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Inner magnetosphere coupling
(2017)
The dynamics of the inner magnetosphere is strongly governed by the interactions between different plasma populations that are coupled through large-scale electric and magnetic fields, currents, and wave-particle interactions. Inner magnetospheric plasma undergoes self-consistent interactions with global electric and magnetic fields. Waves excited in the inner magnetosphere from unstable particle distributions can provide energy exchange between different particle populations in the inner magnetosphere and affect the ring current and radiation belt dynamics. The ionosphere serves as an energy sink and feeds the magnetosphere back through the cold plasma outflow. The precipitating inner magnetospheric particles influence the ionosphere and upper atmospheric chemistry and affect climate. Satellite measurements and theoretical studies have advanced our understanding of the dynamics of various plasma populations in the inner magnetosphere. However, our knowledge of the coupling processes among the plasmasphere, ring current, radiation belts, global magnetic and electric fields, and plasma waves generated within these systems is still incomplete. This special issue incorporates extended papers presented at the Inner Magnetosphere Coupling III conference held 23–27 March 2015 in Los Angeles, California, USA, and includes modeling and observational contributions addressing interactions within different plasma populations in the inner magnetosphere (plasmasphere, ring current, and radiation belts), coupling between fields and plasma populations, as well as effects of the inner magnetosphere on the ionosphere and atmosphere.
In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.