THE RELATION BETWEEN LINE RATIO AND EMISSION MEASURE ANALYSES

Spectroscopic diagnosis of the temperature and density structure of ho t optically thin plasmas from emission line intensities is usually des cribed in two ways. The simplest approach, the 'line ratio' method, us es an observed ratio of emission line intensities to determine a 'spec troscopic mean' value of electron temperature [T-e] or electron densit y [n(e)]. The mean value is chosen to be the theoretical value of T-e or n(e) which matches the observed value. The line ratio method is sta ble, leading to well defined values of [T-e] or [n(e)] for each line p air but, in the realistic case of inhomogeneous plasmas, these are har d to interpret since each line pair yields different mean parameter va lues. The more general 'differential emission measure' (DEM) method re cognizes that observed plasmas are better described by distributions o f temperature or density along the line of sight, and poses the proble m in inverse form. It is well known that the DEM function is the solut ion to the inverse problem, which is a function of T-e, n(e), or both. Derivation of DEM functions, while more generally applicable, is unst able to noise and errors in spectral and atomic data. The mathematical relation between these two approaches has never been precisely define d. In this paper we demonstrate the formal equivalence of the approach es, and discuss some potentially important applications of methods bas ed upon combining the line ratio and DEM approaches.