in my humble but extensive playing with this same question; 4mm is what you're looking for. You can use any 12v power supply and adapt it to that size barrel plug but it seems to need/want at least 2 amps to wake up. 1.7mm x 4.0mm DC Coaxial Power Plug AKA Philmore 240. Rabbit hole of barrel plugs but that seems to work. it's a sub genre / standard of barrel plugs that seems to come from higher end audio standards.