Synchrotron x-ray radiation from laser wakefield accelerated electron beams was characterized at the HERCULES facility of the University of Michigan. A mono-energetic electron beam with energy up to 400 MeV was observed in the interaction of an ultra-short laser pulse with a super-sonic gas jet target. The experiments were performed at a peak intensity of 5×1019 W/cm2 by using an adaptive optic. The accelerated electron beam undergoes a so called "betatron" oscillation in an ion channel, where plasma electrons have been expelled by the laser ponderomotive force, and, therefore, emits synchrotron radiation. We observe broad synchrotron x-ray radiation extending up to 30 keV. We find that this radiation is emitted in a beam with a divergence ...