On the definition and calculation of a generalised McIlwain parameter

Abstract

The L parameter, which indicates the distance where a magnetic field line crosses the equatorial plane, is defined only for an aligned magnetic dipole field. For a realistic planetary magnetic field, however, neither a definition nor a method to calculate this parameter are available so far. We therefore extent the definition of the McIlwain parameter for an arbitrary planetary magnetic field and numerically calculate it for the actual geomagnetic field. In order to do so, we first calculate the Earth's magnetic field for 2008 with the IGRF model. To motivate a proper definition for a general L parameter, each component of this field will be illustrated and discussed. In a second step, we present four possible definitions for the L parameter and discuss their properties and differences with respect to the question in how far they reflect the field geometry. We contrast our method with the traditional derivation of the L parameter employing numerical simulations of the cut-off rigidities of energetic particles and an empirical relation between the latter and L . © 2010 Author(s).