Muzzleflash Particle Problem

I made a muzzleflash with the firecloud particle. But since IRL muzzle flashes are cones, not balls, I made a system like this:
Particles get smaller over lifetime, and go forward really fast.
So it makes a really cool cone effect. but when the gun recoils back and forth, it spawns particles inside the gun. Is there a way to parent particles to their emitter?

Yes. Set the Simulation Space option to Local in the main ParticleSystem overview.