Feasibility of Electrical jet engine is it possible to create an  electrical analogue of jet engines?How is its efficiency compared to ion ejection engines?
 A: Well I might be about to answer the wrong question here, but assuming for the moment that you mean the thing on a 747 and the thing on a spacecraft...
is it possible to create an electrical analogue of jet engines
Absolutely.
In the most basic sense, all a jet engine does is expand air by heating it, and then direct it for thrust. We use jet fuel for the heat source because it's energy dense, but you can replace that source with any other.
In the 1950s, they experimented with replacing it with a nuclear reactor - the heat from the reactor was put into a fluid, piped to the engine, and then run into a radiator-like arrangement that heated the air. That cooled the fluid, which ran back to the reactor to heat up again. It didn't provide lots of thrust, but it was (in theory) enough to keep the aircraft flying for as long as the reactor could run - weeks or months.
One can imagine taking that engine and replacing the radiator with conventional resistive wires like the ones in baseboard heaters. If one were to build such an engine, its energy efficiency would be similar to the same engine running on jet fuel. That's because the efficiency of a jet engine is defined largely by the temperature of the air at the entrance to the first turbine stage. That's a materials science problem and doesn't change with the type of fuel. One would expect that an electric coil might be slightly more efficient at turning energy into heat, but modern jet engines are likely above 95%, burners are well understood tech.
The problem, of course, is energy density. Airplanes have to lift their energy source, so you want to get the most energy-packed fuel you can. Jet fuel is pretty good. Uranium is even better. Lithium-ion? Not so much.
How is its efficiency compared to ion ejection engines
Assuming you mean ion engines, these are rockets. I mention this because it's key to what follows.
In a jet engine you have two different things, the "working fluid" which is the air, and the heat source, which is normally jet fuel but could be anything. The resulting hot air you squirt out a nozzle.
In a typical chemical rocket the fuel and the working fluid are one and the same. The fuel is burned to produce heat which heats the fuel which you then squirt out a nozzle. That means you have to carry around a lot more fluid in total, whereas a jet just flies right through it. So the Me 163 could fly for eight minutes, while the de Havilland Swallow could fly for about an hour - unless it ripped itself apart in-flight, which is was prone to doing.
In an ion engine, electricity is used to accelerate the working fluid, which is more jet-like in that there is a clear separation between the working fluid and "heat source". But you're still carrying around that working fluid in a tank, and you have to accelerate that. So again, if you were to compare the total amount of impulse you got on the craft as a whole, even the ion engine's high efficiency may result in less bang for the buck.
But what if you took an ion engine and replaced the fuel tank with a tube that's open in the air? Now you have something that is really like a jet engine, but instead of using heat to accelerate the air, you accelerate it directly. Such a thing exists, and it's amazingly efficient, in theory at least, something like 50 times better than burning fuel.
To date, no one's make such an engine that has real-world aircraft-levels of thrust, but you can see tiny versions all over youtube if you look for "ion lifter". Most research into these devices has concentrated on very small designs for cooling computers, and MITs research is the first I've seen even considering larger versions.
