An algorithm for approximating the L * invariant coordinate from the real-time tracing of one magnetic field line between mirror points

The L * invariant coordinate depends on the global electromagnetic field topology at a given instance and the standard method for its determination requires a computationally expensive drift contour tracing. This fact makes L * a cumbersome parameter to handle. In this paper, we provide new insights on the L * parameter and we introduce an algorithm for an L * approximation that only requires the real-time tracing of one magnetic field line between mirrors points. This approximation is based on the description of the variation of the magnetic field mirror intensity after an adiabatic dipolarization, i.e., after the non-dipolar components of a magnetic field have been turned off with a characteristic time very long in comparison with the particles’ drift periods. The corresponding magnetic field topological variations are deduced assuming that the field line foot points remain rooted in the Earth's surface and the drift average operator is replaced with a computationally cheaper circular average operator. The algorithm results in a relative difference of a maximum of 12 % between the approximate L * and the output obtained using the International Radiation Belt Environment Modeling Library (IRBEM-LIB), in the case of the Tsyganenko 89 model for the external magnetic field (T89). This margin of error is similar to the margin of error due to small deviations between different magnetic field models at geostationary orbit. This approximate L * algorithm represents therefore a reasonable compromise between computational speed and accuracy of particular interest for real-time space weather forecast purposes

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