Pulsar Wind Nebulae as Cosmic Pevatrons: A Current Sheet's Tale

I outline, from a theoretical and somewhat personal perspective, significant features of Pulsar Wind Nebulae as Cosmic Accelerators. I discuss recent studies of Pulsar Wind Nebulae (PWNe). I pay special attention to the recently discovered gamma ray flares in the Crab Nebula's emission, focusing on the possibility, raised by the observations, that the accelerating electric field exceeds the magnetic field, suggesting that reconnection in the persistent current layer (a current sheet) plays a significant role in the behavior of this well studied Pevatron. I address the present status of the termination shock model for the particle accelerator that converts the wind flow energy to the observed non thermal particle spectra, concluding that it has a number of major difficulties related to the transverse magnetic geometry of the shock wave. I discuss recent work on the inferred pair outflow rates, which are in excess of those predicted by existing theories of pair creation, and use those results to point out that the consequent mass loading of the wind reduces the wind's bulk flow 4-velocity to the point that dissipation of the magnetic field in a pulsar's wind upstream of the termination shock is restored to life as a viable model for the solution of the "sigma problem". I discuss some suggestions that current starvation in the current flow supporting the structured ("striped") upstream magnetic field induces a transition to superluminal wave propagation. I show that current starvation probably does not occur, because those currents are carried in the current sheet separating there stripes rather than in the stripes themselves.