Cosmological magnetic field seeds produced by the Weibel instabilities

The source of the cosmological magnetic field is still unknown because the widely invoked dynamo processes are only able to regenerate and amplify some initial magnetic field seeds. In the hot and highly ionized intergalactic matter such magnetic field seeds can easily be produced by the (electro-)magnetic instabilities of Weibel type. Here we discuss suplementary mechanisms that can make these Weibel created fields to evolve at large scales presently observed in galaxies and clusters and can also enhance these magnetic field seeds after the dissipation.