Spectrum of Finite Frequency Pump Kinetic Alfvén Wave in the Solar Wind

The nonlinear interaction between the kinetic Alfvén wave (KAW) and the slow magnetosonic wave is studied. The dynamical equation for the slow magnetosonic wave, in the presence of a ponderomotive force due to finite frequency KAW (ω0<ωci\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega_{0}<\omega_{\mathrm{ci}}$\end{document}, where ω0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega_{0}$\end{document} is the frequency of the KAW and ωci\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega_{\mathrm{ci}}$\end{document} is the ion gyro frequency) is developed and then numerically solved for the solar wind parameters around 1 AU. Three different propagation angles of the slow magnetosonic wave (θ=70∘,75∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\theta = 70^{\circ},75^{\circ}$\end{document}, and 85∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$85^{\circ}$\end{document}) are considered. Our results reveal that due to the nonlinear interplay between the waves, the nature of the formation of localised structures becomes complex and depends on the different propagation angles of the slow magnetosonic wave. The power spectrum of a KAW shows the Kolmogorov scaling in larger scales but exhibits steepening in smaller scales. The scaling index of the power spectrum of the KAW depends on the propagation angles of the slow magnetosonic wave. Therefore, the heating of plasma particles in the solar wind may show such dependence. The present results are consistent with the observation of the Cluster spacecraft for the solar wind around 1 AU.