As you would expect from the name, the Mind Control Ray will control the minds of enemies who are hit by it. What this means is that both humans and automechanical enemies hit by this will temporarily be turned into allies, which can be pretty useful for certain situations where there are many enemies attacking you at the same time. It will also deal some plasma damage to enemies who are hit by it.
In order to actually get the Mind Control Ray, you will need to head to Monarch. Go to Fallbrook and head to the store called Fallbrook Dry Goods and Supplies. Talk with Duncan there and see what he has to sell. Buy an item called SubLight datapad from him. This will give you a quest to go to an abandoned lab in Cascadia, also on Monarch.
The quest "Space-Crime Continuum" will also take you to this abandoned lab. Anyway, when you are there, look for a terminal, then turn directly to the left. Jump across to the platform there, then jump further to the platform on the right. The jump can be a bit tricky, but save the game before jumping, and you can just reload if you fail it.
Now climb up two sets of ladders to reach the small area where the Mind Control Ray is located. Simply loot this, and it's yours to keep! Congrats on finding this science weapon, and have fun turning enemies into allies for a few seconds.