We present a design for an atomic synchrotron consisting of 40 hybrid magnetic hexapole lenses arranged in a circle. We show that for realistic parameters, hydrogen atoms with a velocity up to 600 m/s can be stored in a 1-meter diameter ring, which implies that the atoms can be injected in the ring directly from a pulsed supersonic beam source. This ring can be used to study collisions between stored hydrogen atoms and molecular beams of many different atoms and molecules. The advantage of using a synchrotron is two-fold: (i) the collision partners move in the same direction as the stored atoms, resulting in a small relative velocity and thus a low collision energy, and (ii) by storing atoms for many round-trips, the sensitivity to collisions is enhanced by a factor of 100-1000. In the proposed ring, the cross-sections for collisions between hydrogen, the most abundant atom in the universe, with any atom or molecule that can be put in a beam, including He, H$_2$, CO, ammonia and OH can be measured at energies below 100 K. We discuss the possibility to use optical transitions to load hydrogen atoms into the ring without influencing the atoms that are already stored. In this way it will be possible to reach high densities of stored hydrogen atoms.
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