System and process of thermal neutron ﬂux producing by means of an accelerator base electron of 18 MeV

Neutrons are produced in accelerators by irradiating heavy targets with an electron or proton beam. Produced neutrons are of high energy. The purpose of our work is optimization the neutron ﬂux by MCNP-6 code for production the thermal neutron ﬂux using a moderator and for convertation the fast neutron ﬂux into a thermal neutron ﬂux. In this article, we are interested in a thermal neutron ﬂux due it is useful for method of neutron activation analysis. In conventional sources, the moderator is usually a large volume of water or para ﬃ n around the source. Initially, fast neutrons have energy above 1 MeV, and then slow down to energies below 1 eV.


Introduction
Today, more than 40 million people undergo some form of nuclear medicine procedures. Generally, it's diagnosis and treatment of cancerous diseases. Despite the widespread use of radioisotopes in the world, the production of these is available only in developed countries. Although, the production of radioisotopes includes a nuclear reactor [1][2][3][4][5], a source of alpha-beryllium [6][7][8] and an accelerator [9]. In these recent years, global demand for molybdenum radioisotopes has increased significantly, with 90% of these was producted by five old reactors located in Canada, Belgium, the Netherlands, South Africa and France. Unfortunately, these five reactors have been in the final stage of being stopped more than 50 years. Researchers have developed other production methods, which are mainly improvements in spallation neutron sources and particle accelerators [10][11][12][13][14].
Theoretically, the neutron flux in particle/cm 2 can be simulated using following formula [15]: With, A is the surface area (cm 2 ) ; E is the total energy deposited; − −−−−− → r, Ω, E, t is particle position vector (cm); direction vector, energy (MeV); and time and Ψ is angular flux generated from nuclear reactor.

Theory
The availability of the Monte Carlo MCNP-X and MCNP-6 codes used as a simulation tool [15][16][17] makes it possible to pretend an electron beam in thick targets X. The optimization of the conception (design) of the target bound directly to the production and the generation of the yield on Bremsstrahlung of photon neutron [18][19][20][21]. Figure 1, show the geometry used in this work. In this article, we interested in the production of neutrons using a system of acceleration of the electron beam of the energy of 18 MeV and moderation of the neutron using a water cylinder thickness of 7 cm and a diameter of 5 cm. We have devoted the study to the production of thermal neutrons using a (water). Figure 1 schematizes the device used for an accelerator base electron and the moderator used.

Results
The thermal neutron flux generated by the Lead target  Discretization at the level of energy groups in the thermal domain. We find Figure 3, which represents the neutron flux as a function of neutron energy in the thermal domain, clearly, that in the zone of low energy the thermal neutron flux and more intense to compare with the other the rate without a moderator or the flux is almost zero. The variation of the thermal flux profile produced by the Lead target gives the results mentioned in Figure 3. The thermal zone is not well-defined, so we thought about to realize another energy discretization in the thermal zone as indicated, in Figure 4. First, note that the neutron flux in the case of the moderator in the way that the large production of thermal flux on the contrary, to the absence of moderator the curve in red the zero flux over the thermal zone. The neutron simulation of an accelerator base electron using the Lead target for produce fast neutrons, which are moderate by a cylinder filled with water placed directly on the upper face of the target; simulation using the MCNP-6 code gives the results shown in Table 1: the variation of flux as a function of thickness. Note that the thermal flux of neutron and the thermal rate increase in the moderator along with the thickness, until the thickness equal to 4 cm ( 2.97 × 10 10 n/cm 2 s ), after the flux begins to decrease until arriving at the value of ( 1.77 × 10 10 n/cm 2 s ). Note also that the very high epi-thermal flux rate, which reaches 72.25 % which explains why most of the flux was at a very high energy, by the successive interactions of the neutrons with the hydrogen atoms they lose their energy, in addition, the fast neutron decreased to 24.25 %.  Figure 5 represents the neutron flux distribution as a function of moderator thickness, the fast-flux decreases with increasing the thickness, whereas the thermal flux increases as a function of thickness. In order to visualize the changes in the thermal flux as a function of the thickness, we have shown in Figure 6 that the thermal neutron flux increases with a thickness of up to 4 cm with a value of ( 2.97 × 10 10 n/cm 2 s ), after it undergoes a decrease.
The neutron flux distribution (thermal, epi-thermal and fast) by the meshing method as illustrated in Figure 7. On the way that the flux includes a small change

The thermal neutron flux generated by the Tantalum target
The present graph represents the neutron flux with moderator and without a moderator, noting that it is less intense than the neutron flux with a moderator in the range of energy higher than 0.5 MeV, whereas in the zone less than 0.1 MeV the flux with Moderator is more abundant, figure 8. According to the previous figure, it is noted that the neutron flux is more intense with moderation in the zone of less than 0.1 MeV, for this we have discretized this energy zone to reduce it, on the way that the moderate flux superior to the flux without a moderation in the thermal zone less than 0.05 MeV, figure 9.  noting that the thermal flux is maximum in the case where X = 4 cm and equal to ( 2.83 × 10 10 n/cm 2 s ). The graph of Figure 11 represents the rapid and thermal distribution of the flux as a function of the thickness. It is observed that the fast flux decreases slowly with the thickness, on the contrary, the thermal flux augments to a maximum at the thickness 4 cm, after which it decreases.

Conclusion
A theoretical study of two models of calculations using the MCNP-6 code, first with the Lead target and the second with the Tantalum target. Which are driven to two different results regarding the neutron flux produced. The findings found in this study, we condense a validation of our study. We conclude that the stochastic code MCNP-6 can be used to effectively evaluate the neutron behavior of different targets. In this work, we have improved the optimal thicknesses of 4, 5 and 3 cm respectively so that the thermal neutron flux will be more intense in the moderator block that contains water. In addition, in this study, the effect of target thickness, different target materials (Ta and Pb), and proton beam energy on the neutron flux parameter was studied.