IANUS
Interdisziplinäre Arbeitsgruppe
Naturwissenschaft, Technik und Sicherheit
Interdisciplinary Research Group Science, Technology and Security
Pu-Production in a Tokamak Fusion Power Reactor
Homogeneous Material Mixtures vs. Breeding Structures
Matthias Englert
Working Paper 2/2011, January 2011
Abstract
To calculate Pu production in a tokamak fusion power plant we used an
MCNP model of the 2006 published concept of the European Power Plant
Conceptual Study. Originally we worked with the assumption of a homogeneous material mixture of water structural materials and the Pb-17Li
alloy in the breeding blanket zone and a replacement of the alloy with different volume percentages of uranium. This is only realistic however, for
very low uranium contents. In this paper we present first calculations with
breeding and cooling structures in the blanket instead of a homogeneous
mixture.
Interdisciplinary Research Group in Science,Technology and Security
Interdisziplinäre Arbeitsgruppe Naturwissenschaft, Technik und Sicherheit
TU Darmstadt (Darmstadt University of Technology)
Alexanderstr. 35-37, D-64289 Darmstadt, Germany
Tel: +49-06151-16-4368, Fax: +49-06151-16-6039
E-Mail: [email protected]
M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
1 Reactor Model
We developed an MCNP [1] model (fig. 2) of the reactor geometry [2, 3], which is the basis of the
reactor description below. Detailed information on the dimensions of the blanket modules was
derived from the MCNP model in [4] and from [5] Annex 4. Additional geometric information was
available from [6, 7, 8]. The thermal power of PPCS-A is 5.5 GW. Including the superconducting
coils the total height of the torus is 18 m. The height of the plasma chamber from the divertor
zone to the top is 10.7 m with a maximal width of 6.7 m. Typically an inner zone (inboard) and
outer zone (outboard) is distinguished. The torus is divided in 20˚-sectors, with a port every
two sectors to exchange the blanket modules with a remote handling machine (about every two
years). The modules have to be small enough to be still transportable, and large enough to allow
for a short maintenance period so that the overall plant capacity factor does not drop below
75-85%. In our MCNP model we used only one 20˚ section of the torus with 3 inboard and 3
outboard modules (figure 2).
The breeding material is lithium (enriched to 90% Li-6) in a liquid lead-lithium alloy (Pb-17Li).
The structural material is the low activation martensitic steel EUROFER [9]. The blankets are
cooled by light water to temperatures below 670K. The inboard modules have four blankets each,
the outer modules five. A real module and each real blanket would have a steel structure with
cooling pipes. In our MCNP model the assumption was made that each part of a module and
each blanket is filled with a homogeneous mixture of the material (H2 O, Pb-17Li, EUROFER)
without any internal blanket structure following a detailed description in [4]. The shielding and
the divertor complete the entire reactor structure.
The source strength for a 20˚ sector and therefore the normalization constant for all MCNP
results is a neutron rate of Rn = 1.08 · 1020 neutrons/s according to to the energy of 4.4 GW
from the 14.1 MeV fusion neutrons in the reactor.
2 Realistic Scenarios
The assumption of a homogeneous mixture of all materials in the MCNP model implies that
the natural uranium has to be diluted in the Pb-17Li alloy. This is only possible to a certain
extent. The phase diagram of the Pb-U system [10] shows that uranium starts to dissolve in Pb
at temperatures higher than 600 K. In [11] the results of several experiments are summarized
and the authors give an empirical temperature dependent formula for the solubility Log[LU ] =
3.921 − 5121
T of uranium in lead. As the maximal working temperature in the PPCS-A concept
should not exceed 475˚C due to increased corrosion at higher temperatures, this temperature
would yield a maximal solubility of about 0.001 at% in the Pb/17Li alloy. For an order of
magnitude higher solubility one would need temperatures up to 800˚C. In standard operation the
solubility would be also different due to temperature gradients and there is the risk that uranium
would crystalize at cool spots. To overcome these difficulties uranium might be added in the form
of small particles. In all cases it will be technically challenging to extract low concentrations of
uranium from big amounts of lead. Anyway production rates at such low concentrations will be
not very attractive.
In the former analysis we did not calculate any structures implemented in the breeding blankets.
Generally one could implement breeding structures like rods or use the wall structures clad them
with corrosion resistant materials or ultimately use moderated breeding structures connected to
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
the light water cooling system. This is leading finally to the design challenges of fusion-fission
hybrid systems.
3 Breeding Structures
The first approach to implement breeding structures was the replacement of the uranium contained in the blanket 2 of the Module II (inboard, straight module) by fuel rods. With a volume
of V = 1.32063 · 106 cm3 and a vol% of 0.1% given a density of 19.05 g/cm3 the mass of the
uranium containe in the blanket is 25.158 kg natural uranium.
To start, we chose a typical light water fuel rod geometry as a breeding structure in the blanket,
which is filled with uraniumoxide UO2 . The fuel rod radius is 0.424 cm with a cladding of 0.5
mm. Thus the total amount of 25.158 kg or uranium within the homogeneous mixture is now
contained in the fuel rods in the form of uraniumdioxide with a density of 10.97 g/cm3 (9.67
gU/cm3 ). There are 11 such fuel rods with a length of 419.6 cmm filling the blanket 2 with
a distance to each other of 20 cm (fig. 1). In between 2 rods is a water cooling pipe with an
inner radius of 2.2 cm and a cladding of 1 mm containing water with a density of 0.7245 g/cm3
the same amount as the 5.4 vol% contained in the homogeneous mixture before. The rest of
the blanket contains still a homogeneous mixture of steel and Pb-17Li alloy, but of course now
without water and uranium.
Figure 1: Inboard module II Blanket structure in a horizontal cut in the xy-plane (compare fig. 2 lower
left cut). Blanket 2 contains the breeding structures, in this case 11 fuel rods and cooling pipes.
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
Shielding
500
Inboard
Outboard
Module III
Module IV
0
(0,0) MCNP
Module II
Module V
-500
z
Module I
y
0
-500
x
500
Module VI
200
z
Divertor
y
0
x
z
400
x
Outboard
Blanket 1
Blanket 1
Blanket 2
Blanket 3
Blanket 4
Inboard
x
20°
Blanket 5
0
Blanket 4
-400
y
x
Blanket 3
z
Blanket 2
-200
toroidal
poloidal
y
Figure 2: MCNP model of PPCS-A fusion power plant (20˚ section). Right: 3d representation. Left:
x-z cut through the model at y=0 cm. Below: x-y cut (z=-82.5 cm). In the MCNP model the origin is at
(-459.82,0,85) cm.
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
4 Plutonium Production
The following simplifying assumptions were made to calculate plutonium production
• The Pu-239 production rate is considered to be only dependent on (n,γ) reactions in
without any burnup calcualtions.1
238 U
• The production rates are strictly taken the production of an excited state in U-239*. As
U-239 and the daughter product Np-239 have a half life much lower than the production
time, the U-239 production rates are almost identical with the Pu-239 production.
• There is no consideration of any time necessary for cooling down the blankets after irradiation and for reprocessing which would be necessary to extract the produced plutonium.
• The production was calculated for a continuous operation and has to be considered as production per year available irradiation time. Ususally maintanance and other interruptions
will occur. To be economical fusion power plants have to reach a capacity factor of at least
75-85%.
• All blanket materials are homogeneous mixtures, no structure is implemented. In reality
higher concentrations of uranium can only be added to the alloy at high temperatures (see
below).
In the former homogeneous calculation with a content of 25.158 kg uranium in the homogeneous
mixture, a total production of 346 g Pu-239 per year was achievable with this 0.1vol% addition
of uranium. The same amount of uranium in the form of uranium hexafluoride in 11 fuel rods
yields only 89 g Pu-239 per year, significantly less.
Two effects could cause this discrepancy according to equation 1 showing the basic equation to
calculate reaction rates Rxi of a process x for a nuclide i
Z ∞
i
dE N i (~r, t)σxi (E)φ(E, ~r, t)
(1)
Rx =
0
with the microscopic cross section σxi (E) and the corresponding flux φ(E, ~r, t) at a specific point
and time.
The effect could be either due to changes to the flux energy spectrum by the geometric separation of the materials, as the thermalization due to the water is now effective mainly in certain
spatial regions in the blanket zone thereby changing the efficiency in the resonance region of the
cross section. The other possibility is the change to the flux intensity in the spatially separated
materials, as self-shielding2 might become important either due to the density change or other
competing processes. In effect the mean free path for a neutron capture in U-238 is different in
the homogeneous mixture versus that in the tubes.
1
2
This corresponds to a continuous immediate extraction of the produced plutonium.
Usually self-shielding refers to the absorption of a neutron emitted by a material by the material itself. Here
self shielding refers to the shielding of parts of the geometry so that e.g. the interior of the fuel rod does not
see more neutrons, because of absorption at the periphery of the rod.
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
Pu [g]
Blanket 1
Blanket 2
Blanket 3
Blanket 4
Tubes
144
77
40
22
Homogeneous
856
346
133
62
Ratio
5.9
4.5
3.3
2.8
Table 1: Production with fuel rods implemented in all blankets compared to homogeneous mixture.
Doubling the amount of fuel rods to 22 with a smaller radius of 0.3 cm yields the same Pu
production of 89 g Pu-239 per year as for 11 rods with bigger radius. Using the same mass of
metallic uranium (19.05 gU/cm3 ) fuel in the 11 fuel rods with a radius of 0.3 cm yields also 80 g
Pu per year. So varying the fuel rod dimensions and the density by using either uranium oxide
(10.97 g/cm3 ) or metallic uranium (10.97 g/cm3 ) does hardly effect the plutonium production
rate and does not explain the huge difference of more than a factor 4 between the homogeneous
production and the production achievable with breeding structures. This indicates that the effect
is not alone geometry or density related, but originates also from different neutron spectra (see
below).
A subsequent calculation without water in the breeding blanket 2 of Module II but with homogeneously dispersed alloy and steel containing 0.01vol% U showed that only 149 g Pu per year
can be produced compared to the 346 g Pu per year in the same geometry with water. This
comparison narrows the effect of the geometry related changes to the drop in Pu production to a
factor of 1.8. An investigation of the fission cross sections in the homogeneous mixture without
water in comparison to the fuel rods could indicate, if additional fission neutrons or fission as
a competing process might explain some of the remaining difference or if the discrepancies are
only due to changes in the spectrum (see discussion below and fig. 7).
The next step consisted in implementing tubes in all four blankets of module II. A simplifying
assumption was made that only the radius of the water cooling pipes change from blanket to
blanket, but not the number of pipes.3 The radius corresponds to the volume percentage of water
in the homogeneous mixture according to [4] which is now implemented in 11 water pipes in all
blankets of module II.
The calculations show that the further away from the plasma the less pronounced is the loss
in production taking fuel rods instead of a homogeneous mixture. Table 1 gives an overview
of the ratios in plutonium production between the homogeneous material mixture models and
models using breeding structures. Whereas in the plasma facing blanket the ratio is almost 6,
i.e. the homogeneous calculations give 6 times higher Pu production rates than with the blanket
structures, the further away from the plasma the lower is the ratio and it falls below 3 in blanket
4. Nevertheless, if breeding structures are going to be used to produce plutonium the numbers
from the parametric study with homogeneous material mixtures in [2] have to be corrected with
a factor of roughly 3-6.
3
The design radius and the nr of cooling pipes as well as other dimensions and the exact geometry of the
blanket structure is not known to the author. The choice of radius and numbers of pipes is arbitrary for this
analysis.
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
Figure 3: Inboard module II Blanket structure in a horizontal cut in the xy-plane (compare fig. 2 lower
left cut). Blanket 2 contains the breeding structures, in this case 11 fuel rods and cooling pipes in all 4
blankets. The radius of the water cooling pipes decreases. This is a simplifying assumption as the radius
should stay constant and the number of pipes should decrease.
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
5 Spectra
Typically in a fusion reactor the fast spectrum from the plasma typically found in the first wall
is slightly softened in the first blanket. But in comparison to a typical LWR spectrum it is still
very hard (fig. 5).
The spectrum in the homogeneous mixture case with water dispersed over the volume of the
blanket is barely effected by adding uranium to the blanket (fig. ??).
However, comparing the spectrum (· · ·) in fig. 5 and 6 for uranium and water homogeneously
dispersed in the blanket zone with the averaged spectrum of the blanket zone (—) in fig. 6
containing water pipes and fuel rods shows significant differences. Looking at the three different
zones reveals that the thermalization in the water pipes (- -) is almost completely decoupled
from the fuel rods (- ·· -) fig. 6 with an extremely hard spectrum. In the alloy containing rest of
the blanket (- cdot -) the spectrum is slightly softened.
A comparison of the homogeneously dispersed water (· · ·) in fig. 5, 6 and 7 with the same blanket
with a homogeneous mixture without water (–) shows that the spectrum then is almost identical
to the spectrum in the fuel rods (- ·· -) fig. 6 and 7.
Thus the spectrum in the fuel does not see the first resonances or the thermal part of the the
cross section, because it is cut of below 100 eV (fig. 8). In the homogeneous case instead the
resonances still influence the reaction rates as the spectrum has low energy tails.
Relative Neutron Flux
0.100
0.010
0.001
0.01
1
100
10
4
10
6
Energy [eV]
Figure 4: Normalised neutron energy spectra in module III in lethargy plot with first wall (...), first
breeding blanket (—) and in comparison to a typical ligh water reactor uranium fuel (- -) [?]. With
homogeneous material mixtures.
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
0.100
Relative Neutron Flux
0.010
0.001
-4
10
-5
10
0.01
1
100
Energy [eV]
104
106
Figure 5: Normalised neutron energy spectra in module III in lethargy plot for the first breeding blanket
with (—) and without (- -) the addition of uranium to the homogeneous mixture.
Relative Neutron Flux
0.100
0.010
0.001
0.01
1
100
10
4
10
6
Energy [eV]
Figure 6: MCNP results for blanket 2 in module II of the flux spectrum in the water filled pipes (- -),
in the Pb-17Li filled blanket zones (-·-), within the fuel rods (- ·· -) and the cumulative spectrum in the
blanket (—) in comparison to the homogenous mixture of all materials in the same blanket (· · ·). MCNP
model of PPCS-A fusion power plant.
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
Relative Neutron Flux
0.100
0.010
0.001
0.01
1
100
10
4
10
6
Energy [eV]
Figure 7: MCNP results for blanket 2 in module II of the flux spectrum within the fuel rods (· · ·) in
comparison to the homogenous mixture of all materials (- ·· -) in the same blanket and a homogeneous
mixture without water (—). MCNP model of PPCS-A fusion power plant.
Figure 8: (n,γ cross section of U238. Data from JANIS 2.2, NEA.)
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
6 Conclusion Outlook
The investigation of a new and so far rather crude model to implement breeding structures in
the PPCS-A model instead of using the simplifying assumption of a homogeneous mixture of
Pb-17Li alloy with uranium showed, that the Pu production rate drops significantly by a factor
of 3-6 depending on the position of the blanket to the plasma with the largest drop in production
happening close to the plasma with a very hard neutron spectrum and less so in the blankets far
from the plasma with already more moderated neutron spectra.
An first analysis showed that the thermalization effect of the water in the homogeneous mixture is
the main reason for this drop in Pu production rates between the heterogenous and homogeneous
case. This also gives a first hint on how the breeding blankets could be optimized. It will be
necessary to moderate the neutron spectrum close to the fuel rods containing the breeding
material.
Therefore it would be helpful to investigate more thoroughly the influence of the water cooling
pipes on moderation effects in the blankets. One could assume e.g. a cooling pipe surrounded by
fuel rods or even rod bundles surrounded by water. In any case to improve bthe breeding rate the
fuel rods have to be placed much closer to water containing areas. Additionally the power release
is of interest and the influence on tritium production. The analysis of the additional fission power
would also indicate how much fuel can be loaded in breeding structures in the different blankets.
In [2] one of the results was, that from an optimizing standpoint it might be interesting to use
the blankets further away from the plasma with high U-238 content for breeding.
A comparison should be made to the literature on fusion-fission hybrids and the breeding blanket
geometries considered in this literature.
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M. Englert - IANUS Working Paper 2/2011 - Pu-Production in a Tokamak Fusion Power Reactor
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