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

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.