Drift Instabilities in a Maxwellian Plasma

TLDR

The graphical technique transparently displays the dispersion relation. The study investigates the stability of two drifting Maxwellian plasma components using a graphical dispersion relation solution. A graphical dispersion relation solution maps instability versus wavelength and drift, revealing dependence on Debye length and plasma frequency ratios. For electron‑proton plasmas, the maximum growth rate and critical drift velocity vary with wavelength and temperature ratios, and the unstable region is delineated by constant‑growth‑rate lines.

Abstract

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.