Nonlinear propagation of whistler-mode in the presence of magnetic Islands in the magnetopause

We develop a framework for studying the nonlinear whistler wave at magnetic reconnection sites generated by energetic electron beam in the presence of magnetic islands as well as the nonlinearity. The governing model equation has been derived using the two-fluid model in the presence of the equilibrium magnetic field, consisting of a guide field and magnetic field due to magnetic islands. The dynamical equation for this nonlinear whistler wave has been solved numerically for the magnetopause region parameters. The findings obtained from simulation show that the contour plot of vector potential and current sheet formation is a result of nonlinearity and field perturbation. The numerically determined spectrum shows an inertial range with a spectral index of nearly - 5/3, followed by steeper scaling. This steepening in the turbulent spectrum is a characteristic of energy transit from larger to smaller scales. A new perspective on the scale size of current sheet is provided by our innovative approach for studying nonlinear whistler by energetic electron beam at the magnetic reconnection locations.