A simple computational method is proposed for estimating the time-dependent flux F-Delta E(t) of an x-ray spectrum S(E,t) over domain Delta E from data D-k(t)(k=1,...,N) obtained by an N-channel array of filtered detectors. It is assumed that the data are related to the spectrum by a discrete, inhomogeneous, first-kind Fredholm integral equation D-k=integral S(E,t)R-k(E)dE, where R-k(E) is the known response function for each detector channel of the diagnostic. The proposed method constructs a spectral sensitivity H-LS(E) for the diagnostic array as a linear combination Sigma(k=1)(N)a(k)R(k)(E) of the responses, where the coefficients a(k) are obtained by a least-squares criterion plus a constraint. The a(k) values, once determined, apply as long as the responses are valid. The flux estimate is then simply F-LS(t)=Sigma(k=1)(N)a(k)D(k)(t), without a spectral unfold of the data. The method is useful for quick analyses of time-dependent data, for comparisons with other flux-measuring diagnostics, and for the experimental design of filtered-detector arrays. The method is applied to a five-channel array of filtered photoemissive x-ray detectors G. A. Chandler , Rev. Sci. Instrum. 70, 561 (1999), used for z-pinch measurements at the Z-accelerator facility R. B. Spielman , Phys. Plasmas 5, 2105 (1998). Comparisons with unfold results are made, and a first-order analysis of error propagation into F-LS(t) is presented. (c) 2005 American Institute of Physics.
展开▼
