Bubbling balls of leptons: review on MHD simulations of PWNe
PWN make up the majority of the identified galactic TeV sources and are a key ingredient to understand the high energy sky. In this contribution, I will review recent progress in magnetohydrodynamic and particle transport modeling of PWN, highlighting advances with fully three-dimensional global models. It is now clear that the MHD kink- and Kelvin Helmholtz-type instabilities lead to turbulent flows in the nebula with direct impact on dynamics and morphology. Close to the termination shock, the telltale jet and torus structure is still well recovered by the simulations, with varying strengths of the two features depending on the pulsar obliqueness. Emergence of current sheets and magnetic dissipation govern the turbulent nebula proper. The high velocity fluctuations give rise to efficient eddy-diffusive transport of particles, indicating that both advection and diffusion play an important role in particle transport. TeV emission due to inverse Compton upscattering from the nebula leptons has so far only been incorporated in 2D simulations. I will comment on the status of high energy modeling and conclude with a discussion of solved and unsolved problems posed by PWNe.