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X-ray lines of helium-like calcium (Ca xix) between 3.17 and 3.21 Å and associated Ca xviii dielectronic satellites have previously been observed in solar flare spectra, and their excitation mechanisms are well established. Dielectronic satellites of lower-ionization stages (Ca xvii–Ca xv) are not as well characterized. Several spectra during a large solar flare in 2001 by the DIOGENESS X-ray spectrometer on the CORONAS-F spacecraft show the Ca xvii and Ca xvi satellites, as well as lines of ionized argon (Ar xvii, Ar xvi), including dielectronic satellites. The DIOGENESS spectra are compared with spectra from a synthesis code developed here based on an isothermal assumption with various atomic sources including dielectronic satellite data from the Cowan Hartree–Fock code. Best-fit comparisons are made by varying the temperature as the code’s input (Ar/Ca abundance ratio fixed at 0.33); close agreement is achieved, although with adjustments to some ion fractions. The derived temperature is close to that derived from the two GOES X-ray channels, TGOES. Some lines are identified for the first time. Similar spectra from the P78-1 spacecraft and the Alcator C-Mod tokamak have also been analyzed and similar agreements were obtained. The importance of blends of calcium and argon lines is emphasized, affecting line ratios used for temperature diagnostics. This analysis will be applied to the Solar Maximum Mission Bent Crystal Spectrometer archive and to X-ray spectra expected from the ChemiX instrument on the Sun-orbiting Interhelioprobe spacecraft, while the relevance to X-ray spectra from non-solar sources is indicated. [ABSTRACT FROM AUTHOR]