There aren't perfectly reflecting mirrors, and even if there were you're going to have to hold the cavity perfectly stable, which would require it to sit at 0 K.
And lets say you could, as you increased the energy in the cavity, eventually the electric field would destroy the mirrors.
500 MeV, now that is ambition
As an example, the new injector linac being built for the LHC is only 160 MeV.
http://linac4.web.cern.ch/linac4/
Current tesla cavities are ~35 MV/m ?
LHC RF is 400.789599 MHz
Bunch length is ~ 7.55mm (0.0755m)
http://lhc.web.cern....signReport.html
Chapter 2 is your friend.
It is more of a case of the abort gap for the extraction kicker to fire.
In fact, just ignore that reference entirely.
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