Shear and current driven electrostatic instability in a collisional ionosphere: Numerical analysis of the fluid and kinetic dispersion relations

Using a generalized kinetic shear and current driven electrostatic ion-acoustic instability theory that includes collisions, fluid-like modes have been derived with ion velocity shear, neglecting electron velocity shear, and vice versa. A numerical analysis for both the kinetic and fluid-like expressions was undertaken to determine the threshold conditions for the current (electron-ion relative drift) and shear, for different directions of the wave vector and frequencies.; It has been found that it is essential to retain collisions before assessing threshold conditions for Ti/Te < 0.4. Also, electron velocity shears do not modify much the zero shear threshold requirements. However, the ion velocity shears may lower the field-aligned threshold current by a significant amount. This is especially true for wave vectors in directions close to perpendicularity. In the collisional case with nu i/Oi = 0.01 and nu e/nui = 10, a temperature ratio Ti/T e < 10-2, for piR/kC s < 0.1, and Ti/Te < 10-1, for piR/kCs = 1.01, is required for the fluid dispersion relation to reproduce the results obtained using the kinetic dispersion relation.