[en] A new technique for X-ray spectromicroscopy of fast heavy ion radiation during the ion interaction with stopping media is presented using focusing spectrometers with spatial resolution. Spherically bent crystals of quartz and mica with small curvature radii, R=150 mm, and large apertures were used as dispersive elements in experiments on fast Ni ions with energies of 5.9 and 11.2 MeV/u which are being stopped in different media: Ar gas, SiO₂-aerogels and solid quartz. Spectrally high (λ/Δλ=1000-3000) and spatially high (up to 10-100 μm) resolved Kα-satellite spectra of Ni projectiles as well as of the ionized stopping media were observed