  We explore the role of complex multipolar magnetic fields in determining
physical processes near the surface of rotation powered pulsars. We model the
actual magnetic field as the sum of global dipolar and star-centered multipolar
fields. In configurations involving axially symmetric and uniform multipolar
fields, 'neutral points' and 'neutral lines' exist close to the stellar
surface. Also, the curvature radii of magnetic field lines near the stellar
surface can never be smaller than the stellar radius, even for very high order
multipoles. Consequently, such configurations are unable to provide an
efficient pair creation process above pulsar polar caps, necessary for plasma
mechanisms of generation of pulsar radiation. In configurations involving
axially symmetric and non-uniform multipoles, the periphery of the pulsar polar
cap becomes fragmented into symmetrically distributed narrow sub-regions where
curvature radii of complex magnetic field lines are less than the radius of the
star. The pair production process is only possible just above these
'favourable' sub-regions. As a result, the pair plasma flow is confined within
narrow filaments regularly distributed around the margin of the open magnetic
flux tube. Such a magnetic topology allows us to model the system of twenty
isolated sub-beams observed in PSR B0943+10 by Deshpande & Rankin (1999, 2001).
We suggest a physical mechanism for the generation of pulsar radio emission in
the ensemble of finite sub-beams, based on specific instabilities. We propose
an explanation for the subpulse drift phenomenon observed in some long-period
pulsars.
