Instability of electrostatic modes in partially ionized plasma

A physical background is presented and an analytical description is given for electrostatic modes in partially ionized magnetized plasmas. The presence of neutrals is responsible for the creation of ions due to photo and electron impact ionization. These effects are balanced by a certain number of phenomena in which ions and electrons are lost, like radiative and three-body recombination. Dispersion equations are derived for the drift and the ion-cyclotron modes, with the appropriate instability conditions, indicating that inelastic collisions can make the modes unstable.