Pulsar Mechanics

pulsars are non-aligned rotating magnets

induced electric fields (producing by time varying magnetic fields: Faraday's law)
produce electric forces strong enough
to rip electrons off the neutron star surface

surrounding the neutron star is a conducting plasma (magnetosphere)
dominated by electromagnetic forces (not gravitational)

inside the light cylinder (co-rotation radius ~ c P/2π),
the plasma is frozen into the magnetic field lines...
the whole mess rotates as a solid body

inside light cylinder, B lines are closed,
and therefore electrons (or positrons) spiral around the
magnetic field lines back and forth from pole to pole

these electrons, accelerated by induced emf,
produce the relativistic synchrotron radiation
that seems to fill the interior of the supernova remnant...
these relativistic electrons can emit γ rays energetic enough
to pair produce ( γ + γ -->  e ^- + e⁺ ) more charged particle pairs
    that are accelerated etc etc

but outside the light cylinder, the B lines must be open-ended,
leaking out into space:
particles spiral along the lines that are densest near
(and parallel to) the magnetic poles;
 

these synchrotron-emitting electrons strongly beam
their radiation along the poles
producing the pulsar's lighthouse effect