spectrum of short-pulsed neutron sources from time-of-flight measurements is reported. The first ... tron production and provide up to 1012 neutrons per dis-.
NUCLEAR SCIENCE AND ENGINEERING: 122, 384-394 (1996)
Evaluation of Reconstruction Methods for Time-Resolved Spectroscopy of Short-Pulsed Neutron Sources Ion Tiseanu and Teddy Craciunescu Institute of Atomic Physics, P.O. Box MG-7, R-76900, Bucharest-Magurele, Romania Received October 24, 1994 Accepted June 9, 1995
Abstract—A comparison of five methods for the reconstruction of the time-resolved neutron energy spectrum of short-pulsed neutron sources from time-of-flight measurements is reported. The first method is an analog Monte Carlo reconstruction technique (AMCRT), expressly designed for the optimization of such measurements. It was proved that the studied problem can be treated as a tomographic one with a limited data set. A Fourier convolution and backprojection method and three other tomographic methods, which have been shown to work with a limited data set, are used: the maximum entropy method, the algebraic reconstruction technique, and a Monte Carlo implementation of the backprojection (MCBP) technique. Through numerical tests, the quality of reconstructions in different image geometries at various noise levels has been studied. Besides the AMCR T method, which produces the best results, good reconstructions are also obtained using MCBP and maximum entropy. If computing time must be minimized, the maximum entropy algorithm is most convenient. This algorithm could be used routinely in time-resolved spectroscopy measurements.
I. INTRODUCTION Neutron spectroscopy is an important diagnostic technique used in fusion plasma studies. New insights into the fusion reaction mechanisms of the hot dense plasmas (plasma focus, dense Z pinches, etc.) can be obtained if the time-resolved neutron energy spectrum is determined. These fusion systems are efficient in neutron production and provide up to 1012 neutrons per discharge in deuterium with an emission time in the range of 50 to 500 ns. However, for these neutron source parameters, none of the standard existing spectroscopy methods give satisfactory results. Hence, a new approach in which the neutron pulses are recorded in an extended time-of-flight (TOF) arrangement f r o m a number of detectors placed at various optimized distances from the source was developed 1 ' 2 and applied. 3 , 4 A detector with a fast enough temporal response placed at distance D f r o m the source will record at a given moment all neutrons for which the sum of the emission time and the flight time is constant. Mathematically, the relation between the time-dependent neutron flux S(T,D) recorded at distance D and the
time-energy neutron distribution function fE(t,E) written as r> 2 rE S(T,D) \D) dt\ dEfE(t,E) D (2E/m)wl
is
(1)
where m - neutron mass T = neutron detection time t = emission time. The integral is taken on the hyperbolic arch T= t +
D (2 E/m) 1/2
(2)
over a time-energy domain limited by tx,t2 and EX,E2, respectively. The separation of the variables (time and neutron velocity) and transformation of the problem in a first kind, one-dimensional Fredholm equation were achieved
by the data analysis method used in Ref. 1. A computerassisted Laplace transformation procedure has been presented in Ref. 2. In Ref. 5, the particle energy distribution function fE(t,E) is determined by an analog Monte Carlo reconstruction procedure, which solves Eq. (1) in integers. As was suggested earlier, 2 the problem described by Eq. (1) can be treated as a tomographic one by changing energy scale E into a reciprocal velocity scale q so that the hyperbolic arches become straight lines (Fig. 1): T = t + Dq .
=f(t,q)-
dq
(4)
dE
In the tomographic approach, a discrete fashion of the reconstruction space, of the unknown distribution, and of line integrals is used; the reconstruction space is divided into a finite number of nonoverlapping elements (pixels), and the unknown distribution is approximated
u
1,1 1,2 2,1
A(Ky) r /
/
cotg(/ m ) =
(3)
In the reconstruction plane t, q, the source-detector distance D determines the direction of the Eq. (3) lines, while for a given source-detector distance, different detection moments T account for different values of flux S(T,D). After the reconstruction of the f(t,q) distribution, the time-dependent energy spectrum fE(t,E) is obtained using the relation Mt,E)
by the values assigned to each pixel f j j ( i j = l,N) by the reconstruction algorithm. Thus, the flux values S(Tk,Dm) are equivalent to the projections pk
