Solar energetic particles intensity variations associated with a tilted-dipole 3D corotating interaction region

The effect of a tilted-dipole three-dimensional corotating interaction region (CIR) on the transport and acceleration of solar energetic particles (SEPs) is studied. In this work, we discussed how the particle intensity longitudinal and radial dependence might be influenced by the background structures. Moreover, we investigate how the spectral index distribution is modulated by the CIR structure. We use the focused transport equation (FTE) to describe the propagation and acceleration of SEPs in a tilt-dipole 3D CIR, generated by the high-resolution 3D magnetohydrodynamic (MHD) model. The forward stochastic differential method is used to solve the FTE. The protons with the E^-4.4 spectrum from 0.5 to 15 MeV are injected uniformly at the heliographic equator of 0.15 AU. Physical quantities are extracted along each interplanetary magnetic field (IMF) line to show the results. In the tilted-dipole CIR background, if injected from the solar equator at the inner boundary, particles in the slow flow are transported to higher latitudes due to the extension of the IMF lines to higher latitudes. The longitudinal patterns of the particles are dominated by the density of IMF lines. The focusing effect modulates the longitudinal variation of the particle intensity and gives rise to new longitudinal intensity peaks. The adiabatic effect largely increases the intensity fluctuation along the longitude. The structure of the solar wind can also lead to the difference of the index \alpha in the empirical function I_\mathrmmax=kR^-\alpha , describing the radial variation of peak intensity according to our simulation. Under the influence of the CIR structure, the index \alpha varies from 1.9 to 3.4 at 0.3−1.0 AU. The variation of the solar wind speed should be considered when estimating the radial dependence of the SEP peak intensity. The spectra indices rise near the CIR boundaries and drop near the stream interface (SI). The adiabatic effect makes the spatial variability of the spectral index larger. The spectral index could be similar at different radial distances in the CIR structure.