Drift Instabilities in a Uniformly Rotating Plasma Cylinder

Abstract

The dispersion relation for low‐frequency, collisional, electrostatic waves in a uniformly rotating plasma cylinder is obtained in terms of several positive‐definite bilinear forms whose magnitude may easily be estimated. The effects of ion transverse collisional viscosity, electron parallel resistivity, ion parallel motion, and an equilibrium radial electric field are included in the theory. The close correspondence between the present dispersion relation and the dispersion relation for localized, slab‐model modes justifies the use of the latter in the interpretation of $Q$ ‐machine experiments. Another result is that ion collisional viscosity stabilizes the density‐gradient driven drift wave if the axial wavelength ${\lambda }_{\Vert }$ satisfies ${\lambda }_{\Vert }{\text{\hspace{0.17em}<\hspace{0.17em}2πσr}}_0{\mathrm{\hspace{0.17em}(M/m}}_e{)}^{\text{1/4}}$ , ($\text{σ\hspace{0.17em}∼\hspace{0.17em}0.7}$ ; $r_0$ is the density gradient scale length; $M$ , $m_e$ are the ion and electron masses, respectively). Overstable waves, which are driven by the centrifugal force and which resemble flutes with a finite parallel wavelength, can exist if ${\lambda }_{\Vert }$ is sufficiently long.