A Monte Carlo Model of the D-D Neutron Source at FNG

A Monte Carlo Model of the D-D Neutron Source at FNG Alberto Milocco 1, Andrej Trkov 1, Roberto Bedogni 2, Mario Pillon 3 1 Jožef Stefan Institute Jamova cesta 39, SI-1000 Ljubljana, Slovenia Alberto.Milocco@ijs.si, Andrej.Trkov@ijs.si 2 ENEA FPN-Fusione Via Enrico Fermi, 45-00044 Frascati, Rome, Italy Mario.Pillon@enea.it 2 Istituto Nazionale di Fisica Nucleare Via Enrico Fermi, 40-00044 Frascati, Rome, Italy Roberto.Bedogni@lnf.infn.it ABSTRACT The Deuteron - Deuteron (D - D) fusion reactions are foreseen for the next stage fusion reactors. The Frascati Neutron Generator (FNG), located near Rome, can produce neutrons of about 3 MeV by accelerating Deuterons onto solid targets containing Deuterium. A computational model is developed for the simulation of the FNG neutron source. It requires the specification of the beam and target characteristics (e. g. Deuteron energy, Deuterium atomic fraction). The model is implemented in the subroutines of the MCNPX and MCNP5 codes, which need so far to be recompiled. The Deuterons are transported inside the solid target by a Monte Carlo method. The neutrons are generated with the angle - energy distribution as defined by the laws and nuclear data for the Deuteron - Deuteron reaction in the ENDF/B-VII library. The sensitivity studies on the input parameters of the D - D model are presented. The modelling of experiments with the D - D neutron source is feasible concerning the main features and associated uncertainties of the source term. Perspective activities would involve validation with experimental data. 1 INTRODUCTION The deuterium is a chemical element consisting of a neutron, a proton and an electron. It has a natural abundance in the oceans of Earth of approximately one atom in 6,500 of hydrogen. It was first detected spectroscopically in late 1931 by Harold Urey, a chemist at Columbia University [1]. Urey was awarded the Nobel Prize in Chemistry in 1934 for this work. He called the new isotope deuterium, from the Greek deuteros (second), and he claimed its nucleus to 1015.1

1015.2 be called deuteron. The major breakthroughs in modern nuclear physics, which took place at the Cavendish Laboratory in the 1930s, have seen the deuteron as an actor. The first device for the acceleration of charged particles was constructed by Sir John Cockcroft and Ernest Walton in 1932. Rutherford asked to Sir Mark Oliphant to construct a high-current 200 KV accelerator to complement the lower intensity and higher voltage equipment of Cockcroft and Walton. An increased accuracy was thus pursued for the mass measurements of light elements. At the end of 1933, the chemist Gilbert Lewis from Berkeley brought to England two tiny phials, each containing one drop deuterium oxide (i. e. heavy water). They were entrusted to Sir Mark Oliphant to see whether he could extract some deuterons to use as bombarding particles. He found that deuterons interact with other deuterons according to the reactions 2 H(d, p) 3 H and 2 H(d, n) 3 He [2]. The new element 3 H (or tritium) was produced. The Q value of the latter reaction is 3.27 MeV and the maximum of the cross section occurs at 2 MeV. This means also that intense neutron fields can be produced with low-accelerated deuterons. The deuteron-deuteron (D-D) reaction has been addressed for its importance in basic nuclear physics, nuclear weaponry and fusion reactors. The current projects on fusion power (e. g. ITER [3]) require thorough investigations into the materials to employ in this and future fusion reactors. In future, also nuclear power plants based on D-D reactions are foreseen [4]. Experiments have been performed and planned for testing the neutronic properties of the components. The nuclear data are needed at higher energies then those concerning fission neutronics and with high accuracy and precision. In particular, The D-D neutrons span the MeV energy range. The uncertainties in the experimental data need to be carefully assessed. Those concerning the neutron source are of particular importance because these propagate to the final results. The neutron generators for experimental activities usually consist of a linear accelerator that produces a low energy and collimated D-beam, a target containing deuterium and auxiliary structures, such as detector system, cooling system, room walls, etc. 2 THE D-D SOURCE ROUTINE Simple models for the representation of a D-D neutron source can be found in the literature, which provide an evaluations of the average neutron energy and angular yield as a function of the emission angle [5]. The effect of the deuteron slowing down may be included as a thick target assumption. This approach is not sufficiently accurate. In order to improve the model and to assess individually any contribution to the total uncertainty in the source term, it is necessary at least to model the deuteron interactions inside the target and get information on the deuteron energy and direction while slowing down. This issue is a problem of ion transport in matter. For the computer simulation of the slowing down and scattering of ions in materials, the Monte Carlo methods have a number of distinct advantages over analytical formulations based on transport theory. For instance, it allows more rigorous treatment of elastic scattering. Many codes for tackling this problem are available. Among these, the SRIM code [6] and the MCNPX code [7] are well-established ones. Both codes rely on physical models for the deuteron transport in the matter. The MCNPX physics models are designed for 200 MeV and higher D-energies and their application is questionable below a few MeV. On the other hand, SRIM has seen a thorough validation because of its wide range of application (ion stopping and range in targets, ion implantation, sputtering, ion transmission, ion beam therapy). Neither the SRIM nor the MCNPX code can be used to produce the source neutrons. The SRIM code does not include nuclear reactions at all. In the MCNPX code, D-energy cut-off for the D-D fusion reaction is 2 MeV, so neutrons cannot be generated with MCNPX at the low energies of

1015.3 the generators under discussion. So far, specific routines need to be implemented to obtain the neutron spectra at different angles. In general, it is advisable not to introduce unduly approximations in the geometry and material specifications of a neutron transport problem. To this extent, the MCNP family of codes (MCNPX or MCNP5) has become a major tool for nuclear analysts. The coupling of the neutron source evaluations with these transport codes is definitively an asset. In this way, it is straightforward to include the details into a computational model of the experimental set-up, such as the target structures, the detector system or the room walls. The uncertainties relating to the deuteron beam have not yet been considered. The engineering features of the accelerator should be addressed. For instance, the information on the deuteron pulse in pulsed beam experiments may be important. It is possible to overcome this problem with simple mathematical models, which can be included within the MCNPX(5) input files. 2.1 The original FNG source routine The compilation of a benchmark experiment usually requires providing an evaluation of the neutron source term from the experimental facility. For the quality control of the benchmark information, the models employed for the evaluation are sometimes also available. This is the case of the source routine developed at the Frascati Neutron Generator facility (FNG, Rome, Italy [8]) for the simulation of the deuteron-tritium (D-T) source neutrons. The FNG source model became available in the SINBAD database (Shielding International Benchmark Archive Database [9]). The source routine consists of a set of subroutines to compile with the MCNP4C code. These subroutines are SOURCE.F90 (coding the D slowing down in solid titanium-tritium target and modelling the fusion reactions), SRCDX.F90 (specific for transporting neutrons generated in SOURCE to point detectors) and six other subroutines for numeric calculus (e.g. RO- TAS.F90 converts angles from centre of mass to laboratory system). The FNG source routines require the use of the RDUM card in the MCNP input file to specify: deuteron beam energy, target thickness, tritium/titanium atomic fraction, beam width, target axis coordinates. For the modelling of the D-ion transport inside a solid target, the main author M. Pillon translated the statements of an old version (1996) of the TRIM code (TRansport of Ions in Matter, the major section of the SRIM code) into the Fortran language, since the code was originally written in the Basic language. M. Pillon implemented the original part concerning the neutron production by D-T reactions, which depends on the deuteron-interaction cross sections. The model for the tritium target is supposedly valid for the deuterium target too. M. Pillon produced a scratch version of the routine for the D-D neutron source. 2.2 Improvements and extensions The original FNG source subroutines have been revised, improved and extended. Some flaws have been corrected that concerned the range of the deuterons in the target and the deuteron collision spectra. A new condition has been implemented into the SOURCE routine to terminate the Monte Carlo history when the cumulative deuteron free flight path exceeds the target thickness. The FNG source model has been compiled with the latest versions of the MCNP5 and the MCNPX source codes. A major contribution to the source model is represented by the internal calculation of the cross sections. The angle-integrated cross sections and the Legendre coefficients from 0.01 to 10 MeV are copied from the ENDF/B-VII library (MF=5, MT=50 and

1015.4 MF=3, MT=1 respectively) into the SOURCE routine data section. After any deuteron collision, the nuclear data are linearly interpolated, the Legendre polynomials generated and the neutron angular distribution is reconstructed. In the present work, the source model is finally extended to simulate the neutron production with deuterated targets. 3 VERIFICATION 3.1 Checking of the deuteron transport features The TRIM model implemented in the FNG source routine is indeed a simplification of the whole set of patterns, which are implemented in the current version of the TRIM code [10]. For instance, the conditions at the layer edges, such as a special treatment of the first collision, are dropped in the source routine model. Nevertheless, a general consistency is expected about the features concerning the deuteron transport as performed by TRIM (SRIM 2008) or by the source routine. The analytical tools for a proper comparison have been implemented in a test version of the source routine and on MATLAB functions. TRIM is an established code for reference range calculations. The Mean Projected Range is the average distance the deuteron ions travel in the direction of the beam. The radial range is the average radial spread of the ion tracks, assuming cylindrical symmetry. The square root of the variance, which is the second moment of the range distributions, is the Straggling. It is included as an error bar in the present analysis. Figure 1 reports the results of the comparison between TRIM calculations (down to 10 KeV D-energy) of the forward and radial ranges and the same quantities extracted from the source routine. The agreement can be considered fair. Figure 1: forward and radial range with associated straggling for energies from 0.1 to 10 MeV Figure 2: Collision density histogram as retrieved from TRIM EXYZ file and equivalent file from the source routine test version An output file from TRIM contains the printouts of the ion energy after the collisions. A consistent file was generated from the test version of the source routine. The ion energies after any collision are binned in a very fine energy mesh from maximum energy 250 KeV down to the cut-off energy 10 KeV. The d-collision densities are compared in Figure 2. The consistency is satisfactory, also taking into account that the first collision is treated in a different way.

1015.5 TRIM provides complete information on the transmitted ions. In the source routine, the target thickness condition was temporarily used to print out the energies of the ion flux when crossing the edge of the target. Some approximation is introduced because the ion energy is duly calculated at end of any free flight path, and not just at the edge crossing. In the first case (Figure 3), the starting deuteron energy is set to 250 KeV and the target thickness at 0.5 µm. The agreement between the spectra predicted by TRIM and by the source routine are in fair agreement. Figure 4 presents further comparison with the deuteron flux as calculated with MCNPX, which allows the deuteron transport above 2 MeV. The starting deuteron energy is 5 MeV and the target thickness is 50 µm. The most probable energy of the transmitted deuterons for the TRIM and the source routine calculations are quite near, but the the spectra differ. These results do not agree with the MCNPX ones (Figure 4). The latter depend on different stopping power data, as can be inferred from the comparison with the deuteron flux obtained inserting the MCNPX de/dx data in the source routine. The spectrum of the transmitted deuterons indicates that the use of the source routine may be questionable above some energy in the MeV region. Figure 3: Normalised spectrum of the 250 KeV-deuterons transmitted across a 5 µmtarget Figure 4: Normalised spectrum of the 5 MeV-deuterons transmitted across a 50 µm-target 3.2 Control of the nuclear data The source routine calculation of the cross sections is validated against well-known codes for nuclear data representation, namely JANIS [11] and ENDVER [12]. Starting from from the same ENDF/B-VII Legendre coefficients, the neutron angular distributions for 1 MeV incident deuterons are first compared in the CM system (Figure 5) and after transformation into the LAB system (Figure 6).

1015.6 Figure 5: Centre of mass cross section: comparison between source routine calculation and JANIS output Figure 6: Laboratory cross section: comparison between source routine calculation and ENDVER output 3.3 Cross-checking of SOURCE, ROT and SRCDX subroutines In the source routine (SOURCE subroutine), the neutron emission angle is extracted by a rejection method from an angular distribution in the CM system because the Legendre coefficients are evaluated in this frame, then it is converted by subroutine ROT (which is a modification of the original ROTAS subroutine) into the LAB system taking into account also the direction of the ion. The consistency is checked between the sampling in the CM system and the results in the LAB system. First, the deuteron energy is set to 1 MeV to obtain the reference angular distribution (the same as in Figure 6, besides a scaling factor). The effect of the neutron angle sampling is separated by fixing the deuteron forward direction. The application of the rejection method indeed provides the theoretical angular distribution in the LAB system (labelled pure rejection method in Figure 7). The effect of the ion angular deflections in the target is a decrease of the neutron emission anisotropy with respect to the forward direction. This effect is minimised in the thin target case (Figure 7) setting target thickness to some minimal value. With the source subroutine, this is accomplished thanks to the target thickness condition. The neutron energy is calculated from the incident deuteron energy in the target frame, which is as well extracted by a rejection method from the angle-integrated cross section. The parameters needed for the neutron production in the SOURCE subroutine are passed to the SRCDX subroutine, which is needed to perform the deterministic neutron transport to the point detectors defined in the MCNP input. In the SRCDX subroutine, the angular distributions are generated in the LAB system. The consistency is checked between the track length estimator of the cell flux (Tally 4 in the MCNP terminology), which only needs the SOURCE subroutine, and the point detector flux estimator (Tally 5 in the MCNP terminology), both at 0, 60 90, 120 and 180 degrees from the deuteron beam direction and 1 m away from the source (Figure 8). Besides some statistical uncertainty concerning the cell flux, the agreement between the outputs of different subroutines is satisfactory.

1015.7 Figure 7: Checking of the CM into LAB system transformation and thickness condition Figure 8: Tally 4 and tally 5, in the MCNP terminology, from the forward direction (right of the picture) to the backward direction (left of the picture) 4 CONCLUSIONS The source subroutines, which were originally available in the SINBAD database for the simulation of the deuteron-tritium neutron source, were extended to the deuteron-solid deuterated targets. Since the anisotropy of the D-D reaction usually needs to be addressed, a feature to underline is the inclusion of a minimal set of nuclear data (Legendre coefficients) to achieve accurate neutron angular distributions. Moreover, the data range from 10 KeV to 10 MeV incident deuteron energy. A thorough verification on the internal features is presented. The deuteron transport, as performed in the D-D source model, is consistent with the original TRIM code. Concerning the neutron production, the angular distributions are checked in both the centre of mass and laboratory frames. The new source routine perpectively needs to be validated with experimental data. The results presented indicate that the source model may be useful for the D-D source term evaluation at FNG or other facilities. REFERENCES [1] H. C. Urey, Ferdinand G. Brickwedde, G. M. Murphy, A Hydrogen Isotope of Mass 2, Physical Review, 39, 1932, p. 164. [2] M. L. E. Oliphant, P. Harteck, and Lord Rutherford, Transmutation Effects Observed with Heavy Hydrogen, Proc. R. Soc. Lond. A, 144, 1934, p. 692. [3] http://www.iter.org/ [4] R. A. Gross, Fusion Energy,John Wiley and Sons, USA, 1984. [5] J. Csikai, Production of 14 MeV neutrons by low voltage accelerators. In: Proc. of the IAEA Consultants Meeting on Neutron Source Properties, INDC (NDS)-114-GT., Wien, Austria, 1980. [6] http://www.srim.org/

1015.8 [7] https://mcnpx.lanl.gov/ [8] http://www.fusione.enea.it/laboratories/tec/fng.html.it [9] I. Kodeli, E. Sartori, B. L. Kirk, SINBAD Shielding Benchmark Experiments - Status and Planned. In: Proc. of the American Nuclear Society s 14th Biennial Topical Meeting of the Radiation Protection and Shielding Division, Carlsbad, New Mexico, USA, American Nuclear Society, ANS Order No. 700319 on CD, pp 87-92. [10] J. F. Ziegler, J. P. Biersack and M. D. Ziegler, SRIM - The Stopping and Range of Ions in Matter, SRIM co. 2008. [11] http://www.nea.fr/janis/ [12] http://www-nds.iaea.org/ndspub/endf/endver/