Perhaps more importantly, there's the messy consequence that those external fields only work on charged particles. You could (in principle) keep positrons and

Perhaps more importantly, there's the messy consequence that those external fields only work on charged particles. You could (in principle) keep positrons and antiprotons together in a very hot plasma under magnetic confinement, but every pair that binds together into a neutral hydrogen atom can immediately escape and annihilate - turning carefully-stored fuel into gamma rays...