>>298667A coil maintains a magnetic field for a short time even after the power is turned off, it's called hysteresis or something(the current doesn't blank to 0 instantly, but diminishes over time). This magnetic field is decelerating any projectiles that you're accelerating trough your gun.
A quench gun fix this problem by reverting from a superconductive to a non-superconductive state, making the resistance skyrocket, this will cause a very rapid decrease in the magnetic field as a strong breaking force for the current is applied.
Compare it to your car, a normal coil with constant resistance equals you driving at 100mph, shutting of the engine and letting it roll to a stop. a quench equals you slamming the breakes til you stop.
The plasma quench would work by reverting the conductor gas from ionized state(plasma, which is quite a good conductor) to non ionized state(normal gas, which usually have very high resistance) to more or less instantly dissipate the magnetic field.