Is there any possible reason to direct the electron gun specifically towards the ion trail behind an ion thruster?

This answer to Neutralization of ions in the ion thruster quotes the introduction to Wikipedia's Ion thruster:

Temporarily stored electrons are finally reinjected by a neutralizer in the cloud of ions after it has passed through the electrostatic grid, so the gas becomes neutral again and can freely disperse in space without any further electrical interaction with the thruster.

Question: Is neutralization of the ion trail by injecting an equal and opposite amount of charge from the electron gun really important? Does it need to be pointed specifically towards the ion trail behind an ion thruster, or would it be fine pointing in any direction? The light electrons will have such a higher speed than the spacecraft that it's not likely to re-encounter them again no matter where they're pointed

Unrelated gratuitous cropped screen capture from the YouTube video Star Trek - The Galileo Seven - visual effects comparison. Yes I know it's not ion propulsion, but I like to imagine that this is what the light from recombination in an ion plasma would look like.

• As the Author of the initial Answer, i like this question. I think, some parts are obvious: 1.) shooting the electrons in the wrong direction would produce thrust in the wrong direction. 2.) you need to put the electrons somewhere because otherwise your S/C will be charged .... but I think the most important (for me) part is: even if the ions would not be neutralized, would there be a problem with "returning" ions. Jul 23, 2020 at 7:01
• @CallMeTom yep, since momentum per particle is $p=\sqrt{2 m E}$ and the electrons are 2000 times less mass and probably emitted at one tenth of the acceleration voltage, it's like a 1% effect, but that's certainly still very important and worth using correctly. Please feel free to post an answer!
– uhoh
Jul 23, 2020 at 7:07
• I think one significant factor may be that the positive ions pull the electrons, significantly helping the electron gun getting rid of them.
– SF.
Jul 23, 2020 at 9:22
• actually I did that for protons, for ions the mass ratio is another 100 times larger so the electron thrust is less than 0.1% of the ion thrust.
– uhoh
Jul 23, 2020 at 11:50

There are a lot of ions in space already, adding a few from the thruster is not really that big of a deal. They are moving so fast that it won't really make a huge difference being neutral or not, they are going away from the spacecraft, and at the point where electrons are typically injected they are far enough away that it doesn't matter much.

All that being said, the electrons have to be tossed out to make sure the spacecraft doesn't get a charge, and you might as well toss them out in the general direction of motion, it'll give you a small positive velocity. As is shown in this picture, being perfectly aligned with the thrust vector isn't that important. Putting it into the beam seems like a reasonable thing to do, reducing the amount of ions in space, but it doesn't seem to be critical.

• Ya while the annotation does say "...injected into the beam for neutralization" I still can't figure out why that would be important either. Any idea who, or what institution prepared this image? Maybe it's source elaborates on that annotation.
– uhoh
Jul 23, 2020 at 14:48
• My guess is for spacecraft neutralization, but... Will see what else I can dig up. Jul 23, 2020 at 15:31
• This answer seems to be based almost entirely on your guesswork, and the image is just a simplified overview that's useless for estimates of how important some geometric configuration is. You may be right that it basically doesn't matter where the e-gun is pointed, but I'd find it equally plausible that the big current loop you'd create by putting it somewhere else would incur significant and hard to control magnetic interactions. Jul 23, 2020 at 16:31
• Having a large cloud of positive ions behind the spacecraft does indeed alter the field seen by the next ion out. It is, literally, a bunch of space charge that you really don't want. Jul 23, 2020 at 18:17
• @JonCuster That's a really good point! Space charge limitation might be exactly the answer! Ballpark numbers might be 20 kV acceleration voltage and 10 to 100 mA ion current. From that it may be possible to calculate the charge density and the electric field, but it may not be a simple calculation unless one assumes there's no divergence of the beam and that it's a half-infinite cylinder of say 10 to 30 cm in diameter.
– uhoh
Jul 24, 2020 at 1:12