Acceleration mechanism in compact objects

We investigate the kinetic theory of a mixing of rela-tivistic pair plasma in a conventional electron-proton plasma and an intense anisotropic Compton radiation field as those found in the vicinity of a compact object, a neutron star or a black hole. In a two-flow configuration we discriminate two regimes: the first one is realized when the mass energy density of the pair plasma is lower than the ambient (electron-proton) plasma one, whereas the second one is characterized by a more massive relativistic pair plasma. The first stage, called " non rela-tivistic regime " , is entirely treated within the scheme of weak turbulence theory, and leads us to calculate the bulk Lorentz factor, the internal energy and the distribution function of the relativistic particles distribution function. We propose a new scenario to get a power law distribution. For the second stage, called the " relativistic regime " , we mostly calculated an unusual instability triggered by the ambient protons that amplifies the left circularly polarized Alfvén wave of the pair plasma at synchrotron resonance. This instability plays an important role to couple the beam with the ambient plasma, and governs energy and momentum exchanges. The kinetic theory is applied to different astrophysical sources such as Blazar and galactic " micro-Quasar " jets. We calculate the internal Lorentz factor and find it of order of 10 4 for extragalactic black holes, and 10 2 for galactic black holes. The resulting bulk Lorentz factor derived in term of the compact-ness of the soft photon source is of order of 10 for extragalactic sources of order of 5 for galactic sources.