Polarization Properties of Three Dimensional Alfvénic Field Line Resonances in a Compressed Dipole Magnetic Topology

Abstract:

It is well known that closed magnetic field lines in the Earth’s and other planetary magnetospheres support standing shear Alfvén waves (in analogy with waves on a string), with their own natural frequencies of vibration and polarization, which are determined by the distribution of the plasma mass density and magnetic tension along the field line. These modes can be resonantly excited to form strongly peaked Field Line Resonances (FLRs) when free energy is supplied to the system at a driving frequency that matches one of the natural frequencies, for example by MHD fast mode waves. These waves are ubiquitous in the dayside magnetosphere, and are generally excited by Kelvin – Helmholtz instability along the morning and afternoon flanks, or by solar wind buffeting of the dayside magnetopause.

The question of interest in this study is: In the case of a constant frequency fast mode driver, what determines the location and polarization of the (fundamental mode) field line resonance peak, in the general case a non-axisymmetric Alfvén speed and magnetic field topology? In addressing this question we seek to extend the works of: a) Wright et al., (Astrophys. J., 2016), which considered the case of a non-axisymmetric Alfvén speed in a dipole magnetic field; and b) Rankin et al. (Adv. Space Res., 2006) and Kabin et al., (Ann. Geophys., 2007), which considered an arbitrary magnetic geometry but not whether the phase mixing of oscillations on neighboring field lines may impose a constraint on their polarization. A new formulation is attempted that takes this into account and is applicable to arbitrary magnetic topology, and compared against 3D numerical simulations of externally driven FLRs similar to those of Degeling et al., (J. Geophys. Res., 2010, 2018) and Elsden et al., (J. Geophys. Res., 2018).