> There's absolutely no reason to have a turbine at all; you'd just want a plain old expansion nozzle. That means you could pump way more heat into your plasma, making your engine much more power dense.
I agree that replacing the turbine with an electric motor seems to be the only way to go with this, but the point I am trying to make here is that if you merely increase the temperature of the working fluid without changing the pressure ratio, you will get some increase in thrust, but at the cost of a worse Carnot-cycle efficiency: quite a bit of the additional energy input goes to waste in the form of a hotter exhaust, because it cannot be expanded enough to convert it to useful work.
So can we increase the pressure ratio? if it were feasible to do so with current technology, we would already be doing so, as combustion jet engines would also benefit from increasing it. When comparing plasma and combustion jet engines, we must assume that both will be operating at the highest feasible pressure ratio.
That does not automatically rule out this technology, as it may offer something in trade-off for its limited efficiency, but in the case of electric propulsion, the storage options are currently so limited that efficiency is highly valued.
The question to be answered is this: for a given electricity source, will this give me anything of value over using all the power in an electric motor driving a fan? For subsonic flight, I am very skeptical that it can even come close to having anything to offer.
The J58 is often described as a hybrid turbo-ramjet, but that is hype to some extent: it is a low-bypass turbojet with an afterburner and a pressure-recovery intake, but that describes every supersonic airplane. It is the pressure-recovery inlet that makes all these engines somewhat ramjet-like, and in the J58 there is just more of it. The distinction is a matter of degree; even subsonic jets take advantage of pressure recovery.
Pressure recovery does two things: it increases the overall pressure ratio, and it slows down the inflow to the compressor to below supersonic speed. The former is only a benefit for heat engines (Carnot efficiency, again.) Therefore, I think the only reason for having such an inlet in an electric-fan jet engine is if a supersonic fan is infeasible, and they may well be. If so, then it may be the case that makes sense to use some of the available electric power to heat the compressed flow downstream of the fan, but it is not obvious to me that this would be a better use of that power than using it all in a bigger fan.
I see from here [1] that supersonic compressors, and therefore presumably fans, are feasible, though have not been very successful (maybe because pressure recovery is a better option for heat engines.)
By using electric power in a heat engine rather than in a non-thermal process, you are already committed to throwing about two-thirds of it away, so there have to be some quite compelling benefits elsewhere to make it a net win overall.
[1] https://en.wikipedia.org/wiki/Flader_J55