The author's group has been investigating how the performance estimation of nuclear-data benchmark using experiment and its analysis by Monte Carlo code should be carried out especially at 14 MeV. We have recently found that a detector contribution played a benchmark role not only to the neutron producing the detector contribution but also equally to all the upstream neutrons during the neutron history. This result would propose that the benchmark performance could be evaluated only by a forward Monte Carlo calculation.
In this study, we thus defined new functions to give how well the contribution could be utilized for benchmarking using the point detector, and described that it was deeply related to the newly introduced “partial adjoint contribution”. By preparing these functions before benchmark experiments, one could know beforehand how well and for which nuclear data the experiment results could do benchmarking in forward Monte Carlo calculations.
There are a lot of benchmark experiments carried out so far using massive samples and DT neutrons [1], [2], [3], [4] and [5]. They are usually called “integral experiment” and have an important role of checking nuclear data for intermediate energies below 14 MeV as well as at 14 MeV especially for a fusion reactor. The author's group has thus been carrying out investigation of how well integral benchmark experiments with DT neutrons could play a benchmarking role for energies below 14 MeV [6], [7] and [8].
From the results of the series study, especially for the benchmark experiments with DT neutrons, it was found that for gamma-ray spectrum measurements nuclear data at around 14 MeV were dominantly benchmarked. In return, for neutron spectrum measurements those below 14 MeV as well as at 14 MeV were found to be benchmarked fairly well, because neutrons could be rapidly moderated in sample materials. In conclusion, to make benchmark experiments more efficient, use of a spectrum shifter made of beryllium would be quite effective in order to make the incident neutron spectrum softer specifically for the gamma-ray spectrum measurements.
In case of carrying out the above benchmark analysis using experimental results with DT neutrons, it was thought to be reasonable and acceptable to set an energy boundary only at 10 MeV, meaning the number of the energy groups was just two, because the incident neutron is mono-energetic and so that it would be possible to think of neutron energy groups just as 14 MeV (source neutrons) and others (scattering neutrons). This means that discussion could be conducted using “neutron spectrum before last collision”, which was defined as an energy spectrum of neutrons making neutrons or gamma-rays directly detected by a detector in the spectrum measurement. It was confirmed that this process of using two energy groups worked quite well for the benchmark performance analysis for the DT neutron incidence experiments. However, in a general case it seems to be clearly insufficient to employ only one energy boundary. Practically, a crucial problem would possibly exist as in the following. Now, if using finer energy bins for a general benchmark performance analysis, we can consider that there exist neutrons (A) making neutrons conveying contribution to a detector, and also there exist neutrons (B) making neutrons (A), and so on. The key point is that one has to think of not only neutrons (A) but also other neutrons created during a whole particle history starting from the source.
For this problem, we carried out a thought experiment to precisely examine which neutron (nuclear data for the energy) created during a transport history is benchmarked by the detector contribution [9]. The error sensitivity appearing between measurement and calculation was estimated and discussed by using a point detector normally used in Monte Carlo code calculations and assuming a small cross section perturbation. The error sensitivity in the benchmark analysis means which neutron's contribution causes discrepancy between experiment and calculation. From the result, the error sensitivity was found to be “equally” due not only to contribution directly conveyed to the detector, but also due to indirect contribution of neutron (A) making the neutron conveying the contribution to the detector, contribution of neutron (B) making neutron (A) and so on. From this concept, it would be expected to become possible to know from a forward Monte Carlo calculation carried out prior to a benchmark experiment, how well and which neutron (nuclear data for the energy) could be benchmarked in the benchmark experiment.
As well known, this kind of analysis would be realized in principle, if the adjoint function would be evaluated. At present, however, it is still difficult to estimate it especially in Monte Carlo calculations.
In the present study, based on the results of the thought experiment above, we discuss what kind of physical quantities derived from the forward Monte Carlo calculation should be taken into consideration to evaluate the benchmark performance especially from the standpoint of nuclear data. In the following chapters, we define “benchmark performance function”, which shows how efficiently a value in each energy bin in the measured neutron spectrum could contribute to benchmarking of the nuclear data. And in addition, “benchmark performance density function” is defined, which shows how well and to which neutron (which energy of the neutron) the value could contribute to benchmarking. Then it will be shown that the function can be made up by simply summing up newly defined “partial adjoint contribution” constituting of the “adjoint portion” previously defined for the forward Monte Carlo calculation by Murata et al. [10].
When neutron spectrum is measured to benchmark nuclear data via transport calculations, it would be very useful if we could know in advance how well and of which neutron the measured spectrum can be used to benchmark the nuclear data. In the present study, based on the result of the thought experiments carried out so far by the author's group, it was confirmed that the detector contribution could benchmark nuclear data not only for a neutron (A) making the contribution, but also of a neutron (B) making (A) and so on “equally”, and we introduced and defined two new functions to evaluate the benchmark performance for the measured spectrum, i.e., “benchmark performance function” and “benchmark performance density function”. It was confirmed that they could be estimated by simply summing up newly defined “partial adjoint contribution”, which expected to be deeply related to “adjoint portion” used to calculate the adjoint flux with a point detector in forward Monte Carlo transport calculations. By calculating these functions before a benchmark experiment, one can know in advance how efficiently benchmarking of nuclear data could be carried out by the experiment without calculating the adjoint function, i.e., not spoiling merit of use of Monte Carlo transport code.
