The dependence of the parallel and perpendicular mean free paths on the rigidity of the solar energetic particles: Theoretical model versus observations

Context. The dependence of the parallel and perpendicular mean free paths on the particle rigidity is an important topic in the studies of the diffusion and propagation of charged energetic particles in a large-scale turbulent magnetic field. Aims. In this work, we investigate the dependence of the parallel and perpendicular mean free paths on the rigidity of solar energetic particles (SEPs) by means of both the theoretical model and spacecraft observations with regard to several typical SEP events. Methods. A direct method developed by previous studies and derived from the focused transport equation and Taylor-Green-Kubo (TGK) formulation is applied to explicitly determine the parallel and perpendicular mean free paths of SEPs in a turbulent and spatially varying magnetic field. Results. We find that the parallel and perpendicular mean free paths, λ∥ and λ⊥, of energetic protons monotonically decrease with increasing particle rigidity, and the ratio λ⊥/λ∥ monotonically increases with particle rigidity, when the magnetic turbulence is weak. Taking a series of typical SEP events together, it can also be seen that the ratio λ⊥/λ∥ of the perpendicular to the parallel mean free paths remains in the range of 0.001−0.2