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A functional form I_{max}(R)=kR^{-\alpha}, where R is the radial distance ofspacecraft, was usually used to model the radial dependence of peak intensitiesI_{max}(R) of solar energetic particles (SEPs). In this work, thefive-dimensional Fokker-Planck transport equation incorporating perpendiculardiffusion is numerically solved to investigate the radial dependence of SEPpeak intensities. We consider two different scenarios for the distribution ofspacecraft fleet: (1) along the radial direction line, (2) along the Parkermagnetic field line. We find that the index \alpha in the above expressionvaries in a wide range, primarily depending on the properties (e.g., location,coverage) of SEP sources and on the longitudinal/latitudinal separationsbetween the sources and the magnetic footpoints of the observers. Particularly,the situation that whether the magnetic footpoint of the observer is locatedinside or outside of the SEP source is a crucial factor determining the valuesof index \alpha. A two-phase phenomenon is found in the radial dependence ofpeak intensities. The "position" of the breakpoint (transition point/criticalpoint) is determined by the magnetic connection status of the observers. Thisfinding suggests that a very careful examination of magnetic connection betweenSEP source and each spacecraft should be taken in the observational studies. Weobtain a lower limit of R^{-1.7\pm0.1} for empirically modelling the radialdependence of SEP peak intensities. Our findings in this work can be used toexplain the majority of the previous multispacecraft survey results, andespecially to reconcile the different/conflicting empirical values of index\alpha in the literature.

Propagation of Solar Energetic Particles in Three-dimensional Interplanetary Magnetic Fields: Radial Dependence of Peak Intensities