Ping-pong with static electricity

I connected the parallel plates to a potential difference of 4000V. I hung a table tennis ball between the plates on insulating thread. The ball was painted in conducting paint. The ball is touched on the negative plate. Electrons flood onto the ball and is becomes negative so it is repelled from the negative plate and attached to the positive plate. When it touches the positive plate all of the electrons are pulled from the plate. Judging by the force with which the ball is repelled back, this must include delocalised electrons from the graphite-based paint which will leave the ball depleted of electrons and thus positive. The alternative is that it ends up neutral and gravity pulls it back. I doubt that alternative because damping due to air resistance would leave it short of the negative plate. This ping-pong continues backwards and forwards, shuttling electrons one way across the gap. If the plates are closer, the frequency is much higher. Is this because the distance is less or because the field strength is higher?