3D modelling of pulsar wind nebulae

I will review the magnetohydrodynamic modelling of pulsar wind nebulae, highlighting recent advances with 3D global models of the Crab nebula. Earlier 2D MHD models were very successful in reproducing features of the inner Crab nebula such as the jet, concentric wisps and variable knots. However, these models are limited to a purely toroidal field geometry which leads to a strong polar jet accompanied by an exaggerated axial compression of the termination shock – in contrast to the observations. In three dimensions, the toroidal field structure is susceptible to current driven instabilities which imprints on the dynamics of the nebula. In agreement to the observations, the pulsar wind termination shock is more inflated than 1D or 2D models suggest, even for magnetisations around unity. Strong turbulence in the nebula leads to an efficient (diffusive) energy independent transport of relativistic particles which has to be taken into account in spectral modelling of pulsar wind nebulae.