Theoretical and numerical studies of relativistic ion and electron holes in plasmas

Analytical and numerical studies of the dynamics of relativistic electron and ion holes in a collisionless plasma are presented. Ion and electron holes are localized Bernstein-Greene-Kruskal modes characterized by particle populations trapped in the self-consistent electrostatic potential associated with the holes. Electromagnetic radiation can be trapped in relativistic electron holes due to a combination of the density fluctuations and the relativistic mass increase of the electrons, which changes locally the dielectric properties of the plasma and leads to a localization of the electromagnetic wave envelopes. Relativistic ion holes may be formed in active galactic nuclei, supernova remnant shocks, pulsar winds, and gamma-ray burst jets where relativistic plasma streams are thought to exist. The relativistic ion holes may be responsible for the acceleration of particles to GeV energies. The analytic solutions for relativistic electron and ion holes are employed as initial conditions for numerical simulations in which the dynamics and stability of the phase-space holes are investigated. The results have relevance for intense laser-plasma experiments and for astrophysical plasmas.