A nonlinear dynamical analogue model of geomagnetic activity

Abstract

The solar wind‐magnetosphere interaction is discussed within the framework of deterministic nonlinear dynamics. Linear prediction filter studies have shown that the magnetospheric response to energy transfer from the solar wind contains both directly driven and unloading components. These studies have also shown that the response is significantly nonlinear and, thus, the filter technique and other correlative techniques cannot give a complete description of that response. Phase space reconstruction studies have shown that the evolution of the nonlinear solar wind‐magnetosphere system is dominated by only a few degrees of freedom; the system approaches a low‐dimensional attractor on which its behavior can be described using a relatively simple nonlinear dynamical model. An earlier dripping faucet analogue model of the low‐dimensional solar wind‐magnetosphere system is briefly reviewed, and then a plasma physical counterpart to that model is constructed. A Faraday loop in the magnetotail is considered, and the relationship of electric potentials on the loop to changes in the magnetic flux threading the loop is developed. This approach leads to a model of geomagnetic activity which is similar to the earlier mechanical model but described in terms of the geometry and plasma contents of the magnetotail. The model is best characterized as an elementary time‐dependent global convection model. The convection evolves within a magnetotail shape that varies in a prescribed manner in response to the dynamical evolution of the convection. The result is a nonlinear model capable of exhibiting a transition from regular to chaotic loading and unloading. The behavior of the model under steady loading and also some elementary forms of time‐dependent loading is discussed. The model appears to properly account for all macrophysical aspects of magnetotail geomagnetic activity, it incorporates both the directly driven and the unloading components of geomagnetic activity, and it includes, in a fundamental way, the inherent nonlinearity of the solar wind‐magnetosphere interaction.