Ion-beam/plasma modes in ultradense relativistic quantum plasmas: Dispersion characteristics and beam-driven instability

A relativistic quantum-hydrodynamic plasma model is proposed, to model the propagation ofelectrostatic waves in an ultradense quantum electron-ion plasma in the presence of an ion beam. Adispersion relation is derived for harmonic waves, and the stability of electrostatic wavepackets isinvestigated. Three types of waves are shown to exist, representing a modified electron plasma(Langmuir-type) mode, a low-frequency ion acoustic mode, and an ion-beam driven mode, respectively.Stability analysis reveals the occurrence of an imaginary frequency part in three regions.The dependence of the instability growth rate on the ion beam parameters (concentration andspeed) has been investigated.