XYLENE POWER LTD.

NON-PROLIFERATION

By Charles Rhodes, P.Eng., Ph.D.

NON-PROLIFERATION IN THE OTTENSMEYER PLAN:
An important feature of the Ottensmeyer Plan is non-proliferation. The Ottensmeyer Plan prevents nuclear weapon proliferation by both chemically and isotopically polluting Pu-239 that might otherwise be diverted into nuclear weapon production.

The plutonium is chemically polluted with other transuranium actinides including isotopes of Neptunium (Np), Americium (Am), Curium (Cm), Berkelium (Bk) and their decay products. The plutonium isotope Pu-239 is heavily polluted with Pu-240.

In the Ottensmeyer Plan the [Pu-240 / Pu-239] ratio in the core fuel rods is in the range 0.30 to 0.50. This ratio is too high for production of plutonium type atom bombs, which require a [Pu-240 / Pu-239] ratio of less than 0.07. Within a power reactor only in blanket fuel bundles is it physically possible to make military grade plutonium. However, within the power reactor fuel cycle the blanket bundle plutonium production rate is too small to be of practical military interest.

The physical possibility of production of military grade plutonium can be totally eliminated by ensuring that each and every fuel bundle remains in the reactor for the design residency time and by repositioning blanket bundles during their residency time so that they are all equally exposed to the fast neutron flux.

The fuel bundles should move through the reactor and through the perimeter zone of the liquid sodium pool in a consistent first in, first out sequence. Any departure from that sequence not caused by an obvious fuel bundle physical failure is an indication of nefarious intent by the reactor operators.

The effect of adding Pu-240 to the plutonium in an atom bomb is to cause premature detonation so that the bomb blows itself apart before the Pu-239 has had time to fully react. In short, excess Pu-240 causes the bomb to fizzle instead of explode. At:
[Pu-240 / Pu-239] = 0.50
the bomb's explosive energy yield is reduced by about 99%.

In practice it is almost impossible to isotopically separate Pu-240 from Pu-239 so raising the [Pu-240 / Pu-239] ratio is an effective means of preventing plutonium type atom bomb proliferation.

When a FNR is initially started its [Pu-240 / Pu-239] ratio is the same as the [Pu-240 / Pu-239] ratio in the start fuel. According to the Nuclear Waste Management Organization (NWMO) the [Pu-240 / Pu-239] ratio in normal spent CANDU fuel is about 0.40. As the FNR runs the [Pu-240 / Pu-239] ratio gradually rises to a steady state limit of about 0.50. Hence at every stage of implementation of the Ottensmeyer Plan for disposal of spent CANDU fuel the material is unsuitable for military use.

The objects of this web page are to derive the steady state upper limit on the [Pu-240 / Pu-239] ratio in a FNR, to show how fast the [Pu-240 / Pu-239] ratio rises toward its steady state upper limit and to show how the [Pu-240 / Pu-239] ratio affects the performance of plutonium type atom bombs. There is also attention paid to mitigation of risks from either accident or malevolent intent related to storage and shipping of FNR fuel rods and fission products.
 

PARAMETER DEEFINITIONS:
Fn = flux of fast neutrons per unit area per unit time;
A = effective fast neutron cross section
c = subscript indicating fast neutron capture cross section;
f = subscript indicating fast neutron fission cross section;
N = number of atoms / unit volume;
x = subscript indicating U-238;
y = subscript indicating Pu-239;
z = subscript indicating Pu-240;
T = time;

Thus:
Nx = number of U-238 atoms per unit volume
Ny = number of Pu-239 atoms per unit volume;
Nz = number of Pu-240 atoms per unit volume
Axc = U-238 fast neutron capture cross section;
Ayc = Pu-239 non-fission fast neutron capture cross section;
Azc = Pu-240 non-fission fast neutron capture cross section;
Ayf = Pu-239 fission fast neutron capture cross section;
Azf = Pu-240 fission fast neutron capture cross section;
 

DIFFERENTIAL EQUATIONS:
Pu-239 formation/decay:
dNy / dT = Fn [Axc Nx - Ayc Ny - Ayf Ny]
= Fn [Axc Nx - Ny (Ayc + Ayf)]

Pu-240 formation/decay:
dNz / dT = Fn [Ayc Ny - Azc Nz - Azf Nz]
= Fn [Ayc Ny - Nz (Azc + Azf)]
 

STEADY STATE CONDITIONS:
Once the reactor reaches steady state conditions:
dNy / dT = 0
and
dNz / dT = 0

Thus at steady state conditions:
Pu-240 / Pu-239 = (Nz / Ny) = Ayc / (Azc + Azf)
and
Pu-239 / U-238 = (Ny / Nx) = Axc / (Ayc + Ayf)
 

EXPERIMENTAL DATA:
Kaye & Laby give the following data for a FNR core:
Axc = 0.25 b;
Ayc = 0.40 b;
Azc = 0.42 b;
Ayf = 1.7 b;
Azf = 0.37 b

Hence for the FNR core at steady state:
Pu-240 / Pu-239 = Ayc / (Azc + Azf)
= 0.40 / (0.43 + 0.37)
= 0.50
and
Pu-239 / U-238 = Axc / (Ayc + Ayf)
= 0.25 / (0.40 + 1.7)
= 0.25 / 2.1
= 0.119

Hence for the FNR blanket at steady state:
Pu-240 / Pu-239 = Ayc / (Azc + Azf)
= 0.73 / (0.67 + 0.25)
= 0.793
and
Pu-239 / U-238 = Axc / (Ayc + Ayf)
= 0.34 / (0.73 + 2.0)
= 0.34 / 2.73
= 0.125

Note that during FNR operation the Pu-239 and Pu-240 concentrations in the reactor core are relatively stable whereas the Pu isotope concentrations in the blanket gradually rise.
 

CRITERIA FOR NON-PROLIFERATION:
A key question is what is the effect of the Pu-240 / Pu-239 ratio:
(Nz / Ny)
on atomic bomb performance?
 

FISSION DELAY:
Each fission reaction has a characteristic average time delay between the instant when a neutron is absorbed and the instant when the atom fissions. This time delay is known as the fission delay. There is prompt fission and there is delayed fission. When the fission delay becomes really long it appears as if the isotope created by neutron absorption exhibits spontaneous fission.

The isotope Pu-240 exhibits spontaneous fission as well as rapid prompt fission triggered by absorption of yet another neutron.

A practical problem with plutonium type atom bombs is that the fission delay for Pu-240, which is zero due to spontaneous fission, is short compared to the fission delay for Pu-239. A consequence of this time delay relationship is that energy released by rapid fission of Pu-240 tends to blow a plutonium atom bomb apart before the Pu-239 has time to react. To prevent this premature ignition in plutonium type atom bombs the [Pu-240 / Pu-239] ratio is minimized and the radius of the critical mass is reduced by a fast explosive driven implosion.

In military grade plutonium:
(Pu-240 / Pu-239) < 0.07

Hence an effective non-proliferation measure is to raise the [Pu-240 / Pu-239] ratio substantially above the maximum limit for military use.
 

ASSUME THAT THE FISSION DELAYS FOR Pu-239 AND Pu-240 ARE EQUAL:
Consider a solid sphere of pure (Pu-239 + Pu-240) surrounded by a neutron reflector with fractional neutron loss Fl. The condition for no gain or loss in the number of free neutrons inside the reflector is:
{(3.1) [(Ny Ayf) + (Nz Azf)] - (Ny Ayc) - (Nz Azc)}Fn (4 Pi R^3 / 3) - Fl(4 Pi R^2) Fn = 0
where:
(3.1) is the average number of neutrons emitted in a plutonium fission;
R = plutonium sphere radius.

Hence:
{(3.1) [(Ny Ayf) + (Nz Azf)] - (Ny Ayc) - (Nz Azc)}(R / 3) - Fl = 0
or
{(3.1) [(Ny Ayf) + (Nz Azf)] - (Ny Ayc) - (Nz Azc)} = (3 Fl / R)

A specific volume of plutonium contains N atoms. Thus:
Ny + Nz = N
giving:
(3.1) [((N - Nz) Ayf) + (Nz Azf)] - ((N - Nz) Ayc) - (Nz Azc) = (3 Fl/ R)

Thus at state "a" when the sphere is pure Pu-239, Nz = 0 and R = Ra giving:
3 Fl / Ra = N (3.1 Ayf - Ayc)
where Ra is the critical radius at which the reaction commences.

At state "b" when R = Rb, Nz = N / 3 corresponding to a Pu-240 / Pu-239 ratio of 0.5. Then:
3 Fl / Rb = (3.1) N (0.66 Ayf + 0.33 Azf)] - N (0.66 Ayc + 0.33 Azc)

Hence:
(Ra / Rb) = {[(3.1) N (0.66 Ayf + 0.33 Azf)] - N (0.66 Ayc + 0.33 Azc)} / N (3.1 Ayf - Ayc)
= {[(3.1)(0.66 Ayf + 0.33 Azf)] - (0.66 Ayc + 0.33 Azc)} / (3.1 Ayf - Ayc) = {[(3.1) ((0.66) 1.7 + (0.33) 0.37)] - ((0.66) 0.40 + (0.33) 0.42)} / (3.1 (1.7) - 0.40)
= [3.857 - 0.4026] / 4.87
= 0.7093

Thus if Pu-240 / Pu-239 = 0.5 then the sphere's critical radius decreases by a linear factor of 0.7093 which causes a reduction in reacting bomb mass and energy yield of:
(.7093)^3 = 0.3568

Note that if the Pu-239 and Pu-240 fission delays are equal the presence of the Pu-240 does not prevent a bomb being made. It simply reduces the bomb's energy yield.
 

NOW ASSUME THAT Pu-239 HAS A MUCH LONGER FISSION DELAY THAN Pu-240:
That is, a neutron capture by Pu-240 leads to prompt fission whereas a neutron capture by Pu-239 leads to delayed fission. This delayed fission by Pu-239 is also known as "spontaneous fission" by Pu-240. In the short time frame of the initial part of an atom bomb discharge Pu-239 captures neutrons but does not immediately release fission neutrons. However, in that same time frame Pu-240 absorbs neutrons and fissions. Consider a solid sphere of pure (Pu-239 + Pu-240) surrounded by a neutron reflector with fractional neutron loss Fl.

The condition for no gain in the number of free neutrons is:
Fn {(3.1)(Nz Azf) - (Ny Ayf) - (Ny Ayc) - (Nz Azc)}(4 Pi Rc^3 / 3) - Fl Fn (4 Pi R^2) = 0
where the 3.1 is the average number of neutrons emitted in a plutonium fission.

Hence:
{(3.1)(Nz Azf) - (Ny Ayf) - (Ny Ayc) - (Nz Azc)} = 3 Fl/ Rc

A specific volume of plutonium contains N atoms. Thus:
Ny + Nz = N
giving:
(3.1)(Nz Azf) - ((N- Nz) Ayf) - ((N - Nz) Ayc) - (Nz Azc) = 3 Fl / Rc

At state "c" Nz = N / 3:
3 Fl / Rc = [(3.1) N (0.33 Azf) - N( 0.66 Ayf) - N (0.66 Ayc) - N (0.33 Azc)]

Hence:
(Ra / Rc) = [(3.1) N (0.33 Ayf) - N( 0.66 Azf) - N (0.66 Ayc) - N (0.33 Azc)]
/ [ N (3.1 Ayf - Ayc)]
or
(Ra / Rc) = [(3.1)(0.33 Ayf) - (0.66 Azf) - (0.66 Ayc) - (0.33 Azc)] / [(3.1 Ayf - Ayc)]
= [(3.1)(0.33 (1.7)) - (0.66 (0.37)) - (0.66 (0.40) - (0.33 (0.42)] / [(3.1 (1.7) - (0.40))]
= [1.739 - .244 - 0.264 - .139] / [4.87]
= [1.092] / [4.87]
= 0.2242

Thus in this case the bomb yield is reduced by a factor of:
[0.2242]^3 = 0.0113

Thus the effect of Pu-240 / Pu-239 = 0.5
is to reduce the plutonium atom bomb energy yield by a factor of 0.0113. Thus the presence of the Pu-240 with short fission delay as compared to the fission delay of Pu-239 does not prevent a bomb being made. However, it greatly reduces the available explosive energy output from the bomb. The Pu-240 causes the bomb assembly to blow apart before the Pu-239 has time to react.
 

CHOICE OF FNR START FUEL:
A major advantage of deriving FNR start fuel from spent CANDU fuel is that according to the NWMO spent CANDU fuel is characterized by:
(Pu-240 / Pu-239) = 0.40

Hence spent CANDU fuel is already protected against proliferation and FNR start fuel derived from spent CANDU fuel will have at least equal protection against proliferation. If the FNR start fuel comes from some other source such as military grade plutonium then there may be an issue as to how long the plutonium has to remain in the FNR before it forms sufficient Pu-240 to ensure non-proliferation.
 

EXTREME CASE OF Nz = 0 AT T = 0:
In terms of non-proliferation the most extreme case is FNR start fuel that contains almost no Pu-240 as would be the case if the FNR start fuel was derived from military grade plutonium. For that case we need to work out how long it takes the reactor to raise the Pu-240 concentration enough to realize protection against proliferation.
 

RISK MITIGATION:
From the perspective of this author there is far too much concern about nefarious parties attempting to divert plutonium to build fission bombs and not nearly enough concern about the real risks, which are rupture of a container of radioactive and flammable FNR metallic Core rods in an air atmosphere followed by a fire and/or immersion in water, such as might occur as a result of a major road or railway accident in an urban area or at a river crossing.

Combustion products from a metallic fuel fire could potentially spread radio toxic dust over a wide area. Metallic fuel should be packed in silica sand and stored and shipped in a robust argon filled watertight container located within an extremely robust lead shipping container. There should be further provision for immediate smothering of a metallic fuel fire at an accident site with CO2 foam and dry silica sand.

It is important to keep water away from the metallic fuel material to prevent formation of flammable hydrogen and to prevent water soluble radio isotope ions causing local water pollution. It is important to have immediately available enough radiation sensing and personnel protective gear for the first responders to a radioisotope accident site.

From the perspective of this author containers of metallic FNR core rods and fission products should be stored in naturally dry depleted hardrock mines where no matter what a terrorist does the problem can be easily contained.

From the perspective of this author FNR blanket rods should be processed at the reactor site so that at least 90% of their uranium content does not need to be shipped anywhere. The main reasons for processing FNR core rods off site are to reduce costs and to avoid any possibility of a malevolent party causing formation of an uncontrolled critical mass in or near an urban area.
 

This web page last updated June 30, 2015