## 9. Discussion and conclusionIn this paper, we derived the main basic plasma physics rules that govern the interaction of the relativistic pair beam with an MHD plasma. We applied this theory to understand the high energy Inverse Compton emission of both Quasars and micro-Quasars. We considered the Inverse Compton process in the Thomson regime. However, some modifications due to the angular dependence of the Klein-Nishina limit could be relevant in the case of micro-Quasars. The main difference with the previous works is that the pair beam has a highly relativistic internal energy. The kinetic theory is necessary to analyze the effect of the anisotropic radiation field that prevails between and where the Compton rocket effect do work, as discussed in Sect. 8. Particle acceleration can be maintained by the turbulence supplied by the MHD jet (like in Henri & Pelletier 1991), but also by the radiation field itself which was the main topic of this paper. The interaction between the relativistic beam and the jet undergoes two stages. In the first stage (the non relativistic regime), the beam pervades a more massive ambient medium and the interaction is described by the standard weak turbulence theory: quasi linear growth of both Alfvén and Langmuir waves of the cold electron-proton plasma, non-linear mode couplings, and a resolution of a Fokker-Planck equation describing the pair heating processes. The entire acceleration mechanism is self-consistent: The pairs are accelerated by Langmuir turbulence at low energy and Alfvén turbulence at higher energy in the inner part of a cone of half opening angle of where the IC cooling process is less efficient than outside. Although, the Langmuir turbulence is not sufficient to accelerate the particles at the higher energies, it is nevertheless unavoidable and necessary to inject electrons and positrons above the threshold for interaction with Alfvén waves. The high energy pairs are injected in the outer part of the cone, where the pair distribution function tends to be isotropized by Alfvén turbulence. In this angular zone the pairs are submitted to strong IC cooling leading to the formation of a power-law energy distribution with an index of 2. The cooled pairs are then re-injected in the cone by pitch-angle scattering on Langmuir waves. We derived analytically the solution with consistent approximation. However, a Fokker-Planck numerical code would be useful to improve the solution especially to take into account the pair creation. The second stage is rather unusual; this is the relativistic regime where the beam is heavier than the ambient medium. In this case the longitudinal waves are not destabilized, and only the Alfvén waves are amplified at synchrotron resonance by the ambient protons. We did a detailed investigation of this instability and gave some suggestions of its possible non-linear development. The detailed theory of this non-linear evolution is postponed for a future work. Anyway the interesting saturation effect derived from the linear theory has simple and straightforward implications for astrophysical objects such as extragalactic Quasar and galactic "micro-Quasar". © European Southern Observatory (ESO) 1997 Online publication: June 5, 1998 |