Synchrotron radiation and Faraday rotation measurements indicate the existence of regular and turbulent magnetic fields of the order of few micro-gauss in galaxies, and clusters and superclusters of galaxies, with correlation lengths ranging between ~ 1 kpc (for galaxies) and < 1 Mpc (for superclusters). In starburst galaxies the magnetic field intensity can be as large as 100 micro-gauss, and in the intergalactic medium (IGM), though poorly determined, the estimates which are partially constrained by the CMBR and the primordial nucleosynthesis, indicate magnetic fields B ~ nano-gauss in scales of 1 Mpc. Our proposal is to examine pos-recombination astrophysical mechanisms to explain the origin and amplification of the observed large scale magnetic fields embedded in the intra-cluster and IGM media. Assuming the existence of pre-existing seed fields generated, for instance, by the Harrison or the Biermann Battery effects in the proto-galactic clouds or even earlier during the re-ionization, we intend to investigate how such magnetic fields can be amplified and made coherent through magnetohydrodynamical (MHD) turbulence evolution in the IGM and the intra-cluster medium. The injection of small scale fields which are produced within SB and active radio galaxies into the ICM and IGM and their progressive aggregation into larger scale turbulent fields, as required by the observations, will be also investigated, both with the help of numerical codes constructed for the exam of the formation and evolution of MHD turbulence in the IGM and ICM.
We are going to present preliminary results of 3-D numerical simulations performed in a periodic box of the evolution of the magnetic field by MHD turbulence.