I have read ionic/plasma propulsion system don't provide enough thrust to even lift themselves in Earth's atmosphere & photonic beamed propulsion is not in application yet so there any other thrusters that are way better than basic chemical fuel system being used or yet to be used in modern rockets ? Or maybe we can use ionic/plasma thrusters in a better way ?
Any help would be appreciated :)
For inexpensive, especially per ton of payload launched to high velocity you could consider the nuclear shotgun or project orion. There are a few environmental and regulatory issues, and the shotgun is probably not suitable for delicate payloads like humans.
No.
If there were an alternative that is both inexpensive and more efficient than chemical fuels, it would be used already.
There is one promising candidate: several companies are working on rocket engines that burn methane with LOX, with potentially better performance than the usual RP-1/LOX.
The big challenge in ion thrusters is scaling them up and improving the thrust/weight ratio.
Nuclear thermal propulsion offers better specific impulse than chemical fuels, combined with high thrust. The big problem with these engines is their radioactive exhaust products, which makes them unsuitable for launches from Earth. They're also expensive to develop and build, so there's a catch-22 here: you can't get funding until there is high demand for fast interplanetary missions, and there won't be fast interplanetary missions until a high-thust+high-Isp engine is available.
Cold gas thrusters are about the most energy-efficient propulsion system actually used. They can give quite high amounts of thrust (as Mythbusters demonstrated on a couple episodes with things like scuba tanks), and the propellant can literally just be compressed air (nitrogen or helium are more likely), but they are hopelessly low performance for a primary propulsion system for launch vehicles. They are used for maneuvering though, the Falcon 9 first stage being a significant example.
I'm guessing that's not the answer you were expecting, because you seem to be a bit mixed up about energy efficiency and rocket performance. Rockets that are more propellant-efficient (higher specific impulse) are less energy-efficient. All else being equal, doubling your exhaust velocity gives you twice the thrust and twice the total impulse from a given amount of propellant, but requires four times as much power.
Chemical engines are limited by the energy content of the propellant itself. Ion thrusters and such use such high exhaust velocities that to run at a reasonable power requires cutting the mass flow rate down to the slightest trickle, which also cuts the thrust down to something a human would have trouble noticing.
The only way you could improve their energy efficiency would be to reduce their propellant efficiency, but even if you reduced the exhaust velocity of an ion thruster to chemical engine levels, providing the energy to accelerate the propellant from outside is a lot less efficient than doing it by combusting or decomposing chemical propellants. The total power output of a Merlin 1D is around 1.4 gigawatts, and due to regenerative cooling, almost all of the energy goes into the exhaust.
