A low‐dimensional energy‐conserving state space model for substorm dynamics

Abstract

A low‐ (four‐) dimensional state space model for the basic energy components of the night‐side magnetosphere is developed based on truncated descriptions of the collisionless microscopic (Hamiltonian) energy transfer processes occurring in the quasi‐neutral layer. The substorm trigger, due to bifurcation of the system either from magnetic reconnection or from ballooning‐mirror modes, is modeled by a fast unloading above a critical current. For constant southward interplanetary magnetic field solar wind input, the system performs oscillations with recurrence times in the range of 60–70 min. For northward IMF, the system decays to a static MHD equilibrium. For the intermediate case of a weak solar wind input, there occur uncorrelated, isolated substorms. The theoretical basis for a low‐dimensional model may be supported within the framework of self‐organized criticality since the geotail is a highly stressed global system during the growth phase of substorms. The new energy‐conserving state space model eliminates the “dripping faucet” unloading role of the Klimas et al. [1992] model and includes the parallel streaming kinetic energy in the substorm dynamics. The new model shows a wide range of dynamical behavior according to the values of the system parameters and the form of the solar wind input signal.

Estimates of magnetotail reconnection rate based on IMAGE FUV and EISCAT measurements

“…Blanchard et al (1996) estimated a coupling efficiency between the solar wind and the magnetotail reconnection electric field to be 0.1, which is similar to what has been assumed by some modelers (e.g. Horton and Doxas, 1996). Blanchard et al (1996) also reported a peak correlation lagging the solar wind electric field by about 70 min.…”

Testing the SOC hypothesis for the magnetosphere

“…The analogy was developed into a simplified magnetospheric model by estimating the large-scale electrical properties of the M-I system and combining these electrical components into a driven nonlinear oscillator circuit model (Klimas et al, 1992). It has been further developed into a plasma physics model by Horton and Doxas (1996). In the case of a dissipative, driven, autonomous low dimensional system such as the Lorenz model, the dynamics, rather than exploring all of phase space ergodically, collapses onto a low dimensional region called an attractor.…”

Substorm classification with the WINDMI model

“…We define a type III substorm as one that is well described by a linear second order filter (LRC filter) with parameters that are within a range of estimates based on magnetospheric scales (Weimer, 1994;Horton and Doxas, 1996). The WINDMI model with no triggering can be reduced to a model with a response function near that of a LRC filter.…”

“…which is due to plasma convection, arises from the divergence of the ion off-diagonal momentum stress tensor π (Horton and Doxas, 1996). The closure of the I 1 current loop subtracts from these dusk-to-dawn currents flowing from in regions obtained by mapping the auroral field lines to the geotail.…”

“…A direct estimate of the lobe inductance and the plasma sheet capacitance taken from Horton and Doxas (1996) is given as a parameter estimation example. From a magnetic field model such as Tysganenko (1996) we can calculate the lobe area A and the effective length L x of the support of the geotail current density j y (x), then…”