Nonlinear Dynamics in the Relativistic Plasma of Astrophysical High-Energy Sources

Relativistic plasmas are interesting media for particle acceleration, especially when their kinetic pressure is in rough equipartition with the magnetic pressure. Indeed, when in rough equipartition, these relativistic plasmas have generalized Alfvén waves that propagate at velocities close to the velocity of light, which makes the acceleration process more efficient than usual. With this in mind, we have investigated some properties that are of interest to several issues in high-energy astrophysics, such as the source of high-energy cosmic rays, the origin of the high-energy emission of blazars and microquasars, the synchrotron radiation of jets, and the gamma-ray bursts of cosmic fireballs. Three types of relativistic plasmas are considered: plasma dominated by the relativistic proton component (high-energy cosmic rays), plasma dominated by highly relativistic electrons (the protons being nonrelativistic), and plasma dominated by relativistic electron-positron pairs. Electron or pair-dominated plasmas are interesting on the one hand because of their fast dynamics, and on other hand because the energy of magnetic perturbations goes directly into the radiative particles. The energy transfer from the electromagnetic perturbations to the particles depends on the nonlinear dynamics. We derive the nonlinear systems that govern the dynamics of these relativistic plasmas close to equipartition. We discuss the possibility of self-modulation instability and soliton formation and demonstrate the existence of a transition at equipartition that has remarkable mathematical properties. We show that particle acceleration in a pair plasma is efficient only when the plasma pressure is below the equipartition value. We give intuitive arguments that this would also be true for the other plasmas, but we do not yet have firm proof. Thus, a pair plasma has a regulation mechanism toward equipartition, since radiation cooling is not efficiently balanced above equipartition. This is an interesting issue for nonthermal radio sources. We have also devised a new kind of collisionless quasi-parallel relativistic shock when a relativistic pair cloud pervades an ambient medium. The proton backstream in the relativistic front drives a monochromatic wave responsible for strong nonlinearities that heat the relativistic plasma. The instability is quenched when the relativistic plasma has been sufficiently heated.