A high pressure hydrogen gas filled RF cavity has been proposed for use in the muon collection system for a muon collider. It allows for high electric field gradients in RF cavities located in strong magnetic fields, a condition frequently encountered in a muon cooling channel. In addition, an intense muon beam will generate an electron swarm via the ionization process in the cavity. A large amount of RF power will be consumed into the swarm. We show the results from our studies of the HV RF breakdown in a cavity without a beam and present some results on the resulting electron swarm dynamics. This is preliminary to actual beam tests which will take place late in 2010.