Regular and chaotic motion of anti-protons through a nested Penning trap with multipole magnetic fields

The next generation of experiments for making cold anti-hydrogen will attempt to trap them using multipole magnetic fields. We investigate the motion of the anti-protons through the combined electric and magnetic fields of this type of trap. The multipole fields that will prevent the anti-hydrogen from hitting the walls cause the anti-protons to have regions of regular motion and regions of chaotic motion. We find that hexapole fields give motion that would greatly suppress the formation of cold anti-hydrogen; for realistic conditions, less than ∼1/10 could lead to cold anti-hydrogen. For octupole fields, we found that ∼1/4 of the anti-protons could lead to cold anti-hydrogen formation at short times. We discuss the implications of these regions for anti-hydrogen experiments.