A reaction engine is an engine or motor that produces thrust by expelling reaction mass, in accordance with Newton's third law of motion. This law of motion is commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force." Examples include jet engines, rocket engines, pump-jets, and more uncommon variations such as Hall effect thrusters, ion drives, mass drivers, and nuclear pulse propulsion. Discovery The discovery of the reaction engine has been attributed to the Romanian inventor Alexandru Ciurcu and to the French journalist . Energy use Propulsive efficiency For all reaction engines that carry on-board propellant (such as rocket engines and electric propulsion drives) some energy must go into accelerating the reaction mass. Every engine wastes some energy, but even assuming 100% efficiency, the engine needs energy amounting to (where M is the mass of propellent expended and is the exhaust velocity), which is simply the energy to accelerate the exhaust. Comparing the rocket equation (which shows how much energy ends up in the final vehicle) and the above equation (which shows the total energy required) shows that even with 100% engine efficiency, certainly not all energy supplied ends up in the vehicle – some of it, indeed usually most of it, ends up as kinetic energy of the exhaust. If the specific impulse () is fixed, for a mission delta-v, there is a particular that minimises the overall energy used by the rocket. This comes to an exhaust velocity of about ⅔ of the mission delta-v (see the energy computed from the rocket equation). Drives with a specific impulse that is both high and fixed such as Ion thrusters have exhaust velocities that can be enormously higher than this ideal, and thus end up powersource limited and give very low thrust. Where the vehicle performance is power limited, e.g. if solar power or nuclear power is used, then in the case of a large the maximum acceleration is inversely proportional to it. Hence the time to reach a required delta-v is proportional to . Thus the latter should not be too large. On the other hand, if the exhaust velocity can be made to vary so that at each instant it is equal and opposite to the vehicle velocity then the absolute minimum energy usage is achieved. When this is achieved, the exhaust stops in space and has no kinetic energy; and the propulsive