Earth's magnetosphere, which is a cavity formed by the interaction of the turbulent solar wind with the dipole magnetic field, is a key region of geospace involving a broad range of interacting scales, a complex geometry and a rich variety of physical processes. The data from the ground and space based observatories have been used extensively to develop data-derived models of the magnetosphere. The coherence on the global scale, obtained in terms of low dimensionality of its dynamics, and the consequent predictability of its dynamics, has been instrumental in the development of initiatives for forecasting space weather. The multi-scale properties, on the other hand, can not be predicted dynamically and the methods of nonlinear dynamics and statistical physics have been combined to develop comprehensive models that yield deterministic predictions of the global features and probabilistic predictions of its multi-scale aspects. The next challenge lies in the development of the mathematical framework for these results, and requires a strong collaborative efforts between geosciences and mathematics. The multi-scale properties make the fractional kinetic equations, which combines the dynamical and statistical approaches, a natural choice as a mathematical framework for modeling the coupled solar wind - magnetosphere system. The project will develop comprehensive models of multi-scale phenomena of the magnetosphere by combining three approaches, viz., data derived modeling, theory of fractional kinetics, and global MHD simulations. The combination of these three approaches requires a close interdisciplinary collaboration of mathematicians and geoscientists, and will be undertaken by research teams at Courant Institute of Mathematical Sciences and University of Maryland.
The proposed research will have broader impacts by providing a mathematical framework enabling improved forecasting of geospace disturbances. Such a framework is essential for improving the current forecasts of the hazardous events in the near-Earth space. The geospace storms and substorms have serious impacts on modern technological systems such as communication satellites, power grids, human space flight, etc. The improvement of the current capabilities for forcasting the conditions in the different regions of geospace, such as the ionosphere and the radiation belt, is of strategic importance to national security. Further, the development of mathematical framework for multiscale behavior of the geospace will stimulate the understanding of the similar features in the atmosphere, and potentially of the linkages between these two regions and how they are controlled by changes in the solar activity.
