Fundamentals of in-space electric propulsion
Electric propulsion (EP) is used for propulsion of satellites for a combination of practical and economic reasons. These devices that use electric power to accelerate a mass flow exhaust at velocities one or two order of magnitude faster than those achieved in conventional chemical propulsion.
The Tsiolkovsky rocket equation relates the velocity increment ΔV of the payload mass mf the requiered mass of the propellant gas mp and its exhaust velocity vex as,
This ratio is represented in the figure below for typical ΔV corresponding to different orbital maneuvers, such as the Low Earth Orbit (LEO) to Geostationary Earth Orbit (GEO) transference. High exhaust propellant speeds vex exponentially decrease mp/mf and therefore the rocket fuel needs. However, the maximum achievable speeds are limited up to vex ≈ 5.5 Km/s in conventional thrusters due to the physicochemical properties of propellants.
The EP systems make use of physical processes involving electricity to increment the velocity of the exhaust gas stream and/or a plasma flow up to velocities over the 5.5 Km/s limit. For example, particle acceleration by electric forces is an attractive idea because ions reach velocities of vex ≈ 20 Km/s accelerated by a 100 volt voltage drop.
The figure below shows the basic scheme of a electric thruster where the central block symbolizes an idealized engine. The electric power W is employed to heat the propellant mass flow rate ṁp to temperatures T higher than can be achieved using a chemical reaction. The exhaust expands through a solid nozzle and the thrust F = ṁp vex is delivered along the opposite direction. Alternatively, the propellant is ionized, accelerated by electric fields and/or expands through a magnetic nozzle. Since the energy required for particle acceleration is provided in both cases by an external power supply, the exhaust speed vex can be higher than in conventional chemical propulsion systems.
The performances of rocket thrusters are characterized by the specific impulse, which measures the thrust F produced by the weight of propellant consumed by time unit,
where go is the standard Earth gravity and Isp has units of time. Chemical engines have typical I sp < 500 s whereas plasma engines, such as Hall Effect thrusters have values exceeding I sp > 1500 s. However, as propellant mass flows ṁp that can be accelerated by EP technologies up today is much lower these systems deliver smaller thrusts F = ṁp vex .
Therefore, conventional chemical engines deliver high thrusts in sort times with high propellant consumption whereas EP systems give lower impulses F using much less rocket fuel. Their competititve advantage is the total momentum delivered by EP systems, that can be compared with chemical propulsion since they can be operated along very long periods of time using less propellant.
Electric thrusters can be roughly classified in terms of the physical principle for the acceleration of propellant as shows the table below. According on the specific field of application, thrusters falling into one of these three categories can be more or less attractive due to their specific performances such as, delivered thrust, electric power consumptions, etc.
In the following table M and Mi are respectively the masses of molecule and ion, Vac is the acceleration potential of electric charges. The neutral gas or ion temperature is T and J is the electric current density. Acronyms are; ECR, electron cyclotron resonance thruster; GIE, gridded ion engine; FEEP, the field emission electric propulsion ; HET, Hall effect thruster , HEMPT, highly efficient multistage plasma thruster . The applied-field (AF) and self-field (SF) are variants of the magnetoplasmadynamic MPD thruster.
Interested readers are referred to the books [1] and [2] cited below for more information. Reference [3] is an introductory paper in the context of telecommunication satellites and [4] is a comprehensive review of present state-of-the-art of electric propulsion.
[2] Fundamentals of Electric Propulsion. D.M. Goebel and I. Katz. Wiley & Sons. New Jersey (2008).
[3] L. Conde. Plasma propulsion for telecommunication satellites. J. Phys. Conf. Ser. 1326 012001-1,6 (2019).
[4] S. Mazouffre. Electric propulsion for satellites and spacecraft: established technologies and novel approaches. Plasma Sources Sci. Technol. 25 033002–1,27 (2016).
| Physical principle | Thruster | ||
|---|---|---|---|
| Electrothermal |  |
Solid nozzle | Arcjets |
| Resistojets | |||
| Magnetic nozzle | Helicon | ||
| Vasimir | |||
| ECR | |||
| Electrostatic |  |
Externally applied electric field | GIT |
| Colloid | |||
| FEEP | |||
| Self-consistent electric field | HET | ||
| HEMPT | |||
| Multi-cusp | |||
| Electromagnetic |  |
Steady plasma flow | AF-MPD |
| SF-MPD | |||
| Unsteady plasma flow | Pulsed plasma | ||
