Electric Propulsion

Separating energy from propellant

In a chemical rocket the propellant is both the reaction mass and the energy source, and the energy locked in chemical bonds caps the exhaust velocity at about 4.5 km/s. Electric propulsion breaks that link. The energy comes from solar panels or a reactor; the propellant — often a heavy noble gas like xenon — just provides mass to throw. There is no chemical limit on how fast you can throw it.

There is, however, a power limit. The jet carries kinetic power $\tfrac12 \dot m v_e^2 = \tfrac12 F v_e$, supplied by an electrical system of power $P$ with efficiency $\eta$. So

$F = \frac{2\,\eta\,P}{\cvel{v_e}}$

At fixed power, thrust and exhaust velocity trade one for the other. A Hall thruster running on 5 kW, the output of a household oven, produces about a quarter of a newton.

The optimum exhaust velocity

This makes the choice of Isp a real optimization, unlike in chemical rockets. Higher exhaust velocity saves propellant through the rocket equation. But for a given power it lowers thrust, so the burn — and the trip — takes longer. And more power means a heavier power system, whose specific massSpecific mass αPower-system mass per unit electric power (kg/kW), the key parameter of an electric-propulsion system. $\alpha$ (kg per kW) is the key figure of merit.

Three ways to accelerate a gas with electricity

Sutton sorts electric thrusters into three families by how they accelerate the propellant:

• Electrothermal: heat the gas electrically, then expand it through a nozzle like a chemical rocket. A resistojet uses a hot element; an arcjet passes an arc through the flow. Wall materials still limit them, to roughly 300–600 s.
• Electrostatic: ionize the propellant and accelerate the ions with an electric field. In a gridded ion engineGridded ion thrusterIons are extracted and accelerated through charged grids to 30–50 km/s; a neutralizer adds electrons to the beam., two perforated grids at a voltage difference of about a kilovolt pull ions out of a plasma chamber and fling them out at 30–50 km/s. A separate cathode adds electrons to the beam so the spacecraft does not charge up.
• Electromagnetic: accelerate a plasma with combined electric and magnetic fields. The Hall thrusterHall thrusterAn electric thruster in which trapped electrons ionize xenon and a radial magnetic field sustains an axial electric field that accelerates the ions., the most widely flown electric thruster, traps electrons in a radial magnetic field inside an annular channel. The swirling electrons ionize the xenon, and their resistance to moving towards the anode sustains the axial electric field that accelerates the ions — with no grids to erode. Pulsed plasma and magnetoplasmadynamic thrusters belong here too.

For electrostatic thrusters the exhaust speed follows directly from the voltage, $v = \sqrt{2qV/m}$. That is why heavy xenon is prized: for a given voltage it gives lower velocity but more thrust per watt, and it is easy to ionize and store. Krypton and argon are cheaper, and SpaceX's Starlink satellites fly Hall thrusters on krypton and argon at the cost of some efficiency.

The slow way up

Electric thrusters raise satellites from their drop-off orbit to geostationary orbit — the "all-electric" satellites pioneered by Boeing's 702SP in 2015 — and they fly deep-space missions like Dawn, BepiColombo and Psyche. The trajectory looks nothing like a chemical transfer: the spacecraft spirals slowly outward, thrusting almost continuously.

A slow spiral needs more Δv than a Hohmann transfer — about 4.6 km/s instead of 3.9 km/s from a 400 km orbit to GEO — because it cannot take advantage of burning deep in the gravity well (the Oberth effect). But at four or five times the exhaust velocity, it still needs far less propellant. The costs are time — months instead of hours — and months spent crossing the Van Allen belts, where radiation degrades solar cells.

Next: how rockets steer, what their plumes reveal, and how engines are proven on the test stand before they fly.