Two Stream Instability in an Inhomogeneous Magnetized Plasma

A plasma can support several kinds of electrostatic and electromagnetic waves depending upon what the external perturbations are and how the plasma is generated or under what conditions the waves are excited. In the presence of magnetic field, more new kinds of the waves can evolve in the plasma. Moreover, if the free energy is available in the system, then these waves can grow at the cost of this free energy and hence instabilities can take place. In the present investigation, we make an analytical study of a two stream instability in an inhomogeneous magnetized plasma having drifting ions and electrons. We consider a general situation by taking an oblique propagation of the wave from the magnetic field and a constant ionization. Using normal mode analysis, we derive dispersion relation which is solved numerically for the growth rate of the instability. The behavior of growth rate with magnetic field and the propagation angle along with ionization constant has been studied for two different wavelengths of the oscillations. We observe two type of the instabilities out of which one grows at a faster rate and hence is named as fast growing instability. The growth rate of the other slowly growing instability is also examined. We find that the growth rates of both the instabilities attain higher magnitudes at smaller wavelength of the oscillations.