Electric propulsion

Draft

A chemical rocket carries its energy in its propellant, so exhaust velocity is capped by the chemistry. Electric propulsion breaks that link: energy comes from solar arrays or a reactor, and the propellant is merely reaction mass. Specific impulse becomes a design variable rather than a property of the fuel.

The power-limited regime

Removing the chemical ceiling on $v_e$ introduces a different one. Jet power is

P_{\text{jet}} = \tfrac{1}{2}\dot{m}v_e^2 = \tfrac{1}{2}Fv_e

so for a given electrical power $P$ and efficiency $\eta$ :

Thrust in the power-limited regime

F = \frac{2\eta P}{v_e} = \frac{2\eta P}{I_{sp}g_0}

Thrust is inversely proportional to specific impulse. Doubling $I_{sp}$ at fixed power halves the thrust. This is the central trade of electric propulsion, and it has no analogue in chemical systems.

System	$I_{sp}$	Power	Efficiency	Thrust
NSTAR, Deep Space 1 and Dawn	3120 s	2.3 kW	62%	93 mN
NEXT-C, Psyche and DART	4190 s	6.9 kW	70%	236 mN
SPT-100 Hall	1600 s	1.35 kW	50%	86 mN
Chemical apogee motor	320 s	n/a	n/a	400 N

The thrust column is the point. A kilowatt-class ion engine produces roughly the force of a sheet of paper resting on your hand, and it produces it continuously for years. A chemical engine produces thousands of times more for a few minutes.

How gridded ion engines work

Propellant, usually xenon, is injected into a discharge chamber and ionised, either by electron bombardment from a hollow cathode or by radio-frequency excitation. Two closely spaced grids at the downstream end then do the work: the screen grid at high positive potential and the accelerator grid at negative potential establish a strong axial field that extracts ions from the plasma and accelerates them to several tens of kilometres per second.

A neutraliser cathode outside the engine injects electrons into the beam at the same rate ions leave. This is not optional housekeeping. Without it the spacecraft charges negative until it electrostatically recaptures its own exhaust, and thrust falls to zero.

Two limits define the technology.

Space-charge limits the current density. The extracted ions are a unipolar charged beam, and their own space charge opposes further extraction. The Child-Langmuir law caps current density for a given grid gap and voltage, which caps thrust per unit area. Gridded ion engines are therefore large for their thrust.

Grid erosion limits the life. Charge-exchange collisions between beam ions and residual neutrals produce slow ions that are attracted into the accelerator grid and sputter it away. Grid erosion is what ends the engine’s life, and qualifying an engine means running one on the ground for as long as the mission requires. The NSTAR extended life test ran over 30,000 hours.

The optimal specific impulse

Higher $I_{sp}$ means less propellant, which seems unambiguously good until the power system is accounted for. Producing the power requires solar arrays or a reactor whose mass scales with power, and thrust falls as $I_{sp}$ rises, so a higher- $I_{sp}$ mission takes longer or needs more power.

Writing the total of propellant mass and power system mass as a function of $I_{sp}$ gives a curve with a genuine minimum. The optimum depends on the specific mass of the power system, in kilograms per kilowatt, and on the time available.

Short missions or heavy power systems: Favour lower specific impulse. Hall thrusters at 1500 to 2000 s sit here, which is why they dominate commercial station keeping and orbit raising.
Long missions with light power systems: Favour higher specific impulse. Gridded ion engines at 3000 to 4500 s sit here, which is why they dominate deep-space science missions.
Rule of thumb: The optimum exhaust velocity is of the same order as the mission delta-v. A 10 km/s mission wants roughly 10 km/s of exhaust velocity, about 1000 s.
Practical override: Available power is usually fixed by the spacecraft bus before the thruster is chosen, so the true optimisation is often constrained to a narrow range.

Families

Family	Mechanism	$I_{sp}$	Notes
Resistojet	Electrically heated propellant	300 s	Simple; used on early comsats
Arcjet	Arc-heated propellant	500 to 700 s	Higher power density than a resistojet
Gridded ion	Electrostatic acceleration between grids	2500 to 5000 s	Highest efficiency, lowest thrust density
Hall thruster	Crossed-field acceleration in quasi-neutral plasma	1500 to 3000 s	Higher thrust density; see Hall thrusters
Magnetoplasmadynamic	Lorentz force on a self-induced current	2000 to 5000 s	Needs hundreds of kilowatts; no flight heritage at scale
Pulsed plasma	Ablative discharge across a solid propellant	1000 to 1500 s	Very low power, very simple, small satellites
Field emission	Ions extracted from a liquid metal surface	4000 to 8000 s	Micronewton precision; LISA Pathfinder

Propellant

Xenon has been the standard choice: inert, storable at high density as a supercritical fluid, easy to ionise and heavy enough to give good thrust per ion. It is also a trace atmospheric gas produced as an air-separation by-product, priced in the low thousands of dollars per kilogram, with global annual production small enough that a large constellation can move the market.

That constraint has driven a shift. Krypton is substantially cheaper and gives roughly 10% lower specific impulse for the same power. Argon is cheaper still with a further performance penalty. Starlink flew krypton Hall thrusters on early satellites and moved to argon on later ones, which is the first use of argon electric propulsion at operational scale, and it was an economic decision rather than a technical one.

Iodine has been flown in small systems: it is storable as a solid, so the tank is trivial, but it is chemically aggressive and the plume interacts with spacecraft surfaces.

Where it has mattered

Electric propulsion is not a marginal improvement on chemical systems for certain missions; it is the reason they exist.

Dawn orbited two separate main-belt bodies, Vesta and Ceres, entering and leaving orbit around each. It accumulated 11.5 km/s of delta-v from about 425 kg of xenon, more than any spacecraft before it. No chemical system could have carried the propellant for that mission on any available launcher.

BepiColombo uses four T6 gridded ion engines to shed the orbital energy needed to reach Mercury, a destination that is expensive precisely because getting close to the Sun requires losing angular momentum.

Commercial GEO is where the economics show most plainly. An all-electric platform reaches its slot in three to six months instead of a few weeks, and carries roughly three times the payload for the same launch mass. See Hohmann and bi-elliptic transfers for the propellant comparison.

References

Goebel, D. M. and Katz, I. Fundamentals of Electric Propulsion: Ion and Hall Thrusters, JPL Space Science and Technology Series, Wiley, 2008. Freely available and the standard reference.
Jahn, R. G. Physics of Electric Propulsion, McGraw-Hill, 1968; Dover reprint 2006.
Brophy, J. R. “NASA’s Deep Space 1 ion engine”, Review of Scientific Instruments, 73:1071, 2002.
Rayman, M. D., Fraschetti, T. C., Raymond, C. A. and Russell, C. T. “Dawn: A mission in development for exploration of main belt asteroids Vesta and Ceres”, Acta Astronautica, 58:605, 2006.