The nonlinear evolution of kinetic Alfvén wave with the ion acoustic wave and turbulent spectrum in the magnetopause region

Abstract

The mutual nonlinear interplay of kinetic Alfvén wave (KAW) and ion acoustic wave, for the high-β plasma (i.e., m e /m i ≪ β ≪ 1, where β is thermal to magnetic pressure ratio) in the magnetopause, has been considered in the present study. A set of dimensionless nonlinear Schrödinger equations has been derived taking into account the finite frequency as well as ion temperature corrections. The dynamical equation of the ion acoustic wave (propagating at an angle with respect to the background magnetic field) in the presence of ponderomotive nonlinearity due to KAW is also derived. Numerical simulation has been carried out to study the effect of nonlinear interaction between these waves which results in the formation of localized structures and turbulent spectrum, applicable to the high-β plasmas like magnetopause regions. Results reveal that due to the nonlinear interplay between these waves, natures of the formation of localized structures are complex and intense in nature in quasi steady state. From the results, we have found that spectral index follows the scaling ∼k À 3=2 ⊥ at large scale and spectral index follows ∼k À 2:80 ⊥ À Á at small scale. We also found the steepening in the turbulent spectrum. Steepening in the turbulence spectrum has been reported by the Time History of Events and Macroscale Interactions during Substorms spacecraft across the magnetopause, and results are found to be consistent with spacecraft observation.