Evolution of High‐m Poloidal Alfvén Waves in a Dipole Magnetic Field

Abstract

We investigate how initially high‐m, poloidal Alfvén waves evolve using a numerical model solving the ideal, cold, linear magnetohydrodynamic (MHD) equations in a 2‐D dipole coordinate system. The curved magnetic geometry provides a key difference between the poloidal and toroidal Alfvén frequencies of any one field line. A polarization rotation from poloidal toward toroidal predicted from the Cartesian box model theory still occurs but now with the waves following contours of Alfvén frequency, which moves the Alfvén wave across field lines. The structure of these contours depends on the harmonic mode along the field line and the equilibrium. We find that the amplitude peak of the poloidal mode moves significantly radially outward in time. When the typically observed azimuthal phase motion of such waves is included, hodograms show a polarization rotation from purely poloidal to a mixed poloidal/toroidal polarization at all locations. Such features could be used to help interpret satellite observations of Pc4‐5 poloidal ultralow frequency (ULF) waves in Earth's magnetosphere.

Plain Language Summary

Earth's curved magnetic field lines can oscillate (like waves on a string), at a range of frequencies with the lowest being termed ultralow frequency (ULF) waves. In this paper we consider a specific subset of these waves known as high‐m poloidal Alfvén waves, which have the characteristic that the wavelength in the radial direction is much larger than that in the azimuthal (angular) direction. Such waves are of geophysical importance as they can interact with energetic particles that are trapped and drifting in Earth's magnetic field. This has implications for space weather effects with spacecraft operations being negatively affected by such interactions. We perform computer simulations of how these waves evolve in a curved magnetic field like that of the Earth. We show that the structure of these waves changes in time, in a way that is unique to the geometry of the magnetic field, with the development of complex spatial structure. We further comment on how these features could be looked for in satellite observations.