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Polychromatic beams of hard X-rays from ultrafast laser plasma interaction are studied. Just as in a conventional synchrotron, electrons are accelerated and wiggled, but on a much shorter scale of a few millimeters. By focusing a 50 TW CPA laser system (30 fs duration) onto a helium gas jet, we obtained a polychromatic collimated beam (50 mrad) of X-ray radiation in the keV range. In addition, its perfect synchronization with the laser system, its ultrafast duration (⋍30 fs) and its brightness (up to 108 photons/shot/solid angle at 0.1%BW)will make it applicable to both X-ray science and backlighting to address laboratory astrophysics research issues. [ABSTRACT FROM AUTHOR]