Isolating concentric coils
You can't eat that cake then suddenly discover it's still there. The two coils couple magnetically so any ac signal on one will be transferred to the other albeit in a smaller amount depending on turns ratio, coupling factor and loading.

If you want to isolate them then move them apart or set up a high frequency field and run one coil like a metal detector - because it will be tuned it will largely ignore the impulse to drive the projectile and only modulate the RF field as the projectile moves. Far more complex but do-able if you know how.