  Rough estimates and upper limits on current and particle densities form the
basis of most of the canonical pulsar models. Whereas the surface of the
rotating neutron star is capable of supplying sufficient charges to provide a
current that, given the polar cap potential, could easily fuel the observed
energy loss processes, observational and theoretical constraints provide strict
upper limits to the charge densities. The space charge of a current consisting
solely of particles having only one sign creates a compensating potential that
will make the maximum current dependent on potential and distance. In the
non-relativistic case this fact is expressed in the familiar Child-Langmuir
law. Its relativistic generalization and subsequent application to the inner
pulsar magnetosphere provides clear limits on the strength and radial extension
of charged currents originating on the polar cap. Violent Pierce-type
oscillations set in, if one attempts to inject more current than the space
charge limit into a given volume. These considerations apply wherever there is
a significant amount of charged current flow, in particular in the gap regions.
There they can be used to derive limits on the size of such gaps and their
stability.
