Theoretical work aimed at understanding the electrodynamic structure of pulsar magnetospheres and winds has received new impetus from detailed imaging in the optical and x-ray wavelength bands of these objects, and especially of the Crab Nebula. This has motivated two-dimensional relativistic MHD models that have confirmed the low magnetization state of the nebular plasma. The fundamental problems this raises concerning the dissipation of energy and particle acceleration in relativistic plasmas are summarized. It is indicated how recent progress in teraelectronvolt gamma-ray astronomy may help resolve these issues by placing constraints on the sites of dissipation and acceleration in the binary system containing the pulsar PSR B1259 −63.
Numerical solution of the linear dispersion relation in a relativistic pair plasma