The invention relates to an X-ray source (100) with an electron-beam-generator (120) for generating electron beams (B, B′) that converge towards a target (110). Thus the spatial distribution of X-ray focal spots (T, T′) on the target (110) can be made denser than the distribution of electron sources (121), wherein the latter is usually dictated by hardware limitations. The electron-beam-generator (120) may particularly comprise a curved emitter device (140) with a matrix of CNT based electron emitters (141) and an associated electrode device (130).