# How do ion thrusters create a force against the spacecraft?

I recently saw an old thread, How do reaction engines create a force against the rocket?, get bumped up, and it asks a good question: in a chemical rocket, the fact that the rocket exhaust gets propelled away means that Newton's Third Law requires that there be some force acting on the rocket in the other direction, but the Third Law itself does not actually specify what that force is, with the answer being that it's the pressure of the gas in the combustion chamber and on the engine bell that produces an unbalanced force on the engine.

I'd like to ask exactly the same question, but for an ion thruster instead. As in the chemical rocket, the fact that there's an ion stream going away at high velocity implies that there needs to be a point at which the outgoing ions exert some form of electric force on the thruster. So: what is the nature of this force, and how does it work?

• Through electrostatics. Just like a (Cockroft-Walton or Van de Graaff) ion accelerator here on Earth. Raise ion source potential above 'earth' or spacecraft "ground", make ion, and the positive ion accelerates away from the positive potential through Coulomb's law. Feb 19, 2019 at 19:22
• @JonCuster Yes, obviously it's through electrostatics; hence the tag. The rest of your comment just details the mechanism through which the thruster imparts force on the ion, which is not what I'm asking. Feb 19, 2019 at 20:01
• Well, but the ion imparts force right back based on the same Coulomb interaction. So, I'm kind of unclear. The ion source is attached to the spacecraft, the ion isn't, so in the frame of the spacecraft it goes flying off. I know you know this, so I'm king of wondering what kind of an answer you are looking for here. Feb 19, 2019 at 20:04
• @JonCuster I hadn't worked it to my satisfaction, and I figured others would be better placed to write a comprehensive account that would form a valuable resource for future visitors. Feb 19, 2019 at 21:13

The principle is very simple, though of course actually constructing the things is a lot more complicated.

A propellant gas is ionised between two charged plates. The cations are attracted to the negative plate and repelled by the positive plate and acquire an energy $$E = qV$$ and a momentum $$p = \sqrt{2mE}$$.

The plates, due to the potential they're being held to, also carry an electric charge (which is what attracts and repels the ions), and these charges also feel a (small) unbalanced force coming from the ions, so the plates (and the spaceship they are attached to) acquire an equal and opposite momentum $$-p$$. So the electrostatic force pushes the cations one way and the spaceship the other.

The electrons acquire an equal kinetic energy but since they are much lighter than the cations their momentum is negligible. It is the cations that propel the spaceship.

The negative plate is a grid, so the majority of the cations fly straight through the grid and out the other side. At this point the electrons collected at the positive plate are recombined with the charged exhaust gas to neutralise it. The neutralised gas feels no electrostatic force so it shoots off with basically the same momentum as it gained when accelerated between the plates.

The end result is simply that the propellant goes one way and the two charged plates, and the spaceship they are attached to, goes the other way.

• And the electrons don't go flying out the back end of the space craft since they won't get accelerated out of the source (which just leads to having to have an electron gun for charge conservation, but that won't provide much thrust as you point out). Feb 19, 2019 at 22:25
• I've made some slight streamlining edits. Good answer, thanks for writing it. Feb 19, 2019 at 22:27
• – uhoh
Jul 25, 2020 at 7:04