Solution to the Sigma-Problem of Pulsar Wind Nebulae

We present first results of three dimensional relativistic magnetohydrodynamical simulations of Pulsar Wind Nebulae. They show that the kink instability and magnetic dissipation inside these nebulae may be the key processes allowing to reconcile their observations with the theory of pulsar winds. In particular, the size of the termination shock, obtained in the simulations, agrees very well with the observations even for Poynting-dominated pulsar winds. Due to magnetic dissipation the total pressure in the simulated nebulae is particle-dominated and more or less uniform. While in the main body of the simulated nebulae the magnetic field becomes rather randomized, close to the termination shock, it is dominated by the regular toroidal field freshly injected by the pulsar wind. This field is responsible for driving polar outflows and may explain the high polarization observed in pulsar wind nebulae.