The use of hydrogen gas filled RF cavities in muon cooling channels has been proposed by Rolland Johnson. Impressive results have been obtained toward attaining high voltage gradients and rapid training in preliminary tests done at the FNAL MTA facility. However, so far it has not been possible to test them under conditions where they were subject to the transversal of a high intensity particle beam. This note is an attempt to bring together a description of some of the pertinent physical processes that take place in the dilute plasma that is generated in the hydrogen gas by the beam. Two effects dominate. The first is that the free electrons generated can load down the cavity and transfer its energy to heating the gas. The second is a question of what happens to the plasma in the longer term. There is an enormous literature on the subject of the subject of dilute hydrogen plasmas and we can tap into this information in order to understand and predict the behavior of the cavity.
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