Neutron spectra in cores dedicated to waste transmutation

NEUTRON SOURCE SPECTRA

The distribution of neutron energies in a reactor differs from the fission neutron spectrum due to the slowing down of neutrons in elastic and inelastic collisions with fuel, coolant and construction material. Figure 1 shows the fission neutron spectrum for U-235 and Pu-239, approximated by Watt distributions [Brie97].

Figure 1: Fission neutron spectra for U-235 (red line) and Pu-239 (blue line), approximated by Watt distributions.

The median fission neutron energy is 1.6 MeV for Pu-239, and the average energy is 2.1 MeV. While 99.8% of all fission neutrons have energies below 10 MeV, spallation neutrons in sub-critical system may have energies up to the incident charged particle energy i.e. of the order of 1 GeV. As shown in figure 2, the fraction of high energy neutrons (E > 20 MeV) is less than 2% of the spallation neutron flux entering the core. Hence, the contribution of these neutrons to the overall neutron flux in a sub-critical system with a typical neutron multiplication of ~25 will be marginal. However, since the threshold for the (n,a) reaction in construction materials is situated at 3 - 6 MeV, these neutrons will account for about half of the gas production in claddings, ducts and target container, and are therefore of substantial importance in the modelling of radiation damage evolution in sub-critical systems.

Figure 2: Fraction of spallation neutron flux below energy E_n entering the container wall of a lead/bismuth filled target with 20 cm radius. The incident proton beam energy was set to 1 GeV. Note that only 1.4% of the neutron flux is above 20 MeV, with 1.2 % found in the intervall 20 - 150 MeV.

SLOWING DOWN

Materials having a high ratio of energy loss fraction to absorption probability are termed moderators. Examples are water, beryllium and carbon. These are employed in so called thermal reactors in order to slow down neutrons below the resonance capture region (1 eV - 10 keV). Hence, the high ratio of the fission cross section in U-235 and Pu-239 to the capture cross section in U-238 for slow neutrons (E < 1 eV) can be utilized to run power reactors on low enriched (or natural) uranium. If moderators are not present in a sufficient amount, most neutrons will be absorbed in the resonance region. Since the probability of fission in fissile nuclides relative to capture in U-238 is small in this region, a higher fraction of fissile nuclides is necessary to sustain a chain reaction. The necessary enrichment decreases with increasing neutron energies, hence pure metallic fuels (minimizing slowing down in the fuel) allow for lower enrichments and higher breeding ratios in breeder reactors. Unfortunately, one of the main safety mechanisms in critical systems, the enhanced neutron capture due to resonance broadening (the "Doppler" effect) becomes much less effective if the fraction of neutrons with energy below 10 keV shrinks [Walt81]. Therefore a compromise between the better neutron economy of a highly energetic spectrum and the larger safety margins of a slow spectrum constitutes of employing oxide fuels, where slowing down due to both elastic and inelastic collisions with oxygen is comparatively efficient.

TRANSMUTATION EFFICIENCY VERSUS SAFETY

In reactors dedicated to transmutation of long lived radiotoxic waste, one would like to minimize the uranium fraction in the fuel, in order to avoid production of Pu-239 from U-238 (and Np-237 from U-235). Since the Doppler effect is much smaller in all transuranic nuclides, safety margins decrease significantly. Thus, a minimal fraction of 40 - 50% of uranium (either U-238 or U-235) is envisaged for Actinide Burner Reactor (ABR) fuels [Muka98,Lang95]. The energy weighted neutron spectrum of an oxide fuelled, sodium cooled ABR core (32% TRU, 40% U-238, 28% Spinel) is shown in figure 3. The dips at 0.4 MeV and 1.0 MeV are due to inelastic scattering on oxygen. The average flux weighted neutron energy is as high as 460 keV, but 50 % of the flux is still below 130 keV. Eleven percent of the flux, corresponding to 24 percent of all fissions, is potentially affected by Doppler broadening of U-238 resonances below 10 keV.

Figure 3: Energy weighted neutron spectrum in the oxide fuelled core of a sodium cooled burner reactor, as predicted by an MCNP simulation. The core characteristics were analogue to those of the European CAPRA design [Lang95].

In order to maximize the elimination rate of transuranics, one would like to remove uranium from the core. Not only is the production rate of plutonium then minimized (neutron capture on Np-237 and decay of curium remain production channels), but also, since oxygen induced slowing down is no longer of the same significance, neutron flux energies may be raised to increase the fraction of direct fission in even neutron number nuclides like Np-237, Pu-240 and Pu-242. Substituting the oxide fuel with metallic or mono-nitride fuel, or the liquid metal coolant with helium gas leads to an increase in spectrum energies as well as an improvement in neutron economy. Since reactivity safety margins become very small, uranium free fuels are usually supposed to be accompanied by sub-criticality and an external accelerator driven neutron source. (The first fast reactors, Clementine and BR-1, used pure metallic plutonium fuel, but different safety mechanisms operate in small reactors like those.) In figure 4, the energy weighted neutron spectrum in an N-15 nitride fuelled sub-critical core cooled with lead/bismuth is shown [Taki98,Wall98].

Figure 4: Energy weighted neutron spectrum in the nitride fuelled core of a sub-critical, lead/bismuth cooled reactor, as predicted by an MCNP simulation. The core characteristics were analogue to those of JAERI's ADS design [Taki98].

The TRU fuel is diluted with 50% zirconium nitride in order to improve fuel behaviour and increase the volume of the sub-critical configuration. A further dilution would lead to a slower spectrum. The abscence of elastic scattering resonances in N-15 is notable. Consequently, the average neutron energy in the nitride core is as large as 160 MeV, with a median energy of 220 keV. In figure 5 a comparison of the fraction of flux below a given energy is shown.

Figure 5: Fraction of neutron flux below energy E, for the oxide fuelled, sodium cooled core (red line) and the nitride fuelled, lead/bismuth cooled core (blue line).

Note that fluxes above 1.2 MeV are fairly similar. An important difference in the spectra can be found in the region 0.8 - 1.1 MeV, which is the location of the fast fission threshold in Pu-240 and Pu-242. Thus, the spectrum averaged fission cross section for these nuclides increases with about 15% when substituting oxides with nitrides. Fuels having a large fraction of even neutron number nuclides will thus be sensitive to the type of fast spectrum, as seen in Figure 6.

Figure 6: Fraction of fission inducing neutron flux below energy E, for the oxide fuelled, sodium cooled core (red line) and the nitride fuelled, lead/bismuth cooled core (blue line). The TRU composition assumed corresponds to spent MOX-TRU plus minor actinides from the preceeding UOX-burning.

Simultaneously, the effective capture cross section in Pu-240 and Pu-242 is decreased by no less than 35% in the nitride fuelled, lead/bismuth cooled core. The combined effect is an increase in the fission probability in neutron absorptions from ~ 0.35 to ~ 0.50, and hence a significant lowering of the americium production rate. Major problems in fuel behaviour during irradiation caused by appearance of the a-emitters Cm-242 and Cm-244 are expected. Since curium production due to capture in americium is much more difficult to counteract, the importance of minimizing americium production in the second stratum of the nuclear fuel cycle is an additional argument in favour of introducing nitride fuels, in addition to their superiority with respect to thermal conductivity. The resulting lowering of the fission fraction in the resonance region from ~ 25% to ~ 10% (see figure 6), with a a correspondingly smaller Doppler effect, is less problematic if sub-criticality is employed.

REFERENCES