Kinetic Theory for Electrostatic Waves Due to Transverse Velocity Shears.

Shear in the flow velocity of a fluid leads to the low frequency and long wavelength Kelvin-Helmholtz K-H instability. The velocity shear can be generated in a number of ways. In a plasma the existence of an inhomogeneous electric field component transverse to the ambient uniform magnetic field can provide a transverse velocity shear. The evolution of the K-H instability in this configuration has been extensively studied. Recently some space observations and laboratory experiments seem to indicate that ion-cyclotron-like waves are observed for subcritical field aligned currents and therefore the origin of these waves are somewhat mysterious. A crucial feature of these observations and experiments was the presence of a transverse component of a zero order electric field. In order to study the role of the transverse electric fields in the generation of the ion-cyclotron-like waves, we suggested a mechanism based on the coupling of the negative energy ion Bernstein modes or the ion cyclotron modes in the region where the d.c. electric field is localized, with the positive energy ion Bernstein modes or the cyclotron modes in the region where the d.c. electric field is absent. Here we use kinetic theory to obtain the general dispersion relation rigorously, for the electrostatic oscillations in a plasma, in the form of an integral equation for an arbitrary electric profile.