Electrostatic two-stream instability in Fermi-Dirac plasmas

In this paper the electrostatic two-stream instability is investigated for a large range of plasma number-density using the quantum hydrodynamic model by incorporating the relativistic degeneracy, electron-exchange, quantum diffraction and strong parallel quantizing magnetic field effects. It is found that the electron diffraction effect significantly alters the instability growth rate in a wide range of plasma number density. Two cases of classical and quantum Landau quantization limits are compared and the parametric instability condition is closely inspected. It is remarked that for a given streaming speed the instability is bounded by an upper plasma number-density limit. It is also shown that for a given stream speed there is a maximal growth rate corresponding to specific plasma number-density and perturbation wavelength. Current study can help in better understanding of electron-beam plasma interactions and energy exchange for a wide area of number densities ranging from solid density, inertial confined plasmas, big planetary cores and compact stars. It may also be useful in understanding of electrostatic beam-plasma interactions and origin of large magnitude sustainable electrical currents in super-intense plasmas with critically high magnetic fields such as, pulsars, white dwarf interiors and neutron star crusts.