I'm not a quantum physicist by any means, but won't the background radiation be a big problem? LHC is deep underground to keep out even the residual radiation o

I'm not a quantum physicist by any means, but won't the background radiation be a big problem? LHC is deep underground to keep out even the residual radiation of the earth's surface (after filtering by the ionosphere, and atmosphere). What chance does a collider on the moon have?