Fundamental limitations of X-ray spectra as diagnostics of plasma temperature structure

Details Fundamental limitations of X-ray spectra as diagnostics of plasma temperature structure Fundamental limitations of X-ray spectra as diagnostics of plasma temperature structure

Jun 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976a%26a....49..239c&link_type=abstract

Astronomy and Astrophysics, vol. 49, no. 2, June 1976, p. 239-250. Research supported by the Science Research Council.

Physics

132

High Temperature Plasmas, Plasma Diagnostics, Plasma Temperature, Solar Physics, Temperature Distribution, X Ray Spectra, Bremsstrahlung, Continuous Spectra, Fredholm Equations, Kernel Functions, Line Spectra, Numerical Stability, Solar Flares

Scientific paper

The problem of deriving the temperature distribution in hot optically thin plasmas from their X-ray spectra is discussed, and it is argued that X-ray spectral data are fundamentally insensitive to the thermal structure of the source, regardless of the spectral resolution of the observations. The problem is formulated in terms of the integral equation which relates both line and continuous spectra to the differential emission measure of the source. The mathematical difficulties underlying the solution of such integral equations are outlined, emphasizing the key role of the kernel function. Continuous bremsstrahlung spectra are considered, and it is shown that the kernel involved (the Laplace transform) is highly unstable to small perturbations in the spectrum due to the flatness of the kernel function. The line-spectrum problem is examined, and gross errors in the solution are shown to result from very small observational errors. A specific example for solar active regions demonstrates that most existing models for the differential emission measure are likely to be spurious. Suggestions are made for the most realistic and economic approach to analysis of existing spectra as well as for designs of future spectrometers.

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