Dissipation of Alfvén wave pulses propagating along dipole magnetic tubes with reflections at the ionosphere

A ratio of the maximal and minimal cross sections of the magnetic tube (contraction ratio) is a crucial parameter which affects very strongly on reflections of MHD wave pulses propagating along a narrowing magnetic flux tube. In cases of large contraction ratios of magnetospheric magnetic tubes, the wave energy flux at the ionospheric boundary can be rather small. Therefore the dissipation of the wave perturbations can be very weak for each reflection, in spite of a finite conductivity of the planet's ionosphere. The dissipation is stronger for the pulses with shorter wave scales. Because of that, Alfvén wave pulses with sufficiently long wave scales have a very small energy loss for each reflection at the conducting ionosphere, and thus, they have many reflections without a noticeable decrease of their amplitude. This effect related to converging magnetic lines is dependent very strongly on the polarization of the Alfvén wave. In case of a dipole magnetic field, the effect is most pronounced for wave pulses characterized by velocity and magnetic perturbations in the meridional plane.