  Strong-Field Electrodynamics (SFE) is Maxwell theory with a certain
Lorentz-covariant Ohm's law which uses only the electromagnetic degrees of
freedom. We show that SFE is {\it semi-dissipative}: while the dissipation rate
of the electromagnetic energy is non-negative, it can be exactly zero for
non-trivial electromagnetic fields.
  It appears that SFE is well-defined for arbitrary electromagnetic fields. It
should be possible to calculate the dissipative pulsar magnetosphere and
resolve the magnetic separatrix using SFE.
  We show that SFE reduces to Force-Free Electrodynamics (FFE) in the large
conductivity limit. In the regions where the ideal FFE 4-current is space-like,
SFE predicts small dissipative corrections. In the regions where the ideal FFE
4-current is time-like, SFE predicts a zero correction. This indicates that
bright pulsars radiate primarily from the magnetic separatrix.
