“…In particular, periodic orbits in the equatorial plane have been explored extensively 7 , and there are also a few branches of periodic orbits in the Meridian plane at relatively high energies with distinct orbital shapes [3][4][5] . At low energies, due to the presence of approximate adiabatic invariant, the problem can be further simplified 13,14 , and the results, the so-called guiding center approximation, have been applied to studies of pulsars, radiation belts, and dynamics of particles in magnetic confinement devices 12,15,16 .…”