  We present the science case for a broadband X-ray imager with high-resolution
spectroscopy, including simulations of X-ray spectral diagnostics of both
active regions and solar flares. This is part of a trilogy of white papers
discussing science, instrument (Bandler et al. 2010), and missions (Bookbinder
et al. 2010) to exploit major advances recently made in transition-edge sensor
(TES) detector technology that enable resolution better than 2 eV in an array
that can handle high count rates. Combined with a modest X-ray mirror, this
instrument would combine arcsecondscale imaging with high-resolution spectra
over a field of view sufficiently large for the study of active regions and
flares, enabling a wide range of studies such as the detection of microheating
in active regions, ion-resolved velocity flows, and the presence of non-thermal
electrons in hot plasmas. It would also enable more direct comparisons between
solar and stellar soft X-ray spectra, a waveband in which (unusually) we
currently have much better stellar data than we do of the Sun.

Solar and Stellar Astrophysics