Self-Assessment Quiz: Electric Propulsion

Twenty questions on the high-Isp/low-thrust idea, ion and Hall thrusters, the power–thrust trade, and spiral transfers. Answer each before opening the key. Aim for 16 or more. Use $g_0 = 9.81\ \text{m/s}^2$.

Question 1

The single most important thing electric propulsion does, relative to a chemical rocket, is:

A) burn its propellant hotter B) decouple the energy source from the reaction mass C) use a bigger nozzle D) eliminate the need for propellant entirely

Question 2

The effective exhaust velocity of a typical electric thruster, compared with a chemical rocket, is roughly:

A) the same B) about half C) about ten times larger D) about a thousand times larger

Question 3

The thrust of an electric thruster at fixed power obeys $F = 2\eta P/v_e$. Raising the exhaust velocity $v_e$ (at fixed $P$, $\eta$):

A) raises the thrust B) lowers the thrust C) leaves the thrust unchanged D) raises the thrust only in vacuum

Question 4

A gridded ion engine accelerates ions using:

A) a magnetic nozzle B) crossed electric and magnetic fields in a neutral plasma C) a static electric field between perforated grids D) the thermal expansion of a heated gas

Question 5

The standard propellant for both ion and Hall thrusters is:

A) liquid hydrogen B) xenon C) kerosene D) hydrazine

Question 6

A Hall thruster produces more thrust per watt than a gridded ion engine mainly because it:

A) runs at a higher specific impulse B) accelerates ions in a quasi-neutral plasma, avoiding the space-charge limit C) uses a lighter propellant D) has no cathode

Question 7

Compared with a gridded ion engine, a Hall thruster typically has:

A) higher $I_{sp}$ and lower thrust B) lower $I_{sp}$ and higher thrust per watt C) higher $I_{sp}$ and higher thrust D) identical performance

Question 8

An ion engine's thrust is tiny (milli-newtons) primarily because its:

A) exhaust velocity is very low B) propellant mass flow rate is very small C) efficiency is very low D) nozzle is too small

Question 9

The reason electric propulsion cannot be used to launch from Earth's surface is that:

A) it does not work in the atmosphere B) its thrust-to-weight ratio is far below one C) xenon is too expensive D) the exhaust is radioactive

Question 10

An ion engine with $I_{sp} = 3{,}000\ \text{s}$ has an exhaust velocity of about:

A) $300\ \text{m/s}$ B) $3{,}000\ \text{m/s}$ C) $29{,}400\ \text{m/s}$ D) $294{,}000\ \text{m/s}$

Question 11

The neutralizer cathode on an ion engine is required because, without it:

A) the propellant would not ionize B) the spacecraft would charge negative and pull the ejected ions back C) the grids would overheat D) the exhaust would be too fast

Question 12

A low-thrust spiral transfer between two circular orbits, compared with a Hohmann transfer between the same orbits, requires:

A) less delta-v B) the same delta-v C) more delta-v D) no delta-v at all

Question 13

Even though a spiral transfer costs more delta-v, electric propulsion still uses far less propellant for it because:

A) the spiral is shorter in distance B) the thruster's high specific impulse dominates the rocket equation C) low thrust means no propellant is consumed D) gravity does the work

Question 14

The main penalty a spacecraft accepts when it uses electric propulsion instead of chemical is:

A) higher propellant mass B) much longer transfer/maneuver time C) lower specific impulse D) inability to work in vacuum

Question 15 (True/False, justify)

"MPD and VASIMR thrusters do not fly as main propulsion today mainly because the physics doesn't work." True or false? Justify in one sentence.

Question 16 (True/False, justify)

"Because $v_e$ sits in the denominator of $F = 2\eta P/v_e$, a higher specific impulse always makes an electric-propulsion system better." True or false? Explain briefly.

Question 17 (True/False, justify)

"An ion engine and a Hall thruster sit at different points on the same power–thrust–Isp trade." True or false? Say why.

Question 18 (Short answer)

In two sentences, explain why an ion engine's exhaust can be ten times faster than a Merlin's yet its thrust is a hundred-million times smaller. Name the quantity responsible.

Question 19 (Short answer)

A thruster draws $P = 4\ \text{kW}$, runs at $v_e = 20\ \text{km/s}$, and has $\eta = 0.5$. Compute its thrust in milli-newtons (show $F = 2\eta P/v_e$).

Question 20 (Short answer)

Name the first operational use of electric propulsion (a routine, unglamorous job on communications satellites), and say in one sentence why high $I_{sp}$ mattered so much for it.

Answer Key

Q Ans Note
1 B Energy (electricity) is separate from reaction mass (inert gas) — so no chemical ceiling on $v_e$.
2 C Electric $v_e \sim 15$–$40$ km/s vs chemical $\sim 3$–$4.5$ km/s: ~10×.
3 B $F \propto 1/v_e$ at fixed power; higher $v_e$ means lower thrust.
4 C Gridded electrostatic acceleration between a screen grid and an accel grid.
5 B Xenon: inert, easily ionized, heavy, storable as a dense fluid.
6 B No grids → no space-charge limit → higher thrust density.
7 B Hall: lower $I_{sp}$ (~1,500–2,000 s), more thrust per watt.
8 B $F = \dot m v_e$; the mass flow (mg/s) is minuscule.
9 B Milli-newton thrust gives $T/W \ll 1$; it cannot lift its own weight.
10 C $3{,}000 \times 9.81 \approx 29{,}400\ \text{m/s}$.
11 B The beam is positive ions; without neutralization the craft charges up and recaptures them.
12 C The impulsive Hohmann is delta-v-optimal; the continuous spiral costs more.
13 B High $I_{sp}$ makes the exponent $\Delta v/v_e$ small, so propellant is small despite more $\Delta v$.
14 B Continuous low thrust means months-long burns instead of minutes.
15 False The physics is sound and demonstrated in the lab; they lack a power source (hundreds of kW–MW) light enough to fly.
16 False Higher $I_{sp}$ raises the power-to-thrust ratio → less thrust, longer missions, more power-system mass; there is an optimum.
17 True Both accelerate xenon electrically; ion trades thrust for $I_{sp}$, Hall trades $I_{sp}$ for thrust.
18 — Thrust is $F=\dot m v_e$; the ion engine's $v_e$ is ~10× larger but its mass flow $\dot m$ is ~$10^8$× smaller (mg/s vs hundreds of kg/s). The mass flow rate dominates.
19 — $F = 2(0.5)(4{,}000)/20{,}000 = 4{,}000/20{,}000 = 0.2\ \text{N} = 200\ \text{mN}$.
20 — GEO north–south station-keeping; high $I_{sp}$ slashed the propellant needed for ~50 m/s/yr over a 15-year life, freeing mass for payload or life extension.

Topics to review by question

Questions Topic Section
1, 2 The decoupling idea; high-Isp regime §20.1
3, 8, 16, 19 Power–thrust–Isp relation §20.1, §20.5
4, 5, 11 Ion engines and xenon §20.2
6, 7, 17 Hall thrusters; the trade §20.3
9, 14, 18 Why low thrust; why not launch §20.5
12, 13 Spiral vs Hohmann §20.6
15 MPD / VASIMR and the power wall §20.4
10 $I_{sp}$–$v_e$ conversion §20.1
20 Applications §20.6