Dynamical range of the WINDMI model: An exploration of possible magnetospheric plasma states

Abstract

Abstract. This paper explores the dynamical range of the WINDMI model (Horton and Doxas, 1998]. Such low-dimensional models provide us with the tools to understand the relationships of simple physical quantities within the magnetosphere (such as energy deposition, macroscopic currents, cross-tail voltage, etc.) without the necessity of coping with the more complete but unwieldy models (MHD or particle codes, for example). The model is highly versatile: certain regions of the parameter space support stable fixed points, while others contain periodic states that exhibit period doubling, and sometimes chaos. States in each of these regimes (stable, periodic, chaotic) are investigated for their ability to accurately describe the observed properties of the magnetosphere-ionosphere system. A brief discussion of applications of this model to current space physics problems is included.

The dynamics of storms and substorms with the WINDMI model

“…It was thus decided that the parameters a and s i would be fixed at acceptable values so as to prevent the instability from occurring. Further study of the dynamical modes of the WINDMI model can be found in Smith et al (2000) and Horton et al (2001). It was found that with a = 8 · 10 10 [A/(Pa) 1/2 ] and s i = 10 min the instability was avoided for the two storms analyzed here.…”

Chaos and the limits of predictability for the solar-wind-driven magnetosphere–ionosphere system

“…General properties of the four magnetosphere-ionosphere states S1, S2, S3, S4 are discussed in Ref. 3. A system that appears to conform closely to the known wave forms of the classic internally triggered type I substorms is defined by the following parameter values:…”

“…8, and the mathematical properties of the states described by the WINDMI model are given in Ref. 3. Here we focus on the system described as S3 in Smith et al: 3 a state that characterizes many features of the substorm dynamics as the solar wind dynamo voltage, V sw , increases from low to high values.…”

“…The model used for the magnetosphere is the WINDMI model, which is a well-accepted mathematical-physics model for the solar-wind-driven magnetospheric-ionospheric system. The properties of the WINDMI model have been developed in earlier works, with the most recent being Smith et al 3 concerning the bifurcation sequences in the system. The physics of the model and its relation with earlier models is given in the review papers of Klimas et al 4 and Baker et al 5 Here we examine the lack of predictability that is intrinsic to this model for a certain range of the system parameters.…”

Substorm classification with the WINDMI model

“…We are optimizing the parameters of a nonlinear set of differential equations that have a wide variety of possible dynamics including limit cycles, chaotic attractors, and fixed points (Smith et al, 2000). Because this type of minimization, which involves optimizing the parameters of a nonlinear set of differential equations, is not a standard problem, three minimization approaches were used.…”