and/or approved by
may management or by the U.S. Department of Energy.
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