  Solar energetic particles (SEPs) have been observed to easily spread across
heliographic longitudes, and the mechanisms responsible for this behaviour
remain unclear. We use full-orbit simulations of a 10 MeV proton beam in a
turbulent magnetic field to study to what extent the spread across the mean
field can be described as diffusion early in a particle event. We compare the
full-orbit code results to solutions of a Fokker-Planck equation including
spatial and pitch angle diffusion, and of one including also propagation of the
particles along random-walking magnetic field lines. We find that propagation
of the particles along meandering field lines is the key process determining
their cross-field spread at 1 AU at the beginning of the simulated event. The
mean square displacement of the particles an hour after injection is an order
of magnitude larger than that given by the diffusion model, indicating that
models employing spatial cross-field diffusion cannot be used to describe early
evolution of an SEP event. On the other hand, the diffusion of the particles
from their initial field lines is negligible during the first 5 hours, which is
consistent with the observations of SEP intensity dropouts. We conclude that
modelling SEP events must take into account the particle propagation along
meandering field lines for the first 20 hours of the event.
