LANL*V1.0: a radiation belt drift shell model suitable for real-time and reanalysis applications

We describe here a new method for calculating the magnetic drift invariant, L*, that is used for modeling radiation belt dynamics and for other space weather applications. L* (pronounced L-star) is directly proportional to the integral of the magnetic flux contained within the surface defined by a charged particle moving in the Earth's geomagnetic field. Under adiabatic changes to the geomagnetic field L* is a conserved quantity, while under quasi-adiabatic fluctuations diffusion (with respect to a particle's L*) is the primary term in equations of particle dynamics. In particular the equations of motion for the very energetic particles that populate the Earth's radiation belts are most commonly expressed by diffusion in three dimensions: L*, energy (or momentum), and pitch angle (the dot product of velocity and the magnetic field vector). Expressing dynamics in these coordinates reduces the dimensionality of the problem by referencing the particle distribution functions to values at the magnetic equatorial point of a magnetic 'drift shell' (or L-shell) irrespective of local time (or longitude). While the use of L* aids in simplifying the equations of motion, practical applications such as space weather forecasting using realistic geomagnetic fields require sophisticated magnetic field models that, in turn, require computationally intensive numerical integration. Typically a single L* calculation can require on the order of 10(5) calls to a magnetic field model and each point in the simulation domain and each calculated pitch angle has a different value of L*. We describe here the development and validation of a neural network surrogate model for calculating L* in sophisticated geomagnetic field models with a high degree of fidelity at computational speeds that are millions of times faster than direct numerical field line mapping and integration. This new surrogate model has applications to real-time radiation belt forecasting, analysis of data sets involving tens of satellite-years of observations, and other problems in space weather.