  Modeling of time profiles of solar energetic particle (SEP) observations
often considers transport along a large-scale magnetic field with a fixed path
length from the source to the observer. Here we point out that variability in
the turbulent field line path length can affect the fits to SEP data and the
inferred mean free path and injection profile. To explore such variability, we
perform Monte Carlo simulations in representations of homogeneous 2D MHD + slab
turbulence adapted to spherical geometry and trace trajectories of field lines
and full particle orbits, considering proton injection from a narrow or wide
angular region near the Sun, corresponding to an impulsive or gradual solar
event, respectively. We analyze our simulation results in terms of field line
and particle path length statistics for $1^\circ\times 1^\circ$ pixels in
heliolatitude and heliolongitude at 0.35 and 1 AU from the Sun, for different
values of the turbulence amplitude $b/B_0$ and turbulence geometry as expressed
by the slab fraction $f_s$. Maps of the most probable path lengths of field
lines and particles at each pixel exhibit systematic patterns that reflect the
fluctuation amplitudes experienced by the field lines, which in turn relate to
the local topology of 2D turbulence. We describe the effects of such path
length variations on SEP time profiles, both in terms of path length
variability at specific locations and motion of the observer with respect to
turbulence topology during the course of the observations.
