For reasons I can't entirely recall, there are pretty serious limitations on the thrust these can generate. I believe it has something to do with the air becoming "saturated" with ions. The limit on the density of charged particles limits how much mass you have to push on. The aircraft in your link has a top speed of 17km/h.

Heating the air with microwaves or an electric arc could work, since it would just be replacing burning fuel with another heat source. It would still require moving parts though (unless it's only used as a ramjet), since a jet engine has to compress the air before heating it.