We present a spectrometer design candidate for the X-ray Multi-Mirror (XMM) observatory, being planned by the European Space Agency (ESA) as a long-lived large-area array of tele scopes. The science requirement of moderate resolution (E/AE ^ 100) spectroscopy in a two octave region (0.5-2 KeV) with extremely high throughput (effective area > 500 cm2) results in the use of grazing incidence reflection gratings. Due to the low image quality of the telescopes (^ 1 minute of arc), the grating dispersion must be maximized by use of the classical grating mount in which the spectrum is dispersed within the plane of incident radiation. Due to the small field of view afforded by the x-ray telescopes, the gratings must be situated in the converging beam at the exit of the telescope. A spectrometer module consists of a thin-foil conical mirror telescope, a stack of plane varied-space reflection gratings and an imaging proportional counter. This system is analyzed on the basis of dispersion...
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