Yes, why the cover? All of the space antennae I've seen
(pictures of) are naked.
Making the dome extremely thin will minimize bulk charging
and any eventual discharge magnitude. Giving the dome a
better place to zap to, like a grid that's closer to it than
the patch plane is, might be an option.
Also worth checking, is whether there are any non-
conductive or semi-insulating materials which have a
low bulk charging, or tend to recombine charges more
when charge-load gets high. I expect that this info
has been collected by some element of NASA, ESA,
JAXA et al. Where to look, that's on you.