Beam-Generated Collisionless Ion-Acoustic Shocks

A numerical study of a one-dimensional collisionless ion-acoustic shock generated by an injection of a plasma beam is presented. The electrons are assumed to be hot and isothermal, and obey the Boltzmann distribution; the ions are described by the Vlasov equation which is solved by a direct finite difference scheme. There is a threshold beam velocity ubm, above which shock is not generated. ubm is a function of the beam-background density ratio and the electron-ion temperature ratio, and is larger than the limit of the ion-ion two-stream instability uts. For beam velocities ranging from zero to uts a shock is observed followed by a region of fully developed two-stream instability. For beam velocities between uts and ubm, a shock and a phase-space vortex are formed and in between them a quiescent region grows. A stable two-stream remains behind the vortex.