Linear accelerator
Ok - it's a coil. But lots of fun advanced concepts to learn about here.
http://www.doityourselfgadgets.com/p/coilgun-knowledgebase.html
This would be awesome to combine with a vacuum gun. Use the inrush of air for the initial acceleration then let the coils pickup the very end.
Questions
I'm very interested in how the magnetic field collapses. I believe that this is actually working on a "reluctance" mechanism - the magnetic field builds up in the projectile and tries to align with the magnetic flux of the coils. The field won't collapse instantly, so when to cut power is very important.
There will also be hysteresis in the projectile, which means just passing through the coil will slow it down a bit. But if there's enough hysteresis, we could filp the field and actually push the projectile.
The collapse of the field will generate a lot of current. Would it be possible to use this to help power the next stage? In a design that used precise timing rather than sensors, all the coils could be chained together and the natural oscillation of the LC circuit could be timed to drive the projectile.
How do eddy currents in the projectile effect the system?
Universal Motor Design
This would invert the design. The projectile would be an iron core wrapped in a copper coil with "brushes" at either end. The barrel would have a Halbach array as well as the power commutator.