1. 1 Neutron Effective Dose calculation behind Concrete Shielding of Charge Particle Accelerators with Energy up to 100 MeV V. E Aleinikov, L. G. Beskrovnaja, A. R. Krylov Joint Institute for Nuclear Research, Dubna, Russia

2. 2 Introduction All accelerators of the charged particles with energy up to 100 MeV represent a complex geometrical design with set of sources of radiation. The most penetrating component of radiation at the working accelerator is the neutrons of a wide energy spectrum.

3. 3 Introduction Calculations of shielding and the doses of neutrons behind shield are used various methods and, created on their basis, algorithms: Method Monte-Carlo allows carrying out direct modeling of radiation transport through substance in real geometry. The codes, created on its basis, require essential expenses of computer time at account of a dose behind rather thick shields. Much more practicable method is phenomenological approach based on existent experimental and calculated data of dose attenuation by shielding.

4. 4 The purpose is comparison of results of calculations of neutron doses behind concrete shielding by method Monte-Carlo and phenomenological method.

5. 5 Methods used The calculation by a method of Monte- Carlo was carried out with the program MCNP4B (package of libraries DLC189). The statistical error of the calculated data did not exceed 5%.

6. 6 The phenomenological method based on following expression was used : This equation applies to a source of monoenergetic neutrons of energy E with symbols having the following meanings: Е ef (d,Е) is the effective dose behind shield with thickness of d; f is the neutron yield per steradian; R is the distance from the source to the point of interest outside the shield; h(E) is the conversion coefficient that relate neutron fluence to the effective dose; B(E) is the build-up factor of neutrons; (Е) is the attenuation length for effective dose through the shield.

7. 7 The geometry of calculation

8. 8 Comparison between Monte Carlo and phenomenological methods calculated data of neutron effective dose attenuation by concrete. Isotropic point neutron source with energy 5, 20, 50 and 100 MeV at 5 m from shield.

9. 9 The neutron effective dose as a function of incident neutron energy calculated for concrete shield of the thickness indicated. Phenomenological method, Monte-Carlo

10. 10 Comparison of effective dose calculations as a function of a concrete shield thickness when the shield irradiated by neutrons produced in a copper thick target by protons with energies of 72 MeV at an angle of 9 0 with an axis of proton beam : 1 – phenomenological method, 2 - Monte-Carlo

11. 11 Comparison of effective dose calculations as a function of a concrete shield thickness when the shield irradiated by neutrons produced in a copper thick target by protons with energies of 72 MeV at an angle of 90 0 with an axis of proton beam : 1 – phenomenological method, 2 - Monte-Carlo

12. 12. Comparison of effective dose calculations as a function of a concrete shield thickness when the shield irradiated by neutrons produced in a copper thick target by protons with energies of 30 MeV at an angle of 0 0 with an axis of proton beam : 1 – phenomenological method, 2 - Monte-Carlo

13. 13 The variation of the attenuation length of effective dose for monoenergetic neutrons in concrete as a function of neutron energy. 1 – phenomenological method, 2 - Monte-Carlo

14. 14. Build-up factor for effective dose of neutrons: 1 – phenomenological method, 2 - Monte-Carlo

15. 15 Conclusions. Data obtained by these two methods agree within factor 2 over considered range of neutron energies and shielding thickness. Comparison of the results shows that difference in shield’s thickness between calculated by Monte Carlo and phenomenological method is not exceeded half- value layer for neutron effective dose, that is from 10 cm to 30 cm for considered energies and thickness of shields.