Modelling Solar Energetic Particle event onsets in the turbulent heliosphere

Solar Energetic Particles (SEPs), accelerated during solar eruptions, are observed using instruments onboard spacecraft in interplanetary space, at a large distance from their source. As SEPs propagate in the solar wind, they are guided by the interplanetary magnetic field (IMF), which consists of a large-scale Parker spiral magnetic field superposed by turbulent fluctuations. The turbulence causes the SEPs to scatter along the magnetic field lines, resulting in some cases in delayed arrival of SEPs to spacecraft in interplanetary space. It also gives rise to meandering of field lines, which helps to spread SEPs across heliolongitudes, and eventually results in diffusive cross-field propagation of the particles. To investigate how turbulence affects SEP propagation and arrival to observing spacecraft in different locations in the heliosphere, we have developed a novel analytical model of the IMF, where the Parker spiral is superposed with Fourier modes that represent the turbulence. Unlike any previous models, our description reproduces the observed geometry for the main mode of turbulence, the so-called 2D mode, with both the magnetic field disturbance vector and the wavenumber vector normal to the background Parker spiral field. We use 3D test particle simulations to study the propagation of energetic protons in our new turbulent IMF description. Particles are injected close to the Sun and observables derived at different radial distances and heliolongitudes, representing the locations of near-Earth spacecraft as well as locations accessible to Solar Orbiter and Parker Solar Probe. We compare the SEP onset times obtained from our simulations to those obtained with a 1D focused transport model. We find that the turbulence prolongs the field lines, and thus when particle are simulated in our new IMF model, the SEP intensity onsets are delayed compared to those obtained by using a 1D focused transport model. Further, we find that onset delay depends on the longitudinal separation of the SEP source and the heliolongitude of the location where the observables are derived. We discuss the implications of our findings on current understanding of the sources and transport of SEPs.