Instability develops in a long space-charge dominated beam when it is allowed to coast in a storage ring without RF containment. The longitudinal space-charge forces in these intense beams cause it to expand axially, closing on itself and as a result wrapping the accelerator. Simulations and experimental measurements indicate that instability occurs when the leading and trailing ends of the beam spatially overlap the body of the beam. The overlapping beam segments have different velocities, which is the energy source for the instability. Two instabilities have been identified in simulations: a traditional longitudinal two-stream, and a coupled betatron, two stream instability.