The Crab nebula and pulsar – particle acceleration at the limit

The Crab Nebula is the front-page object of multi-wavelength astrophysics and an excellent object to study non-thermal emission and particle acceleration. The Crab Pulsar powers the extreme accelerator regions that inject an ultra-relativistic plasma into the surrounding nebula. The exceptionally well-defined spectral energy distribution has been measured from the lowest accessible frequencies to the highest photon energies beyond 100 TeV. In this talk, I will provide an overview on the recent first-time measurements of spatial extension of the nebula from several GeV to TeV energies and the implications to the magnetic field strength and its spatial dependence in the Nebula. Besides the spatially resolved structure of the nebular emission, we have found episodes of dimming of the synchrotron emission, indicating that the highest energy electrons are confined to a compact region that we tentatively identify with the inner knot close to the pulsar’s position.