N-spline reconstruction of neutron spectra on the basis of activation measurements

Abstract

A new approach to reconstructing the neutron spectra of reactor facilities on the basis of activation measurements is proposed and investigated. A new parameterization of a neutron spectrum is introduced; this representation is in the form of a special "neutron" spline. A generalized algorithm for minimizing the directed deviation is used for the reconstruction. To analyze the possibilities of the approach developed, the spectra of the BARS-5, IGRIK, and YaGUAR reactor facilities are reconstructed on the basis of activation measurements. The reconstructed spectra agree well with previous results.The determination of neutron spectra ϕ(E) on the basis of activation measurements ordinarily reduces to solving a system of integral equations of the form [1,2] (1)where Q i is the number of reactions on a nucleus of the main isotope of the ith indicator, measured with absolute standard error ∆Q i (1σ); E is the neutron energy; σ i (E) is the activation cross section of the ith indicator; i is the number of the indicator; and N is the number of indicators used in the measurements. The existence of a solution of the (1) problem is guaranteed by its physical content, but it is well known that it is an improperly posed problem [1-3]. The many methods existing for finding a solution differ by the form and method of introduction of a priori information. Thus, together with the fact that the solution sought must be positive, the requirements that ϕ(E) be smooth and close to a certain trial function ϕ 0 (E), and so forth are often imposed [1][2][3][4].We note that a great deal of significance has always been attached at the All-Russia Research Institute of Theoretical Physics to the choice of the initial approximation for the neutron spectrum ϕ 0 (E). For this, it was calculated by the Monte Carlo method for each specific case of measurement of a neutron spectrum. A suitable choice of ϕ 0 (E) is especially important in the energy range 10 keV ≤ E ≤ 0.6 MeV; this is due mainly to the inadequacy of the information which sets of activation indicators provide in this region of the spectrum.A group representation of the spectrum ϕ(E) is often used to solve the (1) problem, and the problem reduces to solving a system of linear algebraic equations. Since the cross-sections of many activation reactions are of a resonance character, the number of groups must be large so that the quadrature error due to the transition to a system of equations would be small compared with the measurement errors ∆Q. As a result, the uncertainty (or degeneracy) of the system is large. It has been proposed on the basis of a priori considerations concerning the typical reactor spectrum that a prescribed set of model functions or a piecewise representation of the neutron spectrum be used to decrease the number of parameters sought [4,5]. For Q E Ed E i N i i = = ∞ ∫ σ ϕ ( ) ( ) , ,..., , 0 1