Counter differential rigid-rotation equilibrium of electrically non-neutral two-fluid plasma with finite pressure

Abstract

We derive the two-dimensional counter-differential rotation equilibria of two-component plasmas, composed of both ion and electron ($e^-$) clouds with finite temperatures, for the first time. In the equilibrium found in this study, as the density of the $e^{-}$ cloud is always larger than that of the ion cloud, the entire system is a type of non-neutral plasma. Consequently, a bell-shaped negative potential well is formed in the two-component plasma. The self-electric field is also non-uniform along the $r$-axis. Moreover, the radii of the ion and $e^{-}$ plasmas are different. Nonetheless, the pure ion as well as $e^{-}$ plasmas exhibit corresponding rigid rotations around the plasma axis with different fluid velocities, as in a two-fluid plasma. Furthermore, the $e^{-}$ plasma rotates in the same direction as that of $\\boldsymbol {E \\times B}$, whereas the ion plasma counter-rotates overall. This counter-rotation is attributed to the contribution of the diamagnetic drift of the ion plasma because of its finite pressure.