Proccedings of the ISSSD 2012 ISBN 978-607-00-6167-7

82

A Neutron Spetrum Unfolding Code

Based on Iterative Procedures

J.M. Ortiz-Rodríguez1/*,H.R. Vega-Carrillo1/2

1Unidad Académica de Ingeniería Eléctrica, Universidad Autónoma de Zacatecas, Zacatecas, 98000, México

2Unidad Académica de Estudios Nucleares, Universidad Autónoma de Zacatecas, Zacatecas, 98000, México

Abstract: In this work, the version 3.0 of the neutron spectrum unfolding code called Neutron Spectrometry and Do-simetry from Universidad Autnoma of Zacatecas (NSDUAZ), is presented. This code was designed in a graphical interface under the LabVIEW programming environment and it is based on the iterative SPUNIT iterative algorithm, using as en-trance data, only the rate counts obtained with 7 Bonner Spheres based on a 6LiI(Eu) neutron detector. The main features of the code are: it is intuitive and friendly to the user; it has a programming routine which automatically selects the “ini-tial guess” spectrum by using a set of neutron spectra compiled by the International Atomic Energy Agency. Besides the neutron spectrum, this code calculates the total flux, the mean energy, H*(10), h*(10), 15 dosimetric quantities for radia-tion protection porpoises and 7 survey meter responses, in four energy grids, based on the International Atomic Energy Agency compilation. This code generates a full report in html format with all relevant information. In this work, the neu-tron spectrum of a 241AmBe neutron source on air, located at 150 cm from detector, is unfolded.

Keywords: Neutron; Spectrometry; Dosimetry; SPUNIT algorithm; Iterative procedures; Unfolding codes.

1. Introduction

The process of unfolding the neutron energy spectrum has been the subject of research for many years [1, 2 3]. The spectrum unfolding is expressed by the homogeneous Fredholm equation, whose discrete version is showed in equation (1).

(1) where Rjk is the response of the j

th detector to neutrons

in the kth

energy interval multiplied by the width of the kth

energy interval. M is the number of energy intervals.

Unfolding consists of determining Φ(k) for all energy

groups, given a limited number of detector measurements and an appropriate detector response matrix Rjk [2]. The physical constraints that all matrix elements be non-negative are imposed upon the problem.

________________________________________________

* E-mail corresponding author: morvymm@yahoo.com.mx

Telephone: +52-(492)-922 7043 X 1506

Fax:

Normally, the resolution of the unfolded Φ vector in

terms of the number of energy groups is far greater than the number of sphere measurements practically obtained; this is an undetermined matrix problem, leading to an infinite number of solutions to equation (1).

The goal of the unfolding process is to determine a sin-

gle solution that closely approximates the actual neutron fluence energy spectrum and that produces an associated personnel dose that closely estimates the actual dose [3].

The Bonner spheres System (BSS), has gained wide

spread acceptance as a dose assessment tool since it was introduced in 1961 [4, 5]. Unfolding the neutron spectrum from BSS measured data becomes somewhat complicated as well as tricky and thus requires specialized unfolding techniques [6]. This is because, the number of detectors used is much less compared to the number of energy in-tervals in which the flux distribution is sought at. Therefore, the system of equations to be solved becomes undeter-mined and the numerical algorithm to be used for unfold-ing the data needs validation for specific use.

NjkRCM

i

jkj ,...,2,1)(1

Proccedings of the ISSSD 2012 ISBN 978-607-00-6167-7

83

In general, the desired neutron spectrum is obtained by numerically inverting equation (1) using an unfolding algo-rithm that implicitly defines a solution of this equation [7].

During the past decades have been carried out intents to

develop new neutron spectra unfolding codes like BUNKIUT [8], BUMS [9], FRUIT [6], UMG, etc., to attain im-proved energy resolution through spectrum unfolding.

However, these methods still present serious drawbacks

such as the complexity in their use, the necessity of a very expert user and an initial guess spectrum, where their ap-propriate selection affects in great measure the quality of the obtained solution, however, in the practice the proper selection is a difficult task. Each of the mentioned difficul-ties has motivated the development of alternative tech-niques. In this work, a new version, 3.0, of the neutron spectra unfolding code known as Neutron Spectrometry and Dosimetry from Universidad Autónoma of Zacatecas (NSDUAZ), developed under LabVIEW environment, is pre-sented.

By using the NSDUAZ code, Ver. 3.0, the neutron spec-

trum of three Lineal Accelerators (LINACs), were unfolded.

2. Materials and Methods

In prior works, an earlier version of the NSDUAZ unfold-ing code was designed for a

6LiI(Eu) neutron detector [10,

11, 12, 13]. Main drawbacks associated with this version of the code, 1.0, were that unfolding is carried out using few energy groups using the UTA4 response matrix, expressed in 31 energy bins.

In this work, the version, 3.0 of the NSDUAZ code,

showed in figure1, is presented.

Figure 1. Main window of the NSDUAZ code, Ver.3.0.

In this version, the energy was taken from IAEA compila-tion which is expressed in 60 energy bins. A response ma-trix for a

6LiI(Eu) neutron detector was selected from this

spectrum compendium. 15 dosimetric quantities and 7 survey meter responses are calculated in four energy grids, with the IAEA dose conversion coefficients.

The method for solving the unfolding problem is based

on the SUPNIT iterative algorithm, which was implemented in a programming routine under the LabVIEW program-ming environment.

By using the IAEA neutron spectrum compilation, a pro-

gramming routine was designed in order to automate the selection of the initial guess spectrum. The trend of the count rates plotted against the sphere diameter allows using this information to select the initial guess spectrum.

Once the neutron spectrum is unfolded, the total flux φ,

the mean energy EAv, H∗(10), h∗(10), 15 dosimetric quanti-ties for radiation protection porpoises, and 7 survey meter responses, in four energy grids, are calculated. The numer-ical values of the fluence-to-dose conversion factors for the doses and instruments, h∗Φ(E) and i∗Φ(E) respectively, were taken from the IAEA neutron spectrum compilation.

In NSDUAZ, the BSS count rates are saved in a TXT file

writing the count rates of Balls 0, 2, 3, 5, 8, 10 and 12 in a single column. Once the user calls the TXT file, by clicking the folder icon, the convergence error and the maximum amount of iterations must be input by the user; by default the code has 10% and 1000, respectively. By pressing the “Unfold Spectra” button, the unfolding process begins.

3. Results

In this work, the NSDUAZ unfolding code, Ver. 3.0, was used for unfolding the neutron spectrum of three Lineal Accelerators (LINACs): A 10 MV MEVATRON, a 10 MV PRIMUS and 18 MV Varian respectively.

The BSS rate counts were used as the only entrance data

to the code. Figure 2 through 4, shown the spectra un-folded with the NSDUAZ code. These figures shown the graphical shape of the neutron spectrum unfolded with the SPUNIT algorithm, faced with the initial guess spectrum selected by the automated programming routine.

The numerical values of the maximum number of itera-

tions, the χ2 - value, the total flux φ are calculated. Also,

the mean energy EAv, the Ambient dose equivalent, H∗(10) and the Fluence-to-Ambient dose factor h∗(10), calculated for four energy bin criteria: Lower, Intermediate, Upper and Median, these are shown also shown in the main in-terface of the code.

Proccedings of the ISSSD 2012 ISBN 978-607-00-6167-7

84

Figure 2: Neutron spectrum of a Mevatron Linac with NSDUAZ.

Figure 3: Neutron spectrum of a Primus Linac with NSDUAZ.

Figure 3: Neutron spectrum of a 18 MeV Linac with NSDUAZ.

In order to generate a report of the neutron spectrum unfolding carried out, the user should clicking in the “Gen-erate Report” button.

4. Conclusions

At present there are several unfolding codes which use iterative routines. The main disadvantage of these proce-dures is that require an initial solution to start the unfold-ing process. The quality of the final solution is affected by the initial guess spectrum.

NSDUAZ is a user friendly neutron spectra unfolding

package for a BSS with a 6LiI(Eu) neutron detector and

based on the iterative SPUNIT algorithm. It works with a response matrix taken from IAEA compilation, expressed in 60 energy groups ranging from thermal to 630 MeV.

The main features of the code are: was designed in a

graphical user interface under the LabVIEW programming environment; it is friendly, intuitive and easy to use for the end user; for the deconvolution of the spectrum it uses a programming routine which automate the initial guess spectrum selection from a library of neutron spectrum compiled by IAEA and its corresponding calculated rates counts.

A programming routine was designed in order to gener-

ate a report, in html format, which contains the most im-portant information of the unfolding process. Contrary to the existent iterative codes, the main feature of this tool is the automated selection of the initial guess spectrum by means of a catalogue of neutrons spectra.

Acknowledgements

This work was supported by Fondos Mixtos CONACYT - Gobierno del Estado de Zacatecas (México) under contract ZAC-2011-C01-168387.

References [1] D. J. Thomas, A. V. Alevra, Bonner sphere spectrometers - a

critical review, Nuclear Instruments and Methods in Physics Research Section A 476 (2002) 12–20.

[2] D. J. Thomas, Neutron spectrometry for radiation protection, Radiation Protection Dosimetry 110 (1-4) (2004) 141–149.

[3] M. Matzke, Unfolding procedures, Radiation Protection Dosimetry 107 (1-3) (2003) 155–174.

[4] R. L. Bramblett, R. I. Ewing, T. W. Bonner, A new type of neutron spectrometer, Nuclear Instruments and Methods 9 (1960) 1–12.

[5] T. Bonner, Measurements of neutron spectra from fission, Nuclear Physics 23 (1961) 116–121.

Proccedings of the ISSSD 2012 ISBN 978-607-00-6167-7

85

[6] R. Bedogni, C. Domingo, A. Esposito, F. Fern´andez, FRUIT: An operational tool for multisphere neutron spectrometry in workplaces, Nuclear Instruments and Methods in Physics Research A 580 (3) (2007) 1301– 1309.

[7] S. P. Tripathy, C. Sunil, M. Nandy, P. K. Sarkar, D. N. Sharma, B. Mukherjee, Activation foils unfolding for neutron spec-trometry: Comparison of different deconvolution methods, Nuclear Instruments and Methods in Physics Research A 583 (2007) 421–425.

[8] S. Miller, AFITBUNKI: a modified iterative code to unfold neutron spectra from Bonner sphere detector data, Mas-ter’s thesis (1993).

[9] [13] J. Sweezy, N. E. Hertel, K. Veinot, BUMS - Bonner sphere unfolding made simple: an HTML based multisphere neutron spectrometer unfolding package, Nuclear Instru-ments and Methods in Physics Research A 476 (1-2) (2002) 263–269.

[10] H. R. Vega-Carrillo, J. M. Ortiz-Rodriguez, M. R. Mar-tinez-Blanco, NSDUAZ unfolding package for neutron spec-trometry and dosimetry with bonner spheres, Applied Radi-ation and Isotopes In press (2012) http://dx.doi.org/10.1016/j.apradiso.2012.04.020.

[11] J. M. Ortiz-Rodríguez, Inteligencia Artificial: aplicaciones a la espectrometría y dosimetría neutrónicas, ISBN-978-84-694-9096-9, Ph.D. thesis (2011).

[12] S. Barros, E. Gallego, A. Lorente, I. F. Goncalvez, P. Vaz, H. R. Vega-Carrillo, Dosimetric assessment and characterisation of the neutron field around a howitzer container using a bonner sphere spectrometer, monte carlo simulations and the nsdann and nsduaz unfolding codes, Radiation Protec-tion Dosimetry In press (2012) doi:10.1093/rpd/ncs246.

[13] A. M. Guimaraes, M. A. S. Lacerda, J. A. L. Santos, P. G. M. Maletta, S. L. M. Rodrigues, R. S. Andrade, E. C. Vilela, T. da Silva, Use of a TLD-based multisphere spectrometry system to measure the neutron spectra around a not-self-shielded pet cyclotron: preliminary results, Applied Radiation and Isotopes In press (2012) http://dx.doi.org/10.1016/j.apradiso.2012.05.014.