Drift Instabilities in a Maxwellian Plasma

The stability of two Maxwellian components of a plasma, which have different drift velocities, is investigated by means of a graphical solution of the dispersion relation. The graphical technique has the advantage of exhibiting the content of the dispersion relation in a transparent manner. By this method we determine the region of instability as a function of the perturbation wavelength λ and the relative velocity of the components, and show how this region depends on the ratio of the Debye lengths and plasma frequencies. In the case of an electron-proton plasma we obtain the maximum growth rate as a function of λ and the critical drift velocity as a function of the temperature ratios. The structure of the unstable region is also indicated by a few lines of constant growth rate.