Convolution of the neutron spectra with cross-sections

We record the neutrons that cross a plane of interest - SSW (Surface Source Write) card.We classify the neutrons at detector positions in energy bins - HTAPE3X.The result is the neutron spectra on the top of the target along its lenght.

The production rates in the detectors are calculated from the neutron spectrum as follows:

n (E) is the energy dependent neutron flux, (E) is the microscopic cross-section at energy E for a specific reaction, C=NA/M is the normalization constant. For neutrons in energy bins we use :

Cross-sections were taken from ENDF library, or were calculated from the experimental data (EXFOR).

Direct calculation of production rates

MCNPX can directly multiply each neutron that crosses the detector with the microscopic cross-section for a given reaction – F4 card with FM multiplier card.

The direct method is faster, the cross-sections are taken from “la150n” library. The results have to be multiplied with the normalization constant C=NA/M, where NA is Avogrado’s number and M is the molecular mass of the detector material.

Problem : the results from two methods are not always the same !

Motivation

ADS are future technology, the combination of a classical reactor with an accelerator. The basic principle is to produce a large number of neutrons in the spallation process (relativistic ions + heavy metal target), and to introduce them into a sub-critical reactor assembly. Extra neutrons are used to produce fuel from 232Th, and/or to transmute long-lived nuclear waste to short-lived isotopes.

At the JINR, series of experiments with different targets (lead, tungsten, bismuth cylinders, surrounded with polyethylene or with natural uranium and polyethylene) were performed. The physical aim of the experiments was to study nuclear processes that occur in the target, to measure the transmutation rates for higher actinides and fission products, to measure the heat production, etc. The NAA (Neutron Activation Analysis) was mostly used to measure the neutron field and the transmutation rates.

The experimental results are used to test two calculation codes: DCM (Dubna Cascade Model) and MCNPX (LAHET in combination with MCNP). This paper is focused on the calculations with MCNPX 2.4.0 of the the Phasotron experiment.

MCNPX Benchmark Tests of Neutron Production in Massive Lead Target

24Na production rates

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Results with HTAPE3X method, simple target, beam in the center

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Mitja Majerle1*, J. Adam1, P. Čaloun1, S. A. Gustov2, V. Henzl1, D. Henzlová1, V. G. Kalinnikov2, A. Krása1, M. I. Krivopustov2, F. Křížek1, A. Kugler1, I. V. Mirokhin2, A. A. Solnyshkin2, V. M. Tsoupko-Sitnikov2, V. Wagner1

*) Electronic address: majerle@ujf.cas.cz

1) Nuclear Physics Institute of the Academy of Science of the Czech Republic, Prague, The Czech Republic

2) Joint Institute for Nuclear Research, Dubna, Russia

The PHASOTRON experiment

We used continuos, intensive (1013 protons/s), stable beam of protons with the energy 660 MeV from the Dubna Phasotron.

The protons were directed to a lead target (cylinder with r=4.8 cm and d=4x12cm). The target was placed in a long, narrow corridor, bounded with concrete walls.

A set of monitor detectors (few m thick Al and Cu foils) was placed directly in the beam in front of the target. Neutron detectors (Al, Au, and Bi foils) were placed on top of the target, along its whole length.

After the irradiation, the activity of the detectors was measured in HPGe detectors, and the production rates of transmuted elements were calculated.

Calculation principles

Our calculations were done with MCNPX 2.4.0. We described our setup as a cylindrical lead target, to which a proton beam is directed. To compare the calculations with the experimental data, we had to calculate the production rates. We tried two different methods.

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The influence of the setup parts

Conclusions

We are testing the capabilities of MCNPX, exploring which calculation methods are the best for our setups and consequently ADS system. A lot of experimental data from experiments with similar setups waits to be simulated. With MCNPX, we are able to describe the systems similar to ADS with the accuracy of ca. 30%.

Calculating in parallel with MCNPX gives very good results for our setups – the speed almost linearly rises with the number of used processors. Calculating in parallel with PVM is now used at all our calculations.

We want to test the dependency of the speed of simulations on the number of used processors and the number of events to find an optimal number of computers in case of building a computational farm for ADS simulations.

Acknowledgments

The authors are grateful to the staff of the Dubna Phasotron accelerator for providing a good proton beam for our experiment.

These experiments were supported by the Czech Committee for collaboration with JINR Dubna. This work was carried out partly under support of the Grant Agency of the Czech Republic (grant No. 202/03/H043) and ASCR K1048102 (the Czech Republic).

References

On the field of ADS, the author most profited from the articles of K.D. Tolstov, C.D. Bowman, C. Rubbia. Data about the experiment comes from many publications of co-authors and my work. A great guide on how to build the cluster was found on Echelon Beowulf Cluster homepage, and in Linux how-to’s. MCNPX manual and internet forums on RSICC were the main resources when trying to get MCNPX with PVM work and when discovering MCNPX capabilities.

MCNPX in parallel

Four computers from our office with preinstalled systems can be temporarily changed to computing workstations. We used Slackware Linux 10.1 on the server, the Etherboot method to boot hosts, NFS (Network File System) for their file system, directories which need writting permissions were mounted as ramdisks. Hard-drives of hosts were not used. Using this method, we can easily extend the cluster to a random number of computers. The information on how to build such a cluster was found on internet.

To calculate in parallel, a software package that distributes the load on other processors has to be used. MCNPX 2.4.0 has built-in support for PVM (Parallel Virtual Machine). PVM was installed on hosts, MCNPX was compiled with the PVM support, and the efficiency of the parallel computing was tested.

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Schematics of the setup

Experimental results (Al – left, Au – right)

Calculated neutron spectra along the target Calculated production rates

Ratio between results from HTAPE3x and from F4 card methods.

Comparison with experimental data

We found out that we can simplify our simulations to a bare lead target inside concrete corridor, a simple simulation with BERTINI INC is sufficient. Holders, beam tubes, etc. do not need to be taken in account. Knowing the exact position of the beam and its geometry is important.

The influence of the beam geometry

The accelerator beam had a Gaussian shape and was displaced. Extensive simulations on this and other setups taught us that the beam, displaced for 3 mm results in a change of neutron field for ca. 5%.

The influence of the different intra-cascade models

The simulations were done using the intra-nuclear cascade model BERTINI INC. The calculations with two other models - CEM INC and ISABEL INC - showed that the choice of the model does not influence the results. The models describe the nuclear reactions the same in the range of few hundreds MeV.

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Production rates for 198Au

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We included concrete walls in our calculations. They function as a neutron moderator and reflect a significant part of neutrons back. The refleced neutrons are homogeneously distributed along the target lenght. These neutrons produce 198Au in a non-threshold reaction 197Au(n,)198Au.

The iron components do not influence the results significantly. This is expected, iron causes only scattering of neutrons, but our detectors lie on place where these effects are minimal.

Calculated prduction rates for 198Au (left)Comparison of calculations and experimental data (right) –

the agreement is somewhere inside 30%

Calculated neutron spectra for a bare target (left)and for a target inside the corridor (right)

We have two two-processor computers (processors Xeon 2 GHz) with preinstalled Linux, intended for calculations (MCNPX, ROOT,...). In setting up the cluster, we gained experience that helped us to set the machines intended for calculations to work in parallel. They calculated faster than our cluster.

We tried MCNPX, compiled with different compilers (PGF90, G95, GFORTRAN, Intel Fortran Compiler). Intel Fortran Compiler did the best job, MCNPX compiled with it calculates 40% faster than with PGF90.

The dependancy of the speed of calcualtions on the number of used processors for a heterogenous cluster (up) and on

2 two-processor machines (left)

Experimental and calculated (HTAPE3X) rates for Bi

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