Why Are There Two Different Types Of Electric Space Engines, And How Do They Work?

Electric Propulsion is now a dominant force in space propulsion (pun intended) - in the last few decades more and more spacecraft have adopted Ion thrusters for orbit maintenance or deep space maneuvering, enabling performance that was previously beyond the capabilities of chemical thrusters.
There are Two main systems in common use, Gridded Ion thrusters are most used in deep space missions, while Hall Effect Thrusters are commonly found on satellites in Earth Orbit.

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Contains some great animations from:
Thomas Marks
Plasmadynamics and Electric Propulsion Laboratory
University of Michigan
How Hall thrusters work (and why we c...