  Understanding the transport of Solar Energetic Particles (SEPs) from
acceleration sites at the Sun into interplanetary space and to the Earth is an
important question for forecasting space weather. The Interplanetary Magnetic
Field (IMF), with two distinct polarities and a complex structure, governs
energetic particle transport and drifts.
  We analyse for the first time the effect of a wavy Heliospheric Current Sheet
(HCS) on the propagation of SEPs. We inject protons close to the Sun and
propagate them by integrating fully 3D trajectories within the inner
heliosphere in the presence of weak scattering. We model the HCS position using
fits based on neutral lines of magnetic field source surface maps (SSMs).
  We map 1 au proton crossings, which show efficient transport in longitude via
HCS, depending on the location of the injection region with respect to the HCS.
For HCS tilt angles around $30^\circ-40^\circ$, we find significant qualitative
differences between A+ and A$-$ configurations of the IMF, with stronger
fluences along the HCS in the former case but with a distribution of particles
across a wider range of longitudes and latitudes in the latter.
  We show how a wavy current sheet leads to longitudinally periodic
enhancements in particle fluence. We show that for an A+ IMF configuration, a
wavy HCS allows for more proton deceleration than a flat HCS. We find that A$-$
IMF configurations result in larger average fluences than A+ IMF
configurations, due to a radial drift component at the current sheet.
