How does solar electric propulsion (ion propulsion) work?

What happens to the ions once they leave the space craft?

Positive ions shoot out of the back of DS1, making it move forward. At the same time, a beam of electrons with negative charges is shot out of a cathode neutralizer. Things with positive and negative charges are attracted to each other so the negative electrons fly towards the positive ions.

Since a positive ion is an atom that is missing one or more electrons, when the electrons get to the positive ions, they fill in the missing electron's position and make the ion back into a neutral atom. Once the ions have been neutralized, the atoms thus formed float off into the vast emptiness of space.

How does DS1's engine work?
What is an atom?
What is an ion?

What causes ions to leave DS1?
Are ion engines radioactive?
Are ion engines nuclear?
What is a cathode?
What does electrically charged mean?
What's an electron?