Electron density in low orbit space

Question

Assume a spacecraft orbiting earth in about 400km. Now you want to measure the free charge carriers there per volume unit, how would this be done?
I have an idea, please comment on my reasoning: The basic idea is to measure the number of electrons that "crash" onto a copper plane of a specified area on the outer surface of the spacecraft. However, where do these electrons go, after they have crashed onto the copper? Lets say the spacecraft forms a capacitor with infinity (such as a spherical conductor in free space), so we can use the spacecraft metal as a ground. Now, this means that after a while the spacecraft aquires a certain charge, and goes into some kind of equilibrium (means as many electrons enter the spacecraft as do leave it), such that we have a charged spacecraft, no electrons hit the copper-area-sensor, such that I measure nothing anymore. Is this correct?
Second idea: We have two plates, which we put on the surface side by side and build a potential between them (like a capacitor, that is unfolded like two opposite pages of an opened book). Now the charges are attracted slightly more to the positively charged copper-sheet such that we get a current we can measure from positive to negative copper-sheet, right?

Is the second idea a valid approach or am I missing something here?
Can the absolute amount of charges be measured that way?
How does the velocity of the spacecraft go into this whole idea (does this space plasma have a velocity relative to earth)?

Sorry for the many questions, I hope I was clear about the problem I am trying to solve and the thoughtprocess I have made so far.
Thanks

honeste_vivere · Answer

This can be and already has been done on numerous occasions.  An example is the FAST spacecraft that used an electrostatic analyzer kind of like the spherical tophat model found at: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2016JA022583.  The instrument measures energy per charge over some given energy range in some look direction.  After you accumulate counts in all the look directions and energy channels, you can construct velocity distribution functions which can be integrated to give the number density etc.
Spacecraft always float at some potential relative to the plasma because there is no ground in space.  The floating potential, or spacecraft potential, equilibrium is determined by a balance of thermal currents and photoelectron currents.  This can be advantageous if used properly or a severe detriment if not properly accounted for.
In any case, what you are describing sounds, in some ways, like a Faraday cup instrument.

Electron density in low orbit space

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