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Empirical Modeling of 3D Plasma Pressure and Magnetic Field Structures in the Earth’s Plasma Sheet

  • Author(s): Yue, Chao
  • Advisor(s): Lyons, Lawrence R.
  • et al.
Abstract

Ions and electrons in the nightside magnetosphere, driven by the dawn-to-dusk convection electric field, flow earthward and are energized. As a result, plasma pressure is enhanced and magnetic field configuration becomes more stretched, forming the necessary conditions for the development of substorms. Determining the physical processes leading to the changes of the plasma and magnetic field configurations, as well as the processes resulting from the configuration variations, is thus crucial to understanding substorms. Accurate evaluation of these processes, including formation of field-aligned currents (FACs), isotropization by current sheet scattering, and some localized instabilities that may responsible for substorm onset, relies on knowing the realistic 3 dimensional (3D) magnetic field configurations, which cannot be provided by current available empirical models with sufficient accuracy or as a function of growth phase development. Therefore, we have developed a 3D force-balanced empirical substorm growth phase magnetic field model, which allows us to investigate the evolution of these configurations during the substorm growth phase and evaluate the physical processes governing the configuration changes. Here, we first statistically analyzed the growth phase pressures using Geotail and THEMIS data, and identified three primary factors causing the growth phase pressure change: solar wind dynamic pressure (PSW), energy loading, and sunspot number. We then constructed a 2D equatorial empirical pressure model and an error model in the near Earth plasma sheet (r ≤ 20 RE) using the Support Vector Regression Machine (SVRM) with the three factors as input. The model predicts the plasma sheet pressure accurately with median errors of 5%, and the predicted pressure gradients agree reasonably well with observed gradients obtained from two-probe measurements. The model shows that pressure increases linearly as PSW increases, while the pressure responses to energy loading and sunspot number are nonlinear. From these model pressure distributions, we were able to establish a realistic 3D growth phase magnetic field configurations that satisfy the physical constraint of force balance with the plasma pressures using a 3D magnetic field model [Zaharia, 2008]. The force-balanced magnetic field configuration shows that Bz decreases in the near Earth region and increases in the tail due to an increasing perpendicular current peaking at the earthward edge of the plasma sheet. The current peak moves towards the Earth as energy loading increases, indicating earthward penetrating of the plasma sheet. Meanwhile, positive dBz/dz is found to develop late in the growth phase, but a Bz minimum at the equator does not form, unlike the prediction by Saito et al. [2010]. The perpendicular current peaks off the equator plane and its peak moves towards the equatorial plane as the growth phase evolves, indicating the thinning of current sheet. In addition, there are typical Region-1 FACs around 12 to 20 RE at the beginning of substorm growth phase and they gradually evolve to Region-2 FACs in the late growth phase with their earthward boundary moving to smaller r. The model magnetic fields agree quantitatively well with observed fields. The magnetic field is substantially more stretched under higher PSW while the dependence on sunspot number is non-linear and less substantial. The excellent agreements between the model results and observations give us confidence that the realistic model can be used at the first time to understand the pressure and magnetic field changes observed during a substorm event by providing accurate evaluations of the effects of energy loading and PSW, as well as the temporal and spatial effects along a spacecraft trajectory. By applying our modeling to a substorm event, we found that the equatorward moving of proton aurora during the growth phase is mainly due to continuous stretching of magnetic field lines, and the ballooning instability is more favorable at late growth phase around midnight tail where there is a localized plasma beta peak. Furthermore, the equatorial mapping of the breakup auroral arc is X ~ –14 RE near midnight, coinciding with the location of the maximum growth rate for ballooning instability.

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