Velocity shear Kelvin-Helmholtz instability with inhomogeneous DC electric field in the magnetosphere of Saturn

In this paper parallel flow velocity shear Kelvin-Helmholtz instability has been studied in two different extended regions of the inner magnetosphere of Saturn. The method of the characteristic solution and kinetic approach has been used in the mathematical calculation of dispersion relation and growth rate of K-H waves. Effect of magnetic field (B), inhomogeneity (P/a), velocity shear scale length ($A_i$), temperature anisotropy ($T_{\perp }/T_{||}$), electric field (E), ratio of electron to ion temperature ($T_e/T_i$), density gradient (${\epsilon }_n{\rho }_i$) and angle of propagation ($\theta$) on the dimensionless growth rate of K-H waves in the inner magnetosphere of Saturn has been observed with respect to $k_{\perp }{\rho }_i$. Calculations of this theoretical analysis have been done taking the data from the Cassini in the inner magnetosphere of Saturn in the two extended regions of Rs ～4.60–4.01 and Rs ～4.82–5.0. In our study velocity shear, temperature anisotropy and magnitude of the electric field are observed to be the major sources of free energy for the K-H instability in both the regions considered. The inhomogeneity of electric field, electron-ion temperature ratio, and density gradient have been observed playing stabilizing effect on K-H instability. This study also indicates the effect of the vicinity of icy moon Enceladus on the growth of K-H instability.