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Natural Fission Reactors

Stephen Wood

Introduction

Bouzigues at Pierrelatte

Found deficiency in 235U abundance in U ore from Oklo, Gabon

Investigation -> 235U consumed in natural reactors

Several zones found at Oklo, but nowhere else

Fission

Binding energy, 235U, 238U

Fission fragments

Chain reaction

Fission reactors

Moderation, Control

First man-made reactor

Binding Energy

M(A) = A*M(N) – A*BE(A)

Nucleus ~ 1% lighter than parts

M(236) ~= M(139)+M(95)+2M(n) + 180MeV!

Splitting heavy nucleus converts ~ 0.1% of mass into energy.

1ev = 10-19 J, watt=J/sec, 235g = 6.023x1023 U235

1GWatt => .0132g/sec, 12.5x103 kg/30 years

Natural Uranium 0.72% U235

30% efficiency => 6x103 metric tons / life of reactor

Binding Energy/Nucleon

A

Simple Understanding of BE Curve

Radius of Nucleus: ~1.2A1/3 fm

Mass of Nucleus MA:

Volume: A(MN – BE)

Surface Area: ~A2/3

Coulomb Energy: ~Z2/R ~A1.5

Binding Energy/Nucleon

(AMN-MA)/A

BE – c1A-1/3 – c2 A0.5

Bohr-Wheeler, 1939, Spontaneous Fission limit: Z2/A ~ 48

Reed simple derivation:

A~1.686Z1.087

A=N+Z

A

MeV

U235 - U238

Natural Uranium: 235U: 0.72%, 238U: 99.2745%

Half Lives: 7.038x108 yr, 4.468x109 yr

109 yr

%

Z2/A < 48, need to add energy Ef to induce fission. Adding a neutron gives an excited compound nucleus

235U+n -> 236U+6.5 MeV

238U+n -> 239U+4.8 MeV

Fission excitation energies, Ef:

236U: 5.4 MeV Slow neutrons OK

239U: 5.9 MeV Need >1 Mev neutrons

Chain Reaction

Fission releases 2.5 neutrons

Neutron repoduction factor: k

k<1: sub critical, k>1: super critical

Neutron loss:

Neutron (n, gamma) in U238 or other materials (control rods, poisons)

Leakage

Cross sections

Low energy neutron scattering

Elastic scattering

Inelastic scattering

Neutron knockout

Radiative Capture

Fission

Probabilities expressed as cross sections

Geometric areas

235U: 1.72 barn

12C: 0.16 barn

1 barn = 10-24 cm2

R ~ 1.2 A1/3 10-13 cm

Neutron Cross Sections

238U will only fission with fast neutrons, fission competes with other processes

To enhance fission probability:

Enrich 235U

Slow down neutrons to thermal equilibrium

Fission neutron

energy spectrum

Moderation

Slow neutrons down to thermal energy:

Improve 235U fission – 238U capture ratio. Get below resonances.

Increase time between neutron generations

n+p elastic

n+d elastic

Moderator Properties

Moderator properties

Small A. Neutron loses energy by recoil from elastic scattering.

Low capture cross section

Comparison

Need enriched fuel in H2O

Can use natural uranium with graphite or heavy water

Graphite flammable, can breed plutonium in D2O reactor

First Man-made Reactor

Built under grandstand of Stagg Field @ University of Chicago

UO – C lattice 8.25” spacing

7.75 meter diameter, 6 meter height

20,000 3.25” diameter UO2 spheroids

Achieved divergent neutron flux, Dec 2, 1942.

Theory well understood

Many sub-critical built to study neutron dynamics (diffusion)

Reactor Control

On average, want k=1

k<1, reactor shutdown

k>1, divergent

Reactor period T=l/(k-1)

e.g. k=1.001

12C: l=10-3sec, T=1 sec

H2O: l=10-4sec, T=0.1 sec

Fast: l=10-8sec, T=10-5 sec

How to achieve stability?

Design so k=1. Chicago k=1.0006

Change in moderator density

Water -> Steam

Carbon -> Expansion

Delayed Neutrons

Neutron emission from fission fragments.

0.64% 235U neutrons delayed

Mean time 0.1 sec

Keep k < 1.0064

k=1.0064

Oklo

1972 @ French fuel-processing plant, UF6 gas sample with 0.7171% 235U found < solar system wide 0.7202%. Deficiency started 1970. 200kg “missing” 235U

Undepleted ore: no fission fragments

Depleted ore: fission fragments

Low 235U fraction

Low U concentration

Properties of Oklo natural reactors

16 reactor zones

Energy release: 15 GWatt-years

Duration: 150,000 years, average power 100 kW.

Controll: Self stabilizing, cycling, burn like log

>5 tons 235U consumed

Typical neutron fluence (integrated flux) 1020 – 1021 n/cm2

Greater power in cracks

Natural Reactor Conditions

Current 0.72% 235U requires heavy water or graphite lattice

Requirements:

Ore deposited > 1,800 Mya, 235U enrichment

U Concentration > 10%. Oxygen to make U soluble.

Seam thickness > 0.5 m to avoid neutron loss

Moderator: Water

Lack of neutron absorbers/poisons (Li, B, rare earths)

Geological stability

Isotopic analysis

Measure abundance stable/long lived isotopes of a given element. Compare to natural abundance. Deduce reactor properties.

Chemistry has no direct effect on abundances

Nuclear causes, sources and sinks:

Product of fission – well known for U, Pu

Decay (alpha, beta) from other isotopes

Transmutation (neutron capture and decay) to/from other isotopes.

Example: 130Xe 129Xe ratio => neutron fluence

130Xe, 129Xe not fission products

129I captures n (30 barn) or decays to129Xe

Typical fluence 1021 n/cm2

Fission Fragments

235U and 239Pu have distinct fragment distributions

Estimated that half of 235U in reactor areas from 239Pu decay (24,000yr)

No nearby enriched U, no Pu migration.

Pu fission significant contribution to power

239Pu

235U

Plutonium fission contribution

Holloway

Cycling reactor?

Meshik, Hohenberg, Pravdivtseva looked at Xe isotope ratios in U minerals and Aluminum Phosphate grains. (Zone 13).

Distribution of Xe in U, normal, anomalous in Al Phosphate

Xe gas volatile, will migrate in hot medium

Precurses to different Isotopes have varying half lives. Anomalies indicate non-steady state operation.

Xe 131, 132, 134 proportions indicate reactor was on for half hour, off for 2.5.

129Xe fits if assume 1/3 129I leaked out

Time dependence or fundamental constants

Many comparisons of neutron cross sections in natural reactors to present values, to set limits on variation of fundamental constants. (energy shift in resonance changes cross section.) Examples, Shlyakhter, Fujii.

Cross sections averaged over neutron energy distribution. 149Sm, 155Gd

Lamoreaux and Torgerson argue neutron distribution is not MB, affects previous conclusions.

Shift in resonance energy

155Gd average

cross section

Final Notes

Reactors mined out. Mine closed and flooded

Plea made in 1997 to preserve only other known fossil reactor 30 km away from Oklo.

Other reactors may have been dispersed (slight depletion in Colorado ore.)

Implications for storage of nuclear wastes

Georeactor – reactor at earth's core

Bibliography

Bohr and Wheeler, “The mechanism of nuclear fission,” Phys. Rev. 56, 426-450 (1939).

Reed, “Simple derivation of the Bohr-Wheeler spontaneous fission limit,” Am. J. Phys. 71, 3 (2003).

Korea Atomic Energy Research Institute, Plot neutron cross sections, http://atom.kaeri.re.kr/.

Fermi, “Experimental Production of a Divergent Chain Reaction,” American Journal of Physics 20, 536-558 (1952).

Loss, R., “Natural Fossil Fission Reactors,” http://www.curtin.edu.au/curtin/centre/waisrc/OKLO/.

Cowan, G.A., “A Natural Fission Reactor,” Scientific American 235, 781 (1976).

Karam, A, “The Natural Nuclear Reactor at Oklo: A comparison with Modern Nuclear Reactors,” http://www.physics.isu.edu/radinf/Files/Okloreactor.pdf (2005).

Holloway, R., “Plutonium fission in the Oklo natural reactor,” Savannah River DS-MS-80-75, (http://sti.srs.gov/fulltext/dpms8075/dpms8075.pdf).

Meshik, Hohenberg, Pravdivtseva, “Record of Cycling Operation of the Natrual Nuclear Reactor in the Oklo/Okelobondo Area in Gabon,” Phys. Rev. Lett. 93, 182302-1 (2004).

Shlyakhter, A.I., “Direct Test of the Time-Independence of Fundamental Nuclear Constants Using the Oklo Natural Reactor,” arXiv physics/0307023, (1982/2003).

Fujii et.al, “The nuclear interaction at Oklo 2 billion years ago,” Nuclear Physics B 573, 377 (2000).

Lamoreaux, S.K. And Torgerson J.R., “Neutron moderation in the Oklo natural reactor and the time variation of alpha,” Phys. Rev. D 69, 121701(R) (2004).

Weiss, “Primordial Nukes,” Science News 167, issue 11, (2005).

Meijer, van der Graaf, Jungmann, “Quest for a Nuclear GeoReactor”, arXiv physics/0404046, (2004).

http://www.igeb.gov/sa/diagram.shtml

2002-12-11T15:02:15