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of the core, is directly determined by the M s
value, not by k eff .
Figure 3 shows the evolution of the spallation neutron multiplication during a 180-day burn-up
period for the reference core, HYPER-HBA, and HYPER-OBA. Figure 4 compares the proton beam
currents required for 1 000 MW th fission power. It is observed that multiplication of source neutrons at
BOC is quite different from each other, despite that the k eff values are almost the same. Specifically,
M s of HYPER-HBA is significantly smaller that that of the reference core, while HYPER-OBA has a
little larger M s than HYPER-HBA. The small multiplication factor of HYPER-HBA is due to the fact
that a significant fraction of the spallation neutrons, which are generated in the central target zone, is
absorbed by B 4 C before they give birth to their descendants. Meanwhile, the relatively high
multiplication factor of HYPER-OBA is because the inner zone is poisoned with burnable absorbers,
thus the probability for a source neutron to be parasitically absorbed is lower than in HYPER-HBA.
One can see a rapid decrease of the M s
values, in Figure 3, at the early period of depletion. This is
due to the fact that M s
is proportional to 1/(1-k eff ) and partly because fission products are accumulated in
the core. In Figure 3, it is clearly observed that HYPER-HBA has the smallest burn-up reactivity swing
among the three cases. However, if the cycle length is short, e.g. 120 days, this smaller reactivity swing
has little advantage since larger proton beam current is required, as shown in Figure 4. On the contrary,
for a 180-day operation, it is worthwhile to note that total accelerator power is almost comparable to the
reference case and the peak beam current is smaller than that of the unpoisoned core. This advantage is
attributed to the smaller reactivity swing of the HYPER-HBA core.
For HYPER-OBA, one can note that change in M s
is a little smaller than that of the reference due
to reduced reactivity swing. In addition, the M s
value of HYPER-OBA is a little larger except in the
vicinity of BOC, compared with the reference case. From Figure 4, it is clear that HYPER-OBA needs
smaller integrated accelerator power and also smaller peak beam current than the reference HYPER
core, if the depletion period is greater than 60 days. Figures 3 and 4 indicate that HYPER-OBA has
slightly larger reactivity swing than HYPER-HBA. This is mainly because the amount of B 4 C in
HYPER-OBA is about a half of that of HYPER-HBA. If thickness of the B 4 C layer is increased, the
reactivity swing of HYPER-OBA would be reduced further.
Figures 5 to 7 show the normalised radial power distributions at three burn-up points, 0-day,
120-day, and 180-day. In the reference core (see Figure 5), it is seen that slanting of the radial power
distribution is very significant; the inner zone power increased considerably during the burn-up
periods, while the outer zone power decreased. Especially, power density in the innermost fuel
assembly increased by a factor of 1.256 (120-day operation) or 1.394 (180-day operation). Currently,
the maximum allowable radial peaking factor is set to 1.50 for the HYPER core. Consequently, for a
relatively long cycle length, e.g. 180-day, the initial powers of the innermost fuel assemblies should be
much lower than the current values. Of course, the inner zone powers should also be lowered even for
a 120-day operation, since the peaking factor of the inner zone fuel assemblies might be fairly large.
This result confirms that radial power distribution control is a big concern in a sub-critical core with
large reactivity swing. In addition, too large change in the radial power distribution is not favourable
from the discharge burn-up distribution.
For HYPER-HBA in Figure 6, a similar behaviour can be observed as in Figure 5. On the other
hand, one can see quite different trend in the HYPER-OBA core. As shown in Figure 7, the HYPER-
OBA core has also a one-way change in the radial power distribution, i.e. monotonic increase in the
inner zone and decrease in the outer zone. However, the power increasing rate of the innermost
assembly is significantly suppressed, compared with the reference core. In HYPER-OBA, the power
of the innermost assembly is increased by a factor of 1.229 (120-day operation), or 1.300 (180-day
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