Astrophysics and Space Sciences Transactions www.astrophys-space-sci-trans.net 1810-6528 1810-6536 6 1 2010 10.5194/astra-6-9-2010 http://www.astrophys-space-sci-trans.net/6/9/2010/ http://www.astrophys-space-sci-trans.net/6/9/2010/astra-6-9-2010.html http://www.astrophys-space-sci-trans.net/6/9/2010/astra-6-9-2010.pdf 9 17 2010-04-22 On the definition and calculation of a generalised McIlwain parameter J. Pilchowski jpilchowski@alaska.edu A. Kopp K. Herbst B. Heber Geophysical Institute, 903 Koyukuk Drive, Univ. of Alaska, Fairbanks, AK 99775-7320, USA Inst. für Experimentelle und Angewandte Physik, Christian-Albrechts-Univ. zu Kiel, Leibnizstraße 11, 24118 Kiel, Germany The <i>L</i> 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 <i>L</i> parameter, each component of this field will be illustrated and discussed. In a second step, we present four possible definitions for the <i>L</i> 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 <i>L</i> parameter employing numerical simulations of the cut-off rigidities of energetic particles and an empirical relation between the latter and <i>L</i>. Connerney, J.: Magnetic fields of the outer planets, J. Geophys. Res., 18, 659–679, 1993. Gauss, C F.: Allgemeine Theorie des Erdmagnetismus: Resultate aus den Beobachtungen des magnetischen Vereins im Jahre 1836, Göttinger Magnetischer Verein, Leipzig, 1–52, 1836. McIlwain, C E.: Coordinates for Mapping the Distrubution of Magnetically Trapped Particles, J. Geophys. Res., 66, 3681–3691, 1961. Roederer, J., Welch, J., and Herod, J.: Longitude dependence of geomagnetically trapped electrons, J. Geophys. Res., 72, 4431–4447, 1967. Shea, M. and Smart, D.: Estimating cosmic ray vertical cutoff rigidities as a function of the McIlwain parameter for different epochs of the geomagnetic field, Phys. Earth Planet. Interiors, 48, 200–205, 1986. Stern, D P.: Euler Potentials, Am. J. Phys., 4, 494–501, 1969. Størmer, C.: Polar Aurora, Clarendon Press Oxford, 294~pp., 1955. Tsyganenko, N.: A magnetospheric magnetic field model with a warped tail current sheet, Planet. Space Sci., 37, 5–20, 1989.