Theory of relativistic phase-space holes in a hot-electron-positron-ion plasma

A theoretical and numerical study of phase-space holes in a relativistically hot-electron-positron-ion plasma is presented, and their potential and density profiles are calculated numerically for different sets of parameters. The phase-space holes are Bernstein-Greene-Kruskal modes in which particles are trapped in the self-consistent electrostatic potential. Relativistic effects increase the size of the phase-space hole and the amplitude of the associated electrostatic potential. In a pure electron-positron plasma, the phase-space holes must have a minimum speed close to the particle thermal speed. The presence of positively charged ions makes the holes smaller, and stabilizes the holes so that they can propagate with smaller speeds. A numerical Vlasov simulation demonstrates the stability of the holes and that they tend to interact and merge to form new holes