Effects of the magnetic field model and wave polarisation on the estimation of proton number densities in the magnetosphere using field line resonances

The cold, core plasma mass density in the Earth's magnetosphere may be deduced from the resonant behaviour of ultra-low frequency (ULF; 1–100 mHz), magnetohydrodynamic (MHD) waves. Ground-based magnetometers are the most widely used instruments for recording the signature of ULF wave activity in the magnetosphere. For a suitable model of the background magnetic field and a functional form for the variation of the proton number density with radial distance, the resonant frequencies of ULF waves provide estimates of the equatorial plasma mass density. At high latitudes, the magnetic field model becomes critical when estimating the plasma mass density from FLR data. We show that a dipole field model is generally inadequate for latitudes greater than ～65° geomagnetic compared with models that are keyed to magnetic activity, interplanetary magnetic field and solar wind properties. Furthermore, the method often relies on the detection of the fundamental ULF resonance, which changes frequency depending on the polarisation of the oscillation. Using idealised toroidal and poloidal oscillation modes, the range of the derived densities as the ULF wave polarisation changes is of the same order as changing the density function from a constant value throughout the magnetosphere to assuming constant Alfven speed in a dipole geometry.