An electret might work as part of the emitter, but it would be better to use Farnsworth's multipactor cold cathode because you'd get more electrons to accelerate through the curved part of the tube, with the non conductive electret. The best type of emitter is a thin film diamond layer, like is used in some of the flat panel displays such as plasma screens. These have enough power you don't have to have a vacuum interface for the tunneling effect. But you would have to use Helium or some gas which doesn't form negative ions. Ions can eventually reduce an electret's charge.