Multi-scale Properties of Solar Wind - Magnetosphere Coupling During Substorms

The global features of the magnetosphere during substorms is well known from many studies based on observations, modeling and simulations. These arise from processes such as plasmoid formation and ejection, global convection, etc. The analysis of the time series data using nonlinear dynamical techniques has characterized the global dynamics in terms of low dimensional behavior. On the other hand the multi-scale features evident in the power law distribution of many physical variables are not well understood. This property arises from physical processes such as MHD turbulence, bursty bulk flows, current disruption, etc. and are characteristic of open systems in general. These two aspects of the coupled solar wind - magnetosphere are studied by reconstructing a phase space from the time series data such that the trajectories in this space adequately describe the dynamics. The global features, obtained by an averaging of the dynamical trajectories, are described in the mean field manner and are represented by a first order phase transition. The multi-scale substorm activity has features of second-order phase transitions and is characterized by a critical exponent. The power law nature of the the multi-scale behavior then arises from the critical behavior associated with the sudden transitions in the magnetosphere during substorms. The probability distribution functions computed for differnet states show the existence of a two-state system, with the transition between these states exhibiting multi-scale properties.