How does a pulsar wind turn magnetic energy into fast particles?
In plain words
Close to the pulsar the outflowing wind carries its energy almost entirely as magnetic field, yet nebulae such as the Crab require that most of it be in fast particles by the time the wind reaches them.
Precise statement
The magnetization $\sigma$ (Poynting flux over particle energy flux) of a pulsar wind is $\sim 1e4$ or more near the light cylinder, while one-dimensional models of the Crab nebula require $\sigma \sim 1e-3$ at the termination shock ($r \sim 3e17\,\mathrm{cm}$), and ideal MHD acceleration of a radial wind is inefficient. Determine where and how the magnetic energy dissipates: reconnection in the striped-wind current sheet, at the termination shock, or inside the nebula through kink instabilities. Answer: the dissipation site and fraction consistent with nebular spectra, morphology and gamma-ray flares.
What would settle it
Kinetic and 3D MHD models of the wind and nebula that reproduce the Crab spectrum, jet-torus morphology and flare statistics with a stated $\sigma$ profile.
Status in the literature
3D MHD simulations since about 2014 reproduce Crab nebula morphology with $\sigma$ of order 1 at the shock, easing but not removing the problem.