Radial dependence of proton peak intensities and fluences in SEP events: Influence of the energetic particle transport parameters

We study the radial dependence of peak intensities and fluences of solar energetic particle (SEP) events in the framework of the focused transport theory. We solve the focused-diffusion transport equation that includes the effects of solar wind convection, adiabatic deceleration and pitch-angle scattering. We assume a Reid-Axford time profile for the particle injection at the base of a flux tube described by an Archimedean spiral magnetic field whose cross section A(r) expands as r2 cos(ψ), where r is the radial distance and ψ(r) is the angle between the magnetic field line and the radial direction. We assume that energetic particles propagate along the field line. We locate several observers along the flux tube at radial distances ranging from 0.3 to 1.6 AU. Both peak intensities and event fluences decrease with increasing radial distance. We deduce functional forms to extrapolate peak fluxes and fluences with radial distance that depend on the energy of the particles, the pitch-angle scattering conditions, and the duration of the particle injection. The smaller the mean free path of the particles, the larger the decrease of both peak intensities and fluences with radial distance. The smaller the energy of the particles, the larger the decrease of both peak intensities and fluences with radial distance. Extended particle injections contribute to soften the decrease of the peak intensities with the radial distance but have no influence on the event fluence. We note that mobile particle sources (i.e. traveling interplanetary shocks) may vary the radial dependences deduced in this work.