Higher harmonics electrostatic ion cyclotron parallel flow velocity shear instability with inhomogeneous DC electric field in the magnetosphere of Saturn

In present paper higher harmonic electrostatic ion-cyclotron (EIC) parallel flow velocity shear instability in presence of perpendicular inhomogeneous DC electric field with the ambient magnetic field has been studied, in different regions of the magnetosphere of Saturn. Dimensionless growth rate variation of EIC waves has been observed with respect to (k_{ bot } rho _{i}) for various plasma parameters. Effect of velocity shear scale length ((A_{i})), temperature anisotropy ((T_{ bot } /T_{|})), magnetic field ((B)), electric field ((E)), inhomogeneity ((P/a)), angle of propagation ((theta )), ratio of electron to ion temperature ((T_{e}/T_{i})) and density gradient ((varepsilon _{n}rho _{i})) on the growth of EIC waves in the inner magnetosphere of Saturn has been studied and analyzed. The mathematical formulation for dispersion relation and growth rate has been done by using the method of characteristic solution and kinetic approach. This theoretical analysis has been done taking the data from the Cassini in the inner magnetosphere of Saturn in the extended region where ion cyclotron waves have been observed. The change in the growth of these waves due to the presence of Enceladus has been analyzed.