Study on neutron spectrum unfolding method of organic scintillation measurement based on iterative regularization
Introduction
Neutron spectrum information is of interest in various fields, such as workplace dosimetry, fission reactors, and recently in arms-control applications (Flaska and Pozzi, 2007, Klein and Neumann, 2002, Liu et al., 2019). The liquid and plastic organic scintillators are widely used for their good pulse height responses and the ability to separate γ-rays from neutrons. However, neutron spectrum can not be obtained directly through measurements and unfolding techniques are always needed. The relation between incident neutron spectrum and resulting detector PHS (pulse height spectrum) N(L) is given by the first Fredhom integral equation (Reginatto et al., 2002),where R(L,En) is the light output spectrum in response to a mono-energetic neutron of energy En.
Eq. (1) can be discretized as,where m is the number of light output channel and n is the number of energy bins. For organic scintillation measurements, m is normally larger than n so the corresponding unfolding is usually referred to as multi-channel unfolding. Eq. (2) is equivalent to the following linear system,where denotes the neutron spectrum discretized over n energy bins, is light output spectrum discretized over m bins and R is the m × n response matrix of the detector. As stated before, m is normally larger than n, making Eq. (3) over-determined and the solution is the least squares solution (Pehlivanovic et al., 2013).
In most cases, the response matrix R is ill-conditioned, making the solution of Eq. (3) unstable to fluctuations in N, which is unavoidable in real measurements. Hence a good unfolding method should be adaptable to both accurate N and N with large fluctuations.
Several methods have been developed for neutron spectrum unfolding, such as GRAVEL, MLEM and MAXED (Zhu et al., 2019). In this work, an iterative regularization method is proposed with the purpose of unfolding neutron spectrums successfully while N in Eq. (3) is accurate or with large fluctuations. The proposed method is applied to neutron spectrum unfolding of the liquid organic scintillator EJ-301 (Eljen Technology, 2013). Monte Carlo code Geant4 is applied to simulate response functions of the scintillator and PHSs of the neutron spectrums to be unfolded. Four typical neutron spectrums are studied, such as the mono-energetic DD fusion neutron spectrum, 241Am-Be source neutron spectrum, 252Cf neutron spectrum, and Gaussian broadened DT fusion neutron spectrum. Comparison study of the proposed method with the existing unfolding methods, such as GRAVEL, MLEM (Maximum-Likelihood, Expectation-Maximization), and the direct Tikhonov regularization is also carried out.
Section snippets
Existing unfolding methods
a) the GRAVEL method
The GRAVEL method is considered as the most common used unfolding method with iterative rule given by (Chen et al., 2014),where is the estimated neutron spectrum at iteration k, is an estimate of measurement error in the i-th light output bin, and the weight matrix is given by,
Initial neutron spectrum is needed as the prior information for GRAVEL method. As is mentioned, linear system of Eq. (3) is
The test neutron spectrums
Four typical neutron spectrums are unfolded in this work, such as,
1) test spectrum 1: mono-energetic neutron spectrum of DD fusion with the energy of 2.5 MeV;
2) test spectrum 2: neutron spectrum of 241Am-Be neutron source;
3) test spectrum 3: fission spectrum of 252Cf, given by,
where a and b are 1.025 MeV and 2.926 MeV−1 respectively.
4) test spectrum 4: Gaussian broadened DT fusion neutron spectrum, given by,where σ is correlated with the plasma
Conclusion
An iterative regularization method combining GMRES and Tikhonov regularization is proposed and applied to unfolding problems of the EJ-301 liquid organic scintillation measurement. Four typical neutron spectrums are studied to test the adaptability of the proposed method, such as mono-energetic DD fusion neutron spectrum, 241Am-Be neutron spectrum, 252Cf neutron spectrum and Gaussian broadened DT fusion neutron spectrum. The Monte Carlo code Geant4 is used for simulation of the response matrix
CRediT authorship contribution statement
Bin Liu: Conceptualization, Methodology. Huanwen Lv: Software. Hu Xu: Writing - original draft. Lan Li: Writing - original draft. Wei Li: Investigation. Futing Jing: Validation. Zi’an Zhai: Writing - review & editing. Yirui Wu: Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (23)
Geant4: a simulation toolkit
Nucl. Instrum. Methods Phys. Res. A
(2003)- et al.
Identification of shielded neutron sources with the liquid scintillator BC-501A using a digital pulse shape discrimination method
Nucl. Instrum. Methods Phys. Res. A
(2007) - et al.
Neutron and photon spectrometry with liquid scintillation detectors in mixed fields
Nucl. Instrum. Methods Phys. Res. A
(2002) MCNPX-PoliMi for nuclear nonproliferation application
Nucl. Instrum. Methods Phys. Res. A
(2012)Comparison of unfolding approaches for monenergetic and continuous fast-neutron energy spectra
Radiat. Meas.
(2013)- et al.
Spectrum unfolding, sensitivity analysis and propagation of uncertainties with the maximum entropy deconvolution code MAXED.Nucl
Instrum. Methods Phys. Res. A
(2002) - et al.
Calibration of an organic scintillator for neutron spectrometry
Nucl. Instrum. Methods Phys. Res. A
(1968) Geant4 developments and applications
IEEE Trans. Nucl. Sci.
(2006)- et al.
Unfolding the fast neutron spectra of a BC501A liquid scintillation detector using GRAVEL method
Science China
(2014) Comparison of spectrum-unfolding performance of EJ315 and DJ309 liquid scintillators on measured 252Cf pulse-height spectra
Nucl. Instrum. Methods Phys. Res. A
(2013)
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