Different eigenproblem models for field line resonances in cold plasma: Effect on magnetospheric density estimates

Magnetospheric plasma density can be remotely sensed through ground-based magnetometer data using a suitable model for field line resonances (FLRs) formed by standing shear Alfvén wave on closed geomagnetic field lines. The simplest type of FLR model, which is also the most relevant for magnetometer data inversion purposes, is based on solving a certain eigenvalue problem. Over the years a number of such models have been developed [Singer, H.J., Southwood, D.J., Walker, R.J., Kivelson, M.G., 1981. Alfvén wave resonances in a realistic magnetospheric magnetic field geometry. J. Geophys. Res. 86, 4589–4596; Rankin, R., Fenrich, F., Tikhonchuk, V.T., 2000. Shear Alfvén waves on stretched magnetic field lines near midnight in Earthʹs magnetosphere. Geophys. Res. Lett. 27, 3265–3268; Rankin, R., Kabin, K., Marchand, R., 2006. Alfvénic field line resonances in arbitrary magnetic field topology. Adv. Space Res. 38, 1720–1729]. In this paper we summarize the properties of these models and investigate the effect of using these different models on the magnetospheric density inferred from the ground-based magnetometer measurements. We also formulate a simple criterion which can be used to determine which one of these models should be used for a particular field line.