Toroidal quarter waves in the Earth’s magnetosphere: theoretical studies

Abstract

An analytic model has been developed for toroidal quarter wave (QW) oscillations in the Earth’s magnetosphere using idealistic and highly asymmetric ionospheric boundary condition. The background magnetic field is dipolar and plasma density distribution is governed by a power law 1/r m where r is the geocentric distance of any point along the field line and m is the density index. The solution thus obtained has been compared with the numerical solutions. Earlier workers had developed the analytic model for trivial 1/r 6 (m=6) type of plasma density distribution along the field line for which the period of the fundamental is twice that of corresponding half wave (i.e. toroidal oscillation in the symmetric ionospheric boundary). The present analytic model does reproduce this feature. In addition, it is seen that this ratio decreases for lower values of m. Moreover, for a particular value of m, this ratio shows a decreasing trend with increased harmonic number. The spatial characteristics of QW obtained from present analytic model are in excellent agreement with those computed numerically, thereby validating the model. The departure of frequency computed analytically from that obtained numerically is significant only for the fundamental and this departure reduces sharply with the increased harmonic number. It should be noted that there is no such departure for 1/r 6 type of plasma density distribution and spatial structures as well as frequency computed from the present analytic model match perfectly with those computed numerically.