## Basic theory

### Electric propulsion: what for?

The advantage of electric propulsion can be assessed from Tsiolkowski's equation, which states that the initial mass M_{0} of a free body with initial velocity V_{0} required to reach velocity V_{1} with mass M_{1} is:
where V_{sp} is the specific velocity of the propellant (to some extend, the average velocity of exhaust gases).

In the (very) idealized case where the dry mass of the spacecraft is negligible, M_{1} is the payload mass. The advantage of ejecting the propellant at a high velocity becomes then obvious: for a given mass of propellant, the deliverable payload mass can be arbitrarily increased via an adequate increase of the exhaust velocity V_{sp}, which is exactly what electric propulsion allows.

### Limitations of conventional propulsion systems

The performance of classical rocket nozzles is intrinsically limited by the maximal sustainable temperature T_{noz} of its components. The greatest exhaust velocity achievable with a thermodynamic expansion in a nozzle is indeed bounded via a relationship of the type:
where R is the universal gas constant and M_{e} is the average exhaust gas molecular mass. In practice, this sets the limit at V_{sp} ≈ 10 km/s for hydrogen propellant. This restriction applies not only to classical chemical engines, but also to heat-exchanger nuclear rockets and electrojets (rocket engines with resistor or electric arc heating).

In the case of chemical rocket engines, the energy available from the propellant sets an even more restrictive limit on the specific velocity via:
where ΔH_{f} is the reaction enthalpy of the propellant mixture. The most efficient propellant mixture commonly in use is oxygen/hydrogen which develops a specific velocity of the order of V_{sp} ≈ 4 km/s. Only marginal improvements over this figure could yet be achieved with today's knowledge, using e.g. tri-propellant systems.

### Electric propulsion to the rescue

Both of the aforementioned limitations are overcome with advanced electric propulsion systems, which accelerate the working medium with electric or electromagnetic fields.

Even though there is virtually no limit to the achievable specific velocity with electric propulsion, some practical limits arise due to the energetic cost of the specific velocity:
where P is the supplied electrical power and F the developed thrust.
In other words, the specific velocity is now constrained by the amount of available power and the level of thrust required to maneuver within a reasonable timeframe.

As a result, each type of mission defines its own "ideal" specific velocity. For instance, satellite station-keeping and orbit transfers require specific velocities within the range 15-40 km/s in view of the limited amount of power available from the solar panels. Interplanetary missions with nuclear generators would on the other hand be able to use much higher specific velocities. Likewise, accurate spacecraft positioning can be performed with very low thrust systems and thus with high specific velocities.