Electrostatic Equilibrium Real-World Derivation

Imagine you are working for a particle physics research lab and you're trying to "capture" an electron between two other charged particles. Your apparatus allows you to adjust the charge of each of the particles, lets call them A and B, and the distance between the two charged particles. Assuming the electron is going to be placed evenly between the two charged particles such that it has no initial velocity, how would you setup your apparatus so that the electron doesn't move? Here's a diagram for reference:



Now imagine that some jerk superhero named "Captain Hammer" smashes your device the device breaks due to perfectly normal usage. Now B is stuck at -13μC and the distance from A to B is stuck at 0.25m. The charge on A can still be changed and the distance from A to the electron can also be adjusted from 0m to 0.1 m. Given these new parameters how could you keep the electron from moving? Here's another diagram for reference:



Why would stopping an electron make things cold? What are some applications of making things REALLY, REALLY cold?