Propagation modes for a dusty plasma ionization instability under electron beam injection

The low frequency electrostatic linear modes of a dusty plasma penetrated by an energized electron beam are investigated in the frame of a one-dimensional multifluid equations. This plasma contains with thermal and non-thermal electrons, ions and charged dust grains. The stable and unstable modes of the ionization instability are examined in relation to the injected electron beam current density. We pay special attention to the relation of the unstable modes and the injected electron current and ionization cross-section dependence with beam energy, which are proved to be the critical parameters for triggering the instability. This latter could be monitored in the laboratory experiments.