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2014 
Threedimensional stochastic modeling of radiation belts in adiabatic invariant coordinates A 3D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of It\^o stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3D diffusion tensor, including the radiallocal cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90\textdegree is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90\textdegree, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration. Zheng, Liheng; Chan, Anthony; Albert, Jay; Elkington, Scot; Koller, Josef; Horne, Richard; Glauert, Sarah; Meredith, Nigel; Published by: Journal of Geophysical Research: Space Physics Published on: 09/2014 YEAR: 2014 DOI: 10.1002/jgra.v119.910.1002/2014JA020127 adiabatic invariant coordinates; diffusion equation; fully 3D model; Radiation belt; stochastic differential equation 
We expanded our previous work on L* neural networks that used empirical magnetic field models as the underlying models by applying and extending our technique to drift shells calculated from a physicsbased magnetic field model. While empirical magnetic field models represent an average, statistical magnetospheric state, the RAMSCB model, a firstprinciples magnetically selfconsistent code, computes magnetic fields based on fundamental equations of plasma physics. Unlike the previous L* neural networks that include McIlwain L and mirror point magnetic field as part of the inputs, the new L* neural network only requires solar wind conditions and the Dst index, allowing for an easier preparation of input parameters. This new neural network is compared against those previously trained networks and validated by the tracing method in the International Radiation Belt Environment Modeling (IRBEM) library. The accuracy of all L* neural networks with different underlying magnetic field models is evaluated by applying the electron phase space density (PSD)matching technique derived from the Liouville\textquoterights theorem to the Van Allen Probes observations. Results indicate that the uncertainty in the predicted L* is statistically (75\%) below 0.7 with a median value mostly below 0.2 and the median absolute deviation around 0.15, regardless of the underlying magnetic field model. We found that such an uncertainty in the calculated L* value can shift the peak location of electron phase space density (PSD) profile by 0.2 RE radially but with its shape nearly preserved. Yu, Yiqun; Koller, Josef; Jordanova, Vania; Zaharia, Sorin; Friedel, Reinhard; Morley, Steven; Chen, Yue; Baker, Daniel; Reeves, Geoffrey; Spence, Harlan; Published by: Journal of Geophysical Research: Space Physics Published on: 03/2014 YEAR: 2014 DOI: 10.1002/jgra.v119.310.1002/2013JA019350 
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