Via evaluation of the Lyapunov exponent, we report the discovery of three prominent sets of phase space regimes of quasi-periodic orbits of charged particles trapped in a dipole magnetic field. Besides the low energy regime that has been studied extensively and covers more than ∼ 10% in each dimension of the phase space of trapped orbits, there are two sets of high energy regimes, the largest of which covers more than ∼ 4% in each dimension of the phase space of trapped orbits. Particles in these high energy orbits may be observed in space and be realized in plasma experiments on the Earth.