  Solar Energetic Particles (SEPs), a major component of space weather,
propagate through the interplanetary medium strongly guided by the
Interplanetary Magnetic Field (IMF). In this work, we analyse the implications
a flat Heliospheric Current Sheet (HCS) has on proton propagation from SEP
release sites to the Earth. We simulate proton propagation by integrating fully
3-D trajectories near an analytically defined flat current sheet, collecting
comprehensive statistics into histograms, fluence maps and virtual observer
time profiles within an energy range of 1--800 MeV. We show that protons
experience significant current sheet drift to distant longitudes, causing time
profiles to exhibit multiple components, which are a potential source of
confusing interpretation of observations. We find that variation of current
sheet thickness within a realistic parameter range has little effect on
particle propagation. We show that IMF configuration strongly affects
deceleration of protons. We show that in our model, the presence of a flat
equatorial HCS in the inner heliosphere limits the crossing of protons into the
opposite hemisphere.
