  The detection of almost 100% linearly polarized emission from the fast radio
burst source FRB 121102 implies coherent emission of relativistic electrons
moving in perpendicular to the ambient magnetic field. The origin of such a
particle distribution is very intriguing. Given that FRB 121102 is likely
driven by a neutron star, we explored orbits of charged particles trapped in a
dipole magnetic field (the St\"ormer problem). Most previous studies focused on
particles with relatively low energies so that the guiding center approximation
may be applied. High energy particles usually have chaotic orbits except those
on a periodic orbit or near stable periodic orbits. Via evaluation of the
maximum Lyapunov exponent of orbits of particles launched from the equatorial
plane with an axial velocity (the angular velocity sets the length and energy
scales of the system), we found prominent regions of quasi-periodic orbits
around stable periodic orbits in the equatorial plane at high-energies.
Particles in these orbits oscillate around the equatorial plane and their
radial distance from the dipole can vary by a factor of/,2. Relativistic
electrons in such orbits may be responsible for the almost 100% polarized
emission from FRB 121102.
