LEAD CONTAINING MAINLY ISOTOPE 208PB:
NEW NEUTRON MODERATOR, COOLANT AND REFLECTOR
FOR INNOVATIVE NUCLEAR REACTORS
V. Apse1, V. Artisyuk1, E. Kulikov1, G. Kulikov2, A. Shmelev1
1
National Research Nuclear University “MEPhI”, Moscow, Russia
International Science and Technology Center, Moscow, Russia
[email protected]
2
INTRODUCTION
In the 1980s the development of the leadcooled fast reactor BREST began thanks to the
initiative of Professor V.V.Orlov [1]. The leadcooled fast reactor is now one of six systems
under analysis within the frames of the
International Forum Generation-IV project [2].
One of the advantages from using lead in the
fast reactor core is its relatively weak neutron
absorption and elastic scattering. Double-magic
208
nucleus of isotope
Pb is characterized by
extremely small cross-sections of neutron
absorption and inelastic scattering; the latter is
especially important for fast reactors. The
208
possibilities for using mono-isotopic lead ( Pb)
have been investigated in the works [3 – 5].
It may appear paradoxical but, due to the
extremely weak neutron absorption, isotope
208
Pb could be considered as an effective
neutron moderator. As is generally known,
materials containing elements of small atomic
mass such as light and heavy water, graphite,
beryllium oxide, zirconium hydride and some
others are considered as neutron moderators. In
this article it is proposed to use a material
containing nuclides of large atomic mass,
specifically, radiogenic lead containing mainly
208
isotope
Pb as a neutron moderator, coolant
and reflector.
1. NUCLEAR DATA OF LIGHT NUCLIDES,
208
MATERIALS AND
PB
Neutron-physical characteristics of some light
(hydrogen, deuterium, beryllium, graphite,
oxygen) and heavy materials (natural lead and
208
lead isotope Pb) are presented in Table 1 [6].
One can see that elastic cross-sections of
208
Pb do not differ significantly
natural lead and
from
the
others,
being
between
the
corresponding values for hydrogen and other
light nuclides. Neutron slowing-down from 0.1
MeV to 0.5 eV requires from 12 to 102 elastic
collisions with light nuclides while the same
neutron slowing-down requires about 1270
208
elastic collisions with natural lead or
Pb. The
reason is the high atomic mass of lead
compared to the other light nuclides. From this
208
Pb are
point of view neither natural lead nor
effective neutron moderators.
Table 1. Neutron-physical characteristics
of some materials
Number of
th
σ(n,
σelastic collisions
RIn,γ + 1/V
γ)
Nuclide
(barn) (0.1MeV→ (mbarn) (mbarn)
0.5eV)
1
H
30.1
12
332
149
2
D
4.2
17
0.55
0.25
9
Be
6.5
59
8.5
3.8
12
C
4.9
77
3.9
1.8
16
O
4.0
102
0.19
0.16
Natural
11.3
1269
174
95
Pb
208
Pb 11.5
1274
0.23
0.78
Taking into account that capture crosssection at thermal energy and capture
resonance integral of natural lead are much
larger than the corresponding values of the most
light nuclides, it is safe to say that neutrons are
captured during the slowing-down process in
natural lead with a higher probability compared
to the slowing-down process in light materials.
So, only a small part of neutrons will slow down
to thermal energy. This means that thermal
neutron flux in natural lead will be much lower
than in the light materials.
208
At the same time the nucleus of
Pb is a
double magic nucleus with closed proton and
neutron shells. Thanks to this fact the capture
cross-section at thermal energy and capture
208
resonance integral of
Pb is much lower than
the corresponding values of lighter nuclides. We
can therefore expect that even with multiple
208
scattering of neutrons on
Pb during the
process of their slowing-down, they will be
slowed down to thermal energy with a high
probability and thus create a high thermal
neutron flux.
Neutron capture cross-sections of lead
isotopes, their natural mixture, graphite and
deuterium are presented in Fig. 1 [6]. One can
208
see that Pb has a lower capture cross-section
compared to such well-known and effective
neutron moderators as graphite and deuterium
at energies below 100 eV and 1000 eV,
respectively.
204
0.1
Pb
207
Pb
Pb
n
206 at
1E-3
1E-5
Pb
C
12
208Pb
D
10
0.1
1,000
1E+5
1E+7
Neutron energy (eV)
Fig. 1 – Capture cross-section of various
nuclides as a function of neutron energy
Some properties of neutron moderators at
20°С are presented in Table 2 [6–8]. It can be
seen that the average logarithmic energy loss of
neutrons in their elastic scattering by natural
208
Pb is many times less than that for
lead and
light nuclides. The reason is a much heavier
atomic mass of lead compared to atomic mass
of other light moderators. However, thanks to
very low neutron capture cross-section, the
moderating ratio, i.e. the average logarithmic
energy loss times scattering cross-section
208
divided by absorption cross-section, of
Pb is
much higher than that for light moderators. This
208
means that
Pb could be a more effective
moderator
than
such
well-known
light
moderators as light water, beryllium oxide and
graphite.
spectrum at a greater distance from the target
than in light moderators. So, we may obtain
more space for placing the materials to be
transmuted. Also, the problem of neutron
leakage may be weakened.
Note that the diffusion length of thermal
208
neutrons (L) in Pb is much longer than that in
light moderators. Therefore one could expect a
high thermal neutron flux in the blankets
208
Pb at a considerable distance
consisting of
from the ADS target. It is noteworthy that mean
208
lifetime of thermal neutrons in Pb is very large
(about 0.6 s). This effect could be used to
improve drastically safety of fast reactor
operation by slowing down progression of chain
fission reaction on prompt neutrons [9].
As a reflector of thermal neutrons, isotope
208
Pb is inferior to light materials on the reflecting
ability (albedo) with a thickness below 60 cm, but
208
Pb is superior to light materials with a greater
thickness thanks to small capture cross-section
(Fig. 2).
1.00
a
H2O
0.95
70
D2O
0.57
4590
BeO
0.17
247
12
C
0.16
242
Pbnat 0.00962 0.6
208
Pb 0.00958 477
1.35
58
66
160
3033
2979
3
147
37
56
13
341
0.2
130
8
13
0.8
598
Age of neutrons slowed-down in lead is
significantly higher than that in light moderators.
This physical characteristic defines a mean
distance between the place where neutrons
were generated (target) and the place where
they were slowed down. Therefore, the use of
lead in blanket of an accelerator-driven system
(ADS) may allow formation of thermal neutron
D 2O
12C
9Be
0.90
0.85
H 2O
0.80
0.75
0
Pb nat
40
80
120
160
200
Reflector thickness (cm)
Table 2. Neutron moderator properties at 20ºC
ModeAverage rating Neutron
Mean
Diffuage
logalifetime
ratio,
sion
Mode2
rithmic
of thermal
τ (cm )
length
rator
ξΣ
s
energy
neutrons
(0.1MeV
L (cm)
loss, ξ
Tth (ms)
Σ th →0.5eV)
208 Pb
0.95
Albedo
Capture cross-section (barn)
10
Fig. 2 – Comparison of thermal neutron
reflectors: dependence of albedo
on thickness of reflector
Thanks to closed proton and neutron shells of
Pb nucleus, its excitation levels are much
higher compared to other lead isotopes (Fig. 3).
208
Ei ; Ii
Mev
0.0; 0
Mev
Ei ; Ii
Mev
2.38; 6
2.00; 4
1.68; 4
1.34; 3
1.20; 0
0.80; 2
2.34; 7/2
2.61; 3
1.82; 3,4
1.56; 4
1.27; 4
0.90; 2
204Pb
Ei ; Ii
Mev
3.96; 6
3.71; 5
3.48; 4
3.20; 5
206Pb
0.0; 0
Mev
1.63; 3/2
0.89; 3/2
0.57; 5/2
207Pb
0.0; 1/2
Mev
208Pb
0.0; 0
Mev
Fig. 3 – Excitation levels of lead isotopes
Inelastic scattering
cross-section (barn)
3
206
Pb
207
2
Pbnat
1.01
Na
eff
1.00
K
0.99
0.98
0
208 Pb
20
40
60
80
100
Coolant density (%)
204Pb
Fig. 5 – Comparison of coolants:
dependence of Keff on coolant density
Pb
1
208Pb
0
0
Effective neutron
multiplication factor
This results in the fact that the threshold in
208
energy dependence of
Pb inelastic scattering
cross-section is at much higher energy
compared to other lead isotopes (Fig. 4) [6]. This
could drastically improve fast reactor safety
208
when
Pb is used as a coolant thanks to its
more favorable coolant density reactivity effect
by
decreasing
its
unfavorable
spectral
component [3] (this is considered in detail in the
next section).
5
10
15
Neutron energy (MeV)
Fig. 4 – Inelastic scattering cross-section of lead
isotopes as a function of neutron energy
208
2. ADVANTAGES OF
Pb APPLICATION
2.А. IMPROVED SAFETY OF FAST REACTOR
As is known, in a large fast reactor with
uranium-plutonium fuel and sodium coolant, the
spectral component of coolant temperature
reactivity coefficient (TRC) is unfavorable (large
in value and positive, i.e. reactivity increases
when coolant temperature increases) [10]. The
situation is nearly the same in the case when
natural lead is used as a coolant.
Increase of coolant temperature can result in:
• decreasing effective neutron multiplication
factor (Keff) due to larger neutron leakage;
• increasing Keff due to smaller capture of
neutrons;
• increasing Keff due to harder neutron spectrum.
208
Pb as a coolant helps to
The use of
weaken the unfavorable contributions of the last
two components into TRC. Indeed, smaller
208
values of
Pb capture and inelastic scattering
cross-sections
decrease
respective
TRC
components while the favorable component,
associated with neutron leakage, ensures
negative coolant temperature feedback (Fig. 5,
235
fast reactor [1], metal fuel contains 13% of U,
232
53% of Th and 34% of minor actinides).
To find out to what extent the theoretical
208
prerequisites on potential advantages of Pb as
a neutron moderator, coolant and reflector are
well-grounded, the lifetime of prompt neutrons in
the fast reactor core (simplified model) has been
calculated.
Neutron-physical calculations have been
performed using the computer code TIME26
[11], where one-dimensional model of fast
reactor in 26-group diffusion approximation is
considered. Evaluated nuclear data file BNAB-78
was used, which was processed by auxiliary
program ARAMAKO-C1 (preparation of selfshielded micro-constants for every reactor zone)
[12].
One-dimensional axial model of central
region in BREST-300 reactor was analyzed [13].
Main parameters for square elementary cell of
fuel rods are presented in Table 3.
Table 3. Main parameters
of the calculational model
Parameter
Value
Pitch of fuel lattice
13.6
(mm)
Diameter of fuel
7.7
meat (mm)
Thickness of contact
0.2
layer (mm)
Thickness of
0.5
cladding (mm)
Diameter of fuel rod
9.1
(mm)
3
Fuel
(U,Pu)N; γ=14.32g/cm
Natural uranium:
Uranium fraction
235
238
U–0.7%, U–99.3%
Reactor-grade plutonium:
239
240
Plutonium fraction
Pu–60%, Pu–25%,
241
242
Pu–11%, Pu–4%
Plutonium fraction
13.84
content (%)
Core breeding ratio
1.038
(CBR)
Contact layer and
3
Lead; γ=10.47g/cm
coolant
Stainless steel EP-823;
3
Cladding
γ=8g/cm ;
Fe–85%, Cr–12%, Si–3%
Core height (cm)
110
The initial goal was to determine such
neutron-physical parameters of one-dimensional
axial model for central region of BREST-300
core cooled by natural lead which are equivalent
to the parameters of two-dimensional model for
the same region. In subsequent calculations
effects were analyzed which are related to the
208
replacement of natural lead by Pb. As a result
208
the core (cooled by Pb), characterized by the
same values of Keff, CBR and TRC (as for the
core cooled by natural lead), has been chosen,
but the values of core height, pitch of fuel lattice
and content of Pu-fraction were properly
changed (Table 4).
208
Table 4. Replacement of natural lead by Pb:
its influence on the reactor parameters
208
Parameter
Natural lead
Pb
Core height (cm)
110
298
Pitch of fuel lattice (mm)
13.6
23.6
Content of Pu-fraction (%)
13.84
13.58
208
If natural lead is replaced by Pb, then Keff
increases by 7%; 80% of this effect is caused by
change of neutron spectrum while the other 20%
– by smaller neutron absorption. This
circumstance facilitated a significant increase of
fuel lattice pitch (from 13.6 mm to 23.6 mm).
Prompt neutron lifetime lprompt in BREST-300
reactor core is about 0.5 µs [14]. Replacement of
208
208
Pb as a
natural lead by Pb, i.e. the use of
coolant, neutron reflector and moderator,
extended prompt neutron lifetime to 1.35 µs, i.e.
by almost 3 times longer. This became possible
due to wider fuel lattice and better reflecting
208
properties of Pb.
208
If Pb reflector is thickened from 0.5 m to 5
m together with addition of 2-meter graphite
reflector, then prompt neutron lifetime increases
to 1 ms (i.e. by 2000 times!) and becomes
comparable with typical prompt neutron lifetimes
in thermal CANDU-type reactors (Table 5).
208
Table 5. Influence of Pb reflector
on prompt neutron lifetime
208
Thickness of Pb
5 + 2-m
0.5 5
10
reflector (m)
graphite
Prompt neutron
1.35 661 1000
lifetime lprompt (µs)
15
1240 1440
Such a drastical extension of prompt neutron
lifetime is caused by the following effect. Fast
neutrons from the reactor core penetrated
208
deeply into
Pb reflector, multiple neutronnucleus collisions slowed down these neutrons
and they came back to the reactor core after an
essential time delay (due to small absorption and
208
effective albedo of Pb). Since these returning
neutrons, in the terms of their origin, are prompt
neutrons, we can speak about the slowed
progression of chain fission reaction on prompt
neutrons. Let us consider the influence of this
circumstance on the reactor safety parameters.
We consider the reactor kinetics for the stepwise insertion of positive reactivity when positive
reactivity exceeds fraction of delayed neutrons
(ρ > β) and no feedbacks are taken into account.
Time evolution of neutron density can be
described by the following equation where the
first summand defines contribution of prompt
neutrons while the second summand defines
contribution of delayed neutrons:
 λρ 
n(t)
ρ
 t 6 β
=
⋅ exp  +  − ∑ i ⋅ exp  − i ⋅ t 
n(0) ρ − β
T
ρ
−
β

 i =1
 ρ−β  ,
where:
n(t) – neutron density at time moment t;
ρ – reactivity;
β – fraction of delayed neutrons;
βi – fraction of delayed neutrons in the i-th group;
T – reactor period,
T ≡ l prompt
(ρ − β) ;
λi – decay constant of nuclei-emitters of delayed
neutrons in the i-th group.
If transient time is relatively short, then the
second summand (delayed neutrons) may be
neglected. The feedbacks to work, the reactor
period T should be comparable with thermal
inertia parameter of fuel rod, which is within the
time range from 0.1 s for metal fuel to 3 s for
oxide fuel [10]:
T≡
lprompt
ρ−β
= 0.1 ÷ 3 s
This means that permissible step-wise
insertion of positive reactivity could exceed
delayed neutron fraction by no more than ∼
0.001 dollar for BREST-300 reactor core cooled
by natural lead (lprompt≈0.5 µs), and up to several
208
dollars if Pb is used, thanks to a much longer
prompt neutron lifetime (lprompt≈1 ms).
Let us consider the case when the step-wise
insertion of positive reactivity ρ/β=1.1 dollar.
Under these conditions the reactor runaway
without feedback effects is presented in Fig. 6
208
for two cases: natural lead or Pb are used as
coolant and neutron reflector.
Neutron density (relative units)
1E+32
BREST (Pb nat):
T = 0.0014 s
1E+24
1E+16
1E+08
1
0.00
BREST* ( 208 Pb):
T = 2.8 s
4.0
1.9
0.02
0.04 0.06
Time (s)
0.08
0.10
Fig. 6 – Reactor runaway without accounting for
feedbacks induced by the step-wise insertion of
positive reactivity ρ/β = 1.1 dollar
Neutron density upgrades by 32 orders of
magnitude just in 0.1 s in the first case (BREST
project), i.e. this is actually an explosion, and
only by 4 times in the second case (the use of
208
Pb as a coolant, neutron reflector and
208
moderator). So, the use of
Pb as a coolant,
neutron reflector and moderator in fast reactors
could drastically slow down progression of chain
fission reaction on prompt neutrons and thus
essentially improve the reactor safety.
2.B. THERMAL-HYDRAULIC ADVANTAGES
208
OF THE REACTOR CORE COOLED BY Pb
208
As it was shown above, the use of Pb as a
coolant in the fast reactor core leads to much
wider fuel lattice compared to the use of natural
lead thanks to favorable neutron-physical
208
properties of Pb. This opens up a possibility to
improve essentially the thermal-hydraulic
characteristics of the fast reactor core.
One more important issue is connected with
the influence of a wider fuel lattice and higher
core (see Table 4) on a pressure drop for
coolant flow through the reactor core. Evidently,
it is easier to create a regime for natural
circulation of coolant in the case of smaller
pressure drop needed for coolant flow through
the reactor core.
Let us assume that, upon replacement of
208
natural lead by
Pb, the coolant temperature
parameters and the core thermal power
remained the same.
The calculations showed (see Table 6) that
208
application of
Pb as a coolant in the fast
reactor core loaded with mixed uraniumplutonium nitride fuel allows us to achieve a
noticeable gain in the reactor parameters. It was
transpired that replacement of natural lead by
208
Pb while retaining the same values for Keff,
CBR and TRC by introducing proper changes
into content of Pu-fraction, pitch of fuel lattice
and height of the reactor core made it possible to
achieve the following effects:
• the same coolant heating up with a lower
coolant velocity (about 2 times lower);
• an essential reduction of pressure drop for
coolant flow through the reactor core (5 times
lower);
• the same thermal power with a smaller
number of longer fuel rods (2.5 times smaller).
2.C. ASSESSING THE POSSIBILITY OF
REPLACING NITRIDE URANIUMPLUTONIUM FUEL WITH OXIDE FUEL
BREST-300 reactor cooled by natural lead,
as proposed by the developers [14], is
characterized by improved safety and small
reactivity change during the reactor lifetime
(within delayed neutron fraction). This is
achieved mainly through the application of highdensity uranium-plutonium nitride fuel.
Since oxide fuel is commonly used in nuclear
208
reactors, the question arises: could
Pb allow
returning to a more widely used and industrially
established oxide fuel? Evidently, the transition
from (U,Pu)N-fuel to a lower-density (U,Pu)O2fuel will reduce, to a certain extent, the
advantages
that
were
achieved
from
208
replacement of natural lead by Pb.
To
answer
the
question,
numerical
evaluations were carried out in which the
previous approach was applied to definition of
the model parameters: the models are made
equivalent on the values of Keff, CBR and TRC
by introducing the proper changes into content of
Pu-fraction, pitch of fuel lattice and height of the
reactor core. Table 6 shows how content of Pufraction, pitch of fuel lattice and height of the
reactor core had to be changed so that the
replacement of (U,Pu)N-fuel by (U,Pu)O2-fuel
would not change the values of Keff, CBR and
TRC.
208
Pb application,
One can see that with
replacement of nitride fuel by oxide fuel
increased content of Pu-fraction, increased
height of the reactor core and decreased pitch of
fuel lattice. Nevertheless, fuel lattice is still much
wider compared to that if natural lead is used.
As is mentioned above, replacement of
208
natural lead by
Pb results in a remarkable
decrease (almost in 2 times) of coolant velocity
mainly thanks to the wider fuel lattice.
Replacement of nitride fuel by oxide fuel when
natural lead is used as a coolant requires
increasing the coolant velocity (by 60%)
because of tighter fuel lattice and larger height
of the reactor core. Finally, however, the losses
caused by transition from nitride fuel to oxide
fuel are not so large, and they can not nullify the
208
Pb application instead of natural
gains from
lead. Transition from (U,Pu)N-fuel to (U,Pu)O2-
fuel accompanied by replacement of natural lead
208
by
Pb nevertheless results in a desirable
effect, i.e. coolant velocity could be decreased
by 13% (Table 6).
Table 6. Transition from (U,Pu)N-fuel
to (U,Pu)O2-fuel
Natural 208
Parameter
Fuel
Pb
lead
(U,Pu)N
(U,Pu)O2
Pitch of fuel lattice (U,Pu)N
(mm)
(U,Pu)O2
(U,Pu)N
Height of the
reactor core (cm) (U,Pu)O2
(U,Pu)N
Coolant velocity
(relative units)
(U,Pu)O2
Number of fuel
(U,Pu)N
rods (relative
(U,Pu)O2
units)
Pressure drop for (U,Pu)N
coolant flow
through the
(U,Pu)O2
reactor core
(relative units)
Content of Pufraction (%)
13.84
14.81
13.6
12.2
110
125
1
1.60
1
13.58
14.45
23.6
20.4
298
314
0.59
0.87
0.41
0.89
0.39
1
0.18
4.02
0.57
A substantial decrease in the number of fuel
208
rods by switching from natural lead to Pb due
to considerably larger height of the reactor core
is an important effect. The 2.5 times fewer longer
fuel rods are required to obtain the same thermal
power (Table 6).
Transition from nitride fuel to oxide fuel with
natural lead as a coolant significantly increases
(by 3 times) the pressure drop required for
coolant flow through the reactor core. But the
208
gain obtained by replacing natural lead by Pb
is so large that, finally, application of oxide fuel
leads to a remarkable (almost in 2 times)
decrease of the pressure drop required for
coolant flow through the reactor core (Table 6).
2.D. POSSIBILITY OF FUEL BREEDING IN
AXIAL BLANKETS
As is known, application of blankets around
the reactor core is not envisaged in BREST-300
project. So, this reactor is not regarded as a fuel
breeder
[13].
More
favorable
negative
208
feedbacks, when using Pb as a coolant, allow
recovery of the axial and radial blankets in order
to return fuel breeding property to lead-cooled
fast reactors.
In this section the possibility of using an axial
blanket in the examined model of BREST-300
reactor is evaluated, when natural lead is
208
replaced by
Pb. Geometrical model of the
reactor included a core loaded with mixed
uranium-plutonium nitride fuel, an axial blanket
loaded with natural uranium nitride as a fertile
material and a layer of lead after the blanket.
The results reported above, obtained for a core
208
cooled by
Pb, are the input data for the
calculations.
The use of an axial blanket containing natural
uranium nitride can essentially change the model
parameters. Therefore the task involved the
following: first, to find a variant of the model with
the axial blanket which would be equivalent to
the initial model on the values of Keff, CBR and
TRC by varying content of Pu-fraction, height of
the reactor core and pitch of fuel lattice; second,
to evaluate blanket breeding ratio (BBR)
depending on its thickness. Results of the
calculations are presented in Table 7.
Table 7. Influence of axial blanket thickness
on reactor parameters
Axial blanket thickness (cm)
Parameter
0
10
20
40
60
Pu-fraction
13.58 13.51 13.46 13.39 13.35
part (%)
Pitch of fuel
23.6 22.5 21.9 21.4 21.3
lattice (mm)
Height of the
reactor core 298
270
260 256 255
(cm)
CBR
1.038 1.038 1.038 1.038 1.038
BBR
0.000 0.042 0.080 0.124 0.142
It can be seen that the increase of axial
blanket thickness leads to a gradual increase in
BBR, reaching saturation at BBR of about 0.14.
At the same time, content of Pu-fraction
decreases, fuel lattice becomes tighter and
height of the reactor core decreases. Using the
correlations given above, one can evaluate the
influence of axial blanket on coolant velocity and
the number of fuel rods when coolant heating up
and thermal power are kept at the same level.
The use of an axial blanket exerts an influence
on the value of pressure drop required for
coolant flow through the reactor core, axial
blanket and gas cavity. Results of the
evaluations are presented in Table 8. It is
assumed that the contribution of the axial
blanket to coolant heating up is negligible.
One can see that the appearance of the axial
blanket slightly worsened some reactor
parameters in comparison with those in initial
variant: coolant velocity and the number of fuel
rods, when coolant heating up and thermal
power are kept at the same level, somewhat
increased. This effect is mainly caused by a
tighter fuel lattice. The pressure drop for coolant
flow through fuel assembly changed the most
(almost twofold increase in relative units). The
reason is a combined effect from longer fuel rods
(core plus axial blanket and a cavity for
accumulation of gaseous fission products) and
from tighter fuel lattice.
Table 8. Thermal-hydraulic parameters
of models with axial blanket
Thickness of axial blanket
Parameter
(cm)
0 10
20
40
60
Coolant velocity
1 1.02 1.05 1.08 1.10
(relative units)
The number of
fuel rods (relative 1 1.10 1.15 1.16 1.17
units)
Pressure drop
required for
coolant flow
1 1.11 1.28 1.61 1.78
through fuel
assembly
(relative units)
Thus, the use of an axial blanket allowed to
increase the total breeding ratio (by 0.10 – 0.14),
but at the cost of a certain deterioration of some
other parameters. It was necessary to increase
slightly coolant velocity, the number of fuel rods
and, above all, to increase significantly the
pressure drop required for coolant flow through
the reactor core, axial blanket and gas cavity,
which could weaken a role of natural circulation
under emergency conditions.
2.E. HIGH NEUTRON FLUX IN ADS BLANKET
Extremely small capture cross-section and
small average logarithmic energy loss opens up
a possibility to obtain high neutron flux in large
volumes of an ADS blanket.
To find out to what extent theoretical
208
Pb
prerequisites for the advantages from
application correspond to the facts calculational
research was conducted to determine spaceenergy distributions of neutron flux in an ADS
blanket consisting of the following materials:
beryllium oxide, graphite, lead isotopes, natural
lead and bismuth. Light and heavy water were
not studied since their use in the vicinity of a
liquid-metal target in a high-temperature ADS is
quite questionable. The blanket was modeled by
an
infinite
homogeneous
non-multiplying
medium with flat source of fast neutrons at the
beginning of the coordinates.
To demonstrate the basic tendencies, the
energy of emitted fast neutrons was selected
equal to 0.1 MeV because, in this case,
distributions of neutron fluxes can be written in
analytical form [15]. With that, distribution of
slowing-down neutron flux is defined by the
following equation:
Φ sl [ x, u ] =
p ( u ) ⋅ Qf
ξ⋅u
3 ⋅ (1 − 2 3A )
⋅
4π
 x 2 ⋅ ξΣs2 3

⋅ exp  −
⋅ (1 − 2 3A )  (1)
u
4


and thermal neutron flux may be written as
follows:
Φ th ( x ) =
p ( u th ) ⋅ Q f
4 ⋅ Σa ⋅ D
τ th
x
+
 −x

2
⋅ e L ⋅ e L ⋅ 1 − erf ( X1 )  + e L ⋅ 1 − erf ( X 2 )   (2)


where:
X1 2 =
τ th
x
m
,
L
2 τ th
erf ( X ) =
X
2
− t2
e
dt – error function;
π ∫0
p ( u ) – probability for neutrons to avoid capture
in the slowing-down process to the lethargy “u”:
 u Σa ( u′ )

p ( u ) = exp  −∫
du′ (3)
 0 ξΣs ( u′ ) 
where:
x – spatial coordinate;
u – lethargy of neutrons (“th” means thermal
neutron energy - 0.0253 eV);
Qf – intensity of fast neutron source;
A – atomic mass of medium;
D – diffusion coefficient;
τ – neutron age;
L – diffusion length of thermal neutrons.
Results of the calculations showed that
neutron fluxes reached their maximum values in
208
Pb and graphite blankets. So, neutron flux
distributions are comparable in these media.
One can see from Fig. 7 that near the target the
fluxes of both thermal and slowing-down
208
neutrons in
Pb are several times higher than
208
those in graphite, and advantage of
Pb is
strengthened very rapidly when moving off the
target.
Probabilities for neutrons to avoid capture in
the slowing-down process to thermal energy
208
(see Eq. (3)) in
Pb and graphite are close to
each other and approach unity, being 0.993 and
0.997, accordingly, and significantly less unity in
natural lead (0.287). It is explained by the fact
208
that in the slowing-down process in
Pb and
graphite the neutrons are being scattered and
slowed down with much more probability than
they are captured. The opposite case occurs in
natural lead. Note that the average logarithmic
208
energy loss and capture cross-section of Pb is
approximately 17 times less, while the scattering
cross-section is 2 times greater than that for
graphite. This means that, on average, the
208
neutron slowing-down process in
Pb must
have 17 times more elastic collisions than in
208
graphite. However, at each elastic neutron- Pb
1000
208Pb:
Thermal flux
100
10
1
12C:
208 Pb
(P=0.993)
100
10
1
12 C
(P=0.997)
Pbnat (P=0.287)
0.1
0.01
0
40
80
120
160
200
Distance from source of fast neutrons (cm)
Thermal flux
208 Pb:
208
12
C:
1 eV
0.1
10 keV
0.01
0
1000
Thermal neutron flux
(relative units)
Neutron flux (relative units)
collision the probability of neutron scattering and
slowing-down is 34 times higher than the
probability of neutron capture in comparison with
graphite. As a result, it appears that higher
208
thermal neutron flux can be created in Pb than
that in graphite.
40
80
100 eV
120
160
200
Distance from source of fast neutrons (cm)
Fig. 7 – Fluxes of thermal and slowing-down
208
neutrons in Pb and graphite depending
on distance from ADS target
Indeed, near the target the slowing-down
208
neutron fluxes in Pb are higher than those in
graphite, and, when moving off the target, the
fluxes decrease slower than in graphite because
208
Pb has a greater atomic mass and,
accordingly lower average energy loss, which
defines both the amplitude of slowing-down
neutron fluxes near the target and their shape at
a distance from the target (see Eq. (1)). Near the
208
target, thermal neutron flux in
Pb is higher
208
than in graphite since Pb has a larger value of
scattering-to-capture cross-section ratio. When
moving off the target, thermal neutron flux in
208
Pb decreases significantly more slowly than in
208
graphite because diffusion length in
Pb is
considerably longer than in graphite (see Eq.
(2)). Note that thermal neutron flux in natural
lead is almost 3 orders of magnitude less than
208
that in Pb and decreases when moving off the
208
target essentially quicker than in Pb (Fig. 8).
208
Thus, it can be supposed that
Pb is a
number-one candidate for the role of neutron
moderator for creating a high-flux ADS blanket in
both resonance and thermal energy spectra. At
208
the same time, a blanket with Pb can have a
sufficiently large volume to place necessary
quantity of the materials to be transmuted and
solve the problem of neutron leakage.
Fig. 8 – Thermal neutron flux in Pb, graphite
and natural lead depending
on distance from the target
2.F. TRANSMUTATION IN RESONANCE
REGION OF NEUTRON ENERGY
High-energy neutrons leaving the target are
slowing-down as a result of elastic and inelastic
scattering on nuclides of the medium. Inelastic
scattering has a threshold nature and stops
acting, beginning from some, rather large value
of neutron energy. Elastic scattering acts at any
values of neutron energy.
Average part of energy which neutrons lose
as a result of elastic scattering is defined by
atomic mass of medium. In heavy media, for
208
example, in Pb, at each elastic scattering the
neutrons lose only a small part of their energy
while in light media, for example, in graphite,
they lose a significantly larger part of their
energy. As a result, the same resonance of
transmutation cross-section (radiative capture
cross-section for long-lived fission products and
fission cross-section for minor actinides) can be
either “wide” for slowing-down neutrons if they
have multiple scattering acts within the energy
range of this resonance or “narrow” if they are
going through the resonance range almost
without scattering acts [16] (Fig. 9).
σnγ
Neutron
moderator:
208Pb
Pb
(ξ ≅ 0.01)
Graphite
(ξ ≅ 0.16)
En
Fig. 9 – Passage of neutrons through resonance
in heavy and light media
In the first instance the neutrons remain
within the resonance range for a comparatively
long time and so the probability of their
absorption with subsequent transmutation of
long-lived fission products (LLFP) and minor
actinides (MA) increases. The opposite situation
is observed in the second case. Thus, the use of
208
a very heavy neutron moderator ( Pb, for
example) can result in a radical increase of
neutron absorption within the resonance energy
range. This could be attractive for transmutation
of LLFP and MA in the resonance neutron
spectra.
3. RADIOGENIC LEAD DEPOSITS
208
206
207
The isotopes Pb, Pb and Pb are the final
products of the radioactive decay chains of
232
238
235
Th, U and U, respectively:
232Th
α
6·α + 4·β
→ … … … … … … →
14.6 billion years
α
7·α + 4·β
235U → … … … … … … →
0.7 billion years
238U
α
8·α + 6·β
→ … … … … … … →
4.6 billion years
208Pb
207Pb
Table 9. Main deposits of uranium, thorium
and mixed uranium-thorium ores.
Elemental compositions of minerals and isotope
compositions of radiogenic lead
204
Deposit
Monazite
(Guarapari,
Brazil)
Monazite
(Manitoba,
Canada)
Monazite
(Mt. Isa Mine,
Australia)
Monazite
(Las Vegas,
USA)
Uraninite
(Singar Mine,
India)
Monazite
(South Bug,
Ukraine)
Natural lead
206Pb
Therefore radiogenic lead with large
208
Pb could be extracted from
abundance of
thorium and thorium-uranium ores [17-21]
without isotope separation.
The relative contents of lead isotopes in
radiogenic lead depend on the ore age and on
the content of natural lead as an admixture. The
208
206
contents of
Pb and
Pb in natural lead are
52% and 24%, respectively. It should be noted
206
that the capture cross-sections of
Pb,
208
although larger than those of
Pb, are
207
significantly smaller than those of
Pb and
204
Pb. So, at the first glance, it appears that the
208
206
ores containing about 93%
Pb and 6%
Pb
(Table 9) could provide the necessary
composition of radiogenic lead. However, the
first estimations showed that the content of only
204
207
1%
Pb and
Pb (these isotopes have high
values of capture cross-sections) in radiogenic
lead could significantly weaken the advantages
of radiogenic lead.
U/ Th /Pb,
(wt. %)
206
Pb/ Pb / Age,
208
6
Pb / Pb, 10
(at. %)
years
207
1.3 / 59.3 / 0.005 / 6.03 / 520–
1.5
0.46 / 93.5
550
0.3 / 15.6 / 0.010 / 10.2 / 1830–
1.5
1.86 / 87.9 3180
0.0 / 5.73 / 0.038 / 5.44 / 1000–
0.3
0.97 / 93.6 1190
0.1 / 9.39 / 0.025 / 9.07 / 770–
0.4
1.13 / 89.8 1730
64.3 / 8.1 / ––––– / 89.4 /
885
8.9
6.44/ 4.18
0.2 / 8.72 / 0.010 / 6.04 / 1800–
0.9
0.94 / 93.0 2000
––––––
1.4 / 24.1 /
22.1 / 52.4
–––
ACKNOWLEDGMENTS
The authors would like to express their
thanks to Russian-English professional translator
and editor Mr. Simon Hollingsworth for his
assistance with the editing of this work
(http://www.proz.com/profile/819).
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