Arc-fault breaker in sub panel, pigtail to neutral bus or ground bus?
The white pigtail wire coming off of the AFCI is supposed to connect to the neutral bar.  It should technically work either way, as the neutral and ground are bonded together at the service entrance and at the utility transformer, but using the ground as it was is introducing currents into the ground conductor that should not be there.

I'm not sure why the new breaker did not work as intended, but it seems like the old one was working properly.  It seems like the cable feeding that plug has had its insulation damaged.  It also seems like it is coming in contact with a substantial amount of water, and that water is wicking up the dry paper into the outlet box.  If the insulation on the conductors is damaged, that moisture could be creating a high resistance short between two or more of the conductors.