I've actually thought about this a bit, and I think that a really interesting design for a launch gun would be to encase the payload in a cover composed of diamagnetic material and then pump liquid nitrogen through channels made inside the material. The material would become perfectly diamagnetic and it will repel all fields, so you can easily levitate it and use it's tendency to go from a stronger to a weaker field to accelerate it.

I don't know for sure, but I think that the main advantage of doing something like this versus just putting a magnet over there, would be the fact that an accelerating magnet in such an assembly would generate huge amounts of back-emf and you would have to a) sink that and b) compensate for that.

However I don't know much about what other people's designs are, but I would like to change that. Do you know any resource where I can learn more from the scratch on how to build something like this?

Also where can I read more in detail about launch loops, laser launching, and space elevators?