Absolutely no motorized mining gear on any Oregon beach. This applies to gas, electric, even a recric system in gas or electric. If you set it up with a hand operated pump (like the Gold Grabber version), then that's legal.
Panning and sluices allowed, and can take a 5 gallon bucket of black sand per day from the beach, your choice of just dug or processed cons.
State Parks and recreation have control over the beaches. I think they still require a permit, more for your knowing the regulations than anything else. Believe it's still free, and available from either Salem or one of the coast offices like Beverly Beach