Is it possible to charge space debris with an electrospray thruster?

Question

I have been tasked with finding a way to charge conductive space debris via a cubesat. I have been heavily considering electrospray/colloid thrusters to produce this charge however I am having some difficulty coming up with actual specs to aid in my calculations as this is an unconventional use for a ESI thruster. The questions that I cannot seem to find answers to are:

Is there a "charge flow rate" spec for electrospray devices? I think this would be a function of mass flow rate obviously, but I cannot seem to find general specs for the charge "per unit mass" that is emitted from the thruster.

Second, can anyone suggest a good way of developing a method to determine the amount of charge that "lands" on the piece of debris? I cannot seem to wrap my head around this, but I am under the impression that the "landing charge" will be influenced by distance, electrospray nozzle angle, and the charge that is attracted back to the cubesat due to the principle of spacecraft charging.

Any guidance is greatly appreciated, thanks!

Answer 1

Charge flow rate is essentially current, and the emission of electrospray thrusters are characterized by its current emitted at a given flow rate injected into the electorspray emitter. You can get the current from the emitted mass flow rate by:

$I = \dot m \frac{q}{m}$

Where $\frac{q}{m}$ is the charge-to-mass ratio of the emitted species, in Coulombs/kg. You can calculate it yourself: for instance in the Enpulsion indium thrusters, the charge is one elemental charge (they emit singly charged ions) and the mass is the atomic mass of In. You can find the emitted mass flow rate using the thrust equation:

$ T = \dot m c$

Where $c = g_0 I_{sp}$. I think the current emitted per emitter of the FEEP thrusters are in the order of a few $\mu A$. Colloid electrospray thrusters emit a few hundred $nA$ per emitter. In a thruster, many (tens to hundreds) of emitters are multiplexed in the same device.

To charge debris you'd need to shoot positively charged species to the debris, while neutralizing your spacecraft with some kind of electron gun (eg. thermionic emitter) but on the contrary side of the thruster -- if not, you'd immediately neutralize the debris. However, I'm not really sure if you could charge much the debris. The positively charged debris would immediately yield an electric field that would attract free electrons, and possibly the ones emitted by the spacecraft itself, considering they are so mobile. A way this could work would be with colloid thrusters working at different polarity, effectively neutralizing the spacecraft but charging the target that is hit by one of the two thrusters' plume, as the colloids have a high kinetic energy and wouldn't be diverted from their trajectory much towards the debris contrary to the electrons. However, negatively spraying electrosprays are in very early stages of development, and possibly this will never work, as just a slight emitted current imbalance between the positive and negative thruster will quickly charge the spacecraft to one polarity, creating a large electric field around it due to its diminute self capacitance, drawing the ejected species back to the thruster.