Examining the Applicability of Direct Analytic Method (DAM) to Normal Modes of Poloidal Oscillations Under Symmetric and Asymmetric Boundary Conditions

A working Direct Analytic Method (DAM) model is envisaged to explain the normal modes of poloidal Alfven waves in the Earth's magnetosphere. The model solves the ideal, cold, magnetohydrodynamic (MHD) equations associated with transverse components of the magnetic perturbations in a dipolar magnetic field. DAM model is used to study the transverse poloidal waves in different regions of magnetosphere characterized by their L-value and different plasma variability. The plasma density distribution is assumed to be governed by the standard power law, 1/rm, where r is the geocentric distance of any point of interest on the field line and m is the density index. The eigen frequencies and spatial structures are obtained analytically under different ideal ionospheric boundary conditions and the results are compared with the numerical solutions to establish the validity of the model. DAM, being an analytic model, is used to explain the distinctive structural features of transverse poloidal waves which are obtained under different boundary conditions, for different density indices. Furthermore, the application of the analytic model in the computation of eigen frequency as well as plasma density is demonstrated under different observational scenario. An analytic model, Direct Analytic Method (DAM) is used to study the field aligned structure and frequency variation of normal modes of poloidal oscillations DAM is used to explain the peculiar structural features under different boundary conditions and plasma distributions along the field line DAM model can also be applied to the observations of poloidal oscillations to estimate their eigen frequencies or plasma densities