Beam-Generated Collisionless Ion-Acoustic Shocks

Abstract

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 $u_{\mathrm{bm}}$ , above which shock is not generated. $u_{\mathrm{bm}}$ 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 $u_{\mathrm{ts}}$ . For beam velocities ranging from zero to $u_{\mathrm{ts}}$ a shock is observed followed by a region of fully developed two‐stream instability. For beam velocities between $u_{\mathrm{ts}}$ and $u_{\mathrm{bm}}$ , 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.