Simple atom trap in a conical hollow mirror: Numerical analysis

We analyze the trap dynamic in a conical hollow (axicon) mirror system. Atom's trajectory is ring shaped if we move the coil (magnetic field) axis off the mirror axis and if we overlap these two axes trap cloud is ball shaped and it is consistent with experiment. We also make a simple comparison between 6-beam MOT and axicon MOT in the ball shaped case, and it shows that at low velocity limit the axicon MOT and typical 6-beam MOT have nearly same trap properties. The axicon trap may be useful as precooled atom source for many other atomic physics experiments such as cold atomic beam, atom funnel, and atom waveguide.