I've been researching electric jets, and I have seen a number of schemes. What is the most likely way to build an all-electric jet engine, assuming that the power source is available and practical?
Well I suppose one COULD design a brayton cycle gas turbine which uses heat introduced into the gas stream by electrical energy, either in the form of resistive heating elements or high voltage arc flash. Fairly impractical considering that - and especially for a high bypass turbofan engine - it would make more sense to just use a ducted fan driven by an electric motor.
So I guess the real question here is not could you design an electric jet engine, but rather, why would you want to?
If you are expecting efficiency improvements, especially a more exergetically efficient engine, an electric jet makes no sense. An electrically powered ducted fan engine is more practical.
Again we have had this discussion multiple times on this board about the feasibility of large electric aircraft but it always comes down to a problem of energy density in the power source which makes such designs impractical.