Specific storage modes have been identified and explored both experimentally and computationally for a new type of low energy charged particle storage ring for use in Atomic & Molecular Physics experiments [Tessier et al, Phys. Rev. Lett., 99, 253201, (2007)]. These modes offer the possibility of storing monoenergetic charged particle beams injected into the ring. Alternatively, some of the storage modes identified may be appropriate for energy filtering a stored charged particle beam within the ring. The ring is entirely electrostatic and has been shown experimentally to be capable of storing low energy electrons with storage lifetimes in the region 50 microseconds (∼150 orbits) that are vacuum pressure limited. The ring is constructed from two 180° hemispherical deflector analyzers which are interconnected by two identical cylindrical lens stacks. Each lens stack is primarily controlled by 3 voltages. The storage modes observed occur at specific combinations of these voltages and are consistent with a multiple orbit charged particle optics model of the apparatus explored using both a matrix approach and trajectory integration in a 3 dimensional electrostatic model.