Charged-particle motion in vacuum magnetic fields with 2 degrees of freedom has been investigated by numerically integrating the relativistic Lorentz force equation. The numerical simulation demonstrated that collisionless particle losses due to the nonexistence of a globally conserved quantity other than the energy and canonical angular momentum are gyrophase dependent, thus resulting in the existence of multiple particle confinement times. This is consistent with the cited experimental results and, in addition, demonstrates the indistinct nature of the mirror loss cone for ρ/LM < 2 × 10−2.