System and safety studies of accelerator driven transmutation ... - SKB

fission and capture cross-sections for individual nuclides,
σ and σ c , have been calculated, according to
f
∫
, i ( E)
⋅φ(
E)
∫φ
( E)
dE
σ x dE
σ x,
i =
, (3)
where the indices x and i represent the type of reaction and
the respective nuclide. σ x, i ( E)
is the microscopic crosssection
and φ ( E)
is the neutron flux. σ f and σ c have been
calculated for the source neutrons and for the fission neutrons
in zone 1, for all nuclides and for all configurations.
Since the neutron energy spectrum is harder for the source
neutrons than for the fission neutrons, σ f is higher for the
even-N nuclides (those nuclides with even number of neutrons)
and vice versa for the odd-N nuclides, which is shown
in Table IV. The typical energy dependence of σ f for an
TABLE IV
even-N nuclide is characterised by a rapid increase within the
energy region between about 0.1 and 1 MeV. On the other
hand, for the odd-N nuclides, σ f is generally a decreasing
function with energy, which explains the lower values for the
source neutrons than for the fission neutrons. The typical
energy dependence of σ c for all fissile nuclides describes a
continually decreasing function with energy. Therefore, σ c
is considerably lower for the source neutrons than for the
fission neutrons for all of the present nuclides. The largest
relative difference is observed for 239 Pu.
In Table IV, the values of σ have been listed for configuration
I only. However, these values are representative
for all configurations, as there are only minor differences
between the configurations.
Flux-weighted Average Microscopic Fission and Capture Cross-sections, σ f and σ c [barn], for each Nuclide Present in the
Core, in Zone 1 for Configuration I. The relative differences between the values for the source neutrons and the fission neu-
source fission fission
trons, ( σ − σ ) / σ , are also displayed.
σ f
σ c
Nuclide
Fission
neutrons
Source
neutrons
Relative
difference
Fission
neutrons
Source
neutrons
Relative
difference
238
Pu 1.23 1.28 4% 0.42 0.29 -31%
239
Pu 1.70 1.64 -4% 0.37 0.22 -40%
240
Pu 0.41 0.50 22% 0.41 0.28 -31%
241
Pu 2.25 1.93 -14% 0.39 0.29 -25%
242
Pu 0.31 0.40 27% 0.38 0.25 -35%
241
Am 0.29 0.35 22% 1.60 1.20 -25%
243
Am 0.22 0.27 24% 1.36 0.96 -30%
244
Cm 0.48 0.61 27% 0.44 0.33 -25%
245
Cm 2.37 2.06 -13% 0.29 0.23 -23%
V.C.2. Macroscopic Cross-sections
The macroscopic cross-section represents the probability
per unit path length for a reaction to occur in a medium and
is of interest for the analysis of the source efficiency. In
particular the fission probability in the inner part of the core
is of large importance for the magnitude of ψ*. Since the
first fission reaction induced by a source neutron, generally
occurring in the inner part of the core, is the starting point of
each fission multiplication chain in the fuel, and since the
source efficiency is proportional to the total number of neutrons
produced by fission in the core, the larger probability of
the first fission to occur, the larger is the expected value of
ψ*. After the first fission, on the other hand, the multiplication
in the core is to a much higher extent determined by the
fundamental mode of the core. The importance of the secon-
dary source neutrons, i.e. those emitted in the fission reactions
induced by the primary source neutrons, is similar to
the average importance of all fission neutrons, which does
not change between the different configurations. Analogously,
a lower probability for capture of the primary source
neutrons in zone 1 also enhances the overall neutron production,
as well as the source efficiency. However, as was mentioned
above, the effect on the source efficiency is not determined
directly by the absolute macroscopic cross-sections
for the source neutrons, but by the ratio of the reaction probabilities
for the source neutrons over those for the fission
neutrons.
The flux-weighted average macroscopic cross-sections,
Σ x , have been calculated in zone 1 for each of the studied
configurations, according to