An alternative drift shell parameter for modeling trapped particles

The McIlwain L parameter has been widely used to label magnetic drift shells of trapped particles. In a dipolar magnetic field, L gives the equatorial radius of a drift shell. When the total magnetospheric magnetic field is significantly altered by the presence of external magnetospheric currents, particularly during geomagnetically active periods, L has to be calculated by using an appropriate magnetic field model that includes the external fields. Thus, an L value computed at a given local time does not always give the position of a drift shell in configuration (real) space, especially at high L values (>4). Since L is one of the magnetic coordinates typically used to organize trapped particle data, the external current effects on the L calculation need to be assessed. In this paper, we show that by conserving the second adiabatic invariant, I, in a model magnetospheric magnetic field given by the sum of the IGRF and the Tsyganenko T89c models, a configuration-space-based drift shell parameter can be defined. It has been found that for a given mirroring field strength Bm on a magnetic field line, the quantity I is empirically related to the radial distance rt to the point of minimum field strength along that field line. By conserving I, rt measured in units of Earth radii (RE) at any local time can be mapped to its equivalent value Ltn at noon, and vice versa. We show that Ltn can be used as a parameter to label drift shell in configuration space, analogous to the use of L in magnetic space