Moyer Model Research Articles

Phenomenological calculations of shielding spallation neutron sources

The high level of radiation generated by a spallation source requires the design of an appropriate shielding to surround the source in order to fulfill radiation protection standards. A calculation of the spallation neutron attenuation is presented for various shielding materials, using a phenomenological model, based on the Moyer model. In the first step of the calculation, the interaction length of neutrons for each neutron energy and shielding material was estimated using inelastic cross-sections. In the second step the calculation deals with the attenuation of the neutron flux applying the Moyer model, for each material and neutron energy region. The transmission factors were calculated and compared with experimental data collected from the “Gamma-2” and the “E+T” projects running in JINR (Dubna, Russia). The results of the present work were also compared to the data obtained by different Monte Carlo codes such as MORSE, MCNPX, MARS14 and LAHET.

Shielding Experiments at High Energy Accelerators of Fermilab (II) —Spatial distribution measurement of reaction rate behind the shield and its application for Moyer model—

JASMIN - Japanese and American Study of Muon Interaction and Neutron detection - a program for studies of shielding and irradiation effect around high energy accelerators has been started until 2007 using high energy proton accelerators located in Fermi National Accelerator Laboratory (FNAL) as a collaboration of JAPAN and FNAL. The series of the presentations entitled Shielding experiments at high energy accelerators of Fermilab describes the part of the results of this collaboration regarding transport of secondary particles, neutron and muon, from 120 GeV proton induced reactions through experimental data and simulation. In this study, the spatial distribution of reaction rate of activation samples which were placed on pbar anti proton target station were obtained. The measured data shows that the reaction rates on the outer surfaces of the iron and concrete shields increases toward the downstream of the target. The attenuation length for iron were obtained from depth distribution of reaction rates in iron shield. The obtained reaction rates were also fitted to Moyer's formula. The shape of angular distribution of fitted reaction rates agree with that of measured reaction rates for �� = 60 - 120 degrees.

Flux and dose transmission through concrete of neutrons from proton induced reactions on various target elements

Simple empirical expressions for transmission of flux and dose through concrete are presented for neutrons from proton induced reactions. For this purpose the neutron emission from different targets in proton induced reactions in the energy range 25–200MeV have been considered. The calculated effective dose outside a concrete shield shows overall good agreement with the effective dose estimated from measured neutron flux in the framework of the Moyer model. The calculated effective attenuation length shows a rising trend with incident proton energy and shield thickness.

Radiation Shielding Design of a Cancer Therapy Facility using Compact Proton Synchrotron

Radiation shielding design of a cancer therapy facility using compact proton synchrotron was carried out. Foi bulk shielding calculation, the effective dose attenuation formula based on Moyer Model was used. Attenuatioi lengths used in the formula were derived by the one-dimensional discrete ordinate code ANISN using the DLC 119/HIL086 high-energy multi-group cross section library. For skyshine dose calculation, SHINE-III code was used To calculate radiation streaming through mazes and ducts, Nakamura and Uwamino’s formula and DUCT-III code were applied, respectively. As an emission of neutron by proton beam losses, measured neutron yield spectra o1 256MeV incident proton at LANL was used. To determine an emission of gamma ray by the beam losses, the FLUKA routine bundled in GEANT code was used. Results from the calculation satisfy the limits from the domestic law of the radiation protection.

Shielding high energy accelerators.

After introducing the subject or shielding high energy accelerators, point source, line-of-sight models, and in particular the Moyer Model, are discussed. Their use in the shielding of proton and electron accelerators is demonstrated and their limitations noted, especially in relation to shielding in the forward direction provided by large, flat walls. The limitations of reducing problems to those using a cylindrical geometry description are stressed. Finally the use of different estimators for predicting dose is discussed. It is suggested that dose calculated from track-length estimators will generally give the most satisfactory estimate.

Analytical method for calculating neutron bulk shielding in a medium-energy accelerator facility

This investigation aims at an analytical method for calculating neutron bulk shielding in a medium-energy accelerator facility on the basis of the modified Moyer model. Shielding parameters for the analytical formula are obtained using the ANISN one-dimensional discrete ordinate code and the MCNP three-dimensional Monte Carlo code. The dose attenuation length of a concrete shield, which is the most important parameter, is obtained as a function of neutron energies from 0.2 MeV to 400 MeV and of shield thickness from 1 m to 7 m. The equation is also applicable to the estimation of neutron oblique penetration through a concrete shield, so the correction factor for oblique penetration is introduced into the analytical formula. It is expressed as the ratio of dose equivalent as calculated with MCNP for penetration through a relatively thin (1 or 2 m thick) concrete slab shield to that with the analytical equation developed in this work.

Using the Moyer Model at Energies less than 1 GeV

Although many shielding calculations are today done using sophisticated Monte Carlo codes there is still often a need to do quick estimates for simple geometries. Such estimates are usually made using the so-called ‘Moyer Model’. Among the model’s limitations is that it is of limited validity for proton beam energies less than about 1 GeV. One reason is that although above a few GeV almost all protons undergo a nuclear interaction, this is not true at energies below 1 GeV. At lower energies Coulomb interactions and ionization losses predominate and fewer protons participate in non-elastic nuclear interactions. We have modified the Moyer source term, multiplying it by the nuclear interaction probability for protons at the energy of interest. These interaction probabilities have been previously tabulated (1,2)but we have recalculated them for thick targets using the Monte Carlo code FLUKA. Except for hydrogen, the nuclear interaction probability is very nearly independent of the target material. One can prepare a simple table as a function of energy that can be used for all targets except hydrogen.We present a comparison of estimates made using this modified Moyer model and detailed Monte Carlo calculations for a simple geometry as a function of incident proton energy below 1 GeV. The model has been used successfully in the design of the shielding for ISAC a high intensity accelerated ion beam facility at TRIUMF. This facility uses a 0.5 GeV proton beam incident on a thick target to produce the radioactive atoms. Some comparisons between the estimates made using the Moyer model and measurements made during the commissioning of this facility are also presented.

The Shielding of High-Energy Accelerators

After introducing the subject of shielding high-energy accelerators, point-source line-of-sight models, and in particular the Moyer Model, are discussed and the limitations of such models noted. Fermi-Eyges diffusion theory in the scattering of muon beams will be taken as an example of a situation where classical pre-1950s physics is still applicable today for accelerator shielding design. However new physics has affected shield design within several years of the discovery of a phenomenon. The importance of experimental shielding information and the increase in computing power that has become available in recent years is noted. The paper concludes by mentioning the unhelpfulness of many of the dosimetric concepts of the International Commission on Radiological Protection (ICRP) especially and to some extent the International Commission on Radiation Units and Measurements (ICRU).

Shielding of proton accelerators: a comparison between the moyer model and monte carlo calculations

The FLUKA Monte Carlo program was used to calculate the dose equivalent behind a homogeneous concrete shielding for primary energies between 10 and 800 given.

Moyer model approximations for point and extended beam losses

The use of the empirical Moyer model for the determination of transverse neutron shielding for high-energy proton accelerators is described and discussed. It is shown that an important advantage of the Moyer Model is the physical insight it offers towards understanding the complex interactions that comprise the shielding processes. Calculations for pointlike and extended uniform beam loss distributions are discussed and their relationship to practical shielding conditions developed. The calculations required by the model are readily performed on small programmable calculators and thus are widely accessible. Program listings for practical calculations using a Hewlett-Packard HP-97 calculator are available on request.

A bargain theory of pricing: generalization

Describes the Moyer model of price bargaining process with some extensions. Provides evidence supporting the model and findings based on research into part of the UK textile manufacturing and distributive industries. Suggests that the Moyer model provides support to the theory that the channel relationships affect the bargaining interval and buying price.