Steady-state magnetic field models and tearing-mode instabilities for the Earth's magnetotail

Abstract

This thesis addresses a fundamental question in magnetospheric physics, which is whether steady state convection could theoretically exist in the Earth's plasma sheet. By constructing a numerical two-dimensional magnetohydrostatic equilibrium magnetosphere that is consistent with the condition of steady, lossless, adiabatic, plasma-sheet convection, we disprove assertions made by Erickson and Wolf (1980), Schindler and Birn (1982), and Birn and Schindler (1985), concerning the non-existence of a physical steady-state solution within the ideal MHD limit (isotropic pressure, perfect conductivity). The computed steady-state magnetic field model, however, is different both from averaged observations and from standard magnetic-field models in that the equatorial magnetic field strength B$\sb{\rm ze}$ exhibits a very deep broad minimum in the inner plasma sheet. Somewhat similar results were also found in Erickson's (1985) quasi-static adiabatic convection models, in which a shallow, sharp B$\sb{\rm ze}$-minimum developed tailward of the inner-edge of the plasma sheet during the course of earthward convection. To study tearing instability of the configurations that possess a B$\sb{\rm ze}$-minimum in the near-earth plasma sheet in the presence of resistivity, a time-dependent numerical resistive MHD code has been developed. By performing the simulations with two types of initial equilibrium magnetic-field configurations, including the standard model in which B$\sb{\rm ze}$ decreases monotonically down the tail, which is inconsistent with steady-state adiabatic convection, we find that the existence of a B$\sb{\rm ze}$-minimum greatly enhances the growth of resistive tearing-mode instability and that the neutral line is likely to form near the initial B$\sb{\rm ze}$-minimum. In the framework of collisionless plasma theory, it is argued that ideal MHD is likely to be violated near the B$\sb{\rm ze}$-minimum, making the steady-state model susceptible to the collisionless tearing-mode instability. In this respect, our results are consistent with the previous assertions that steady-state convection cannot be sustained in the Earth's plasma sheet. In other words, our calculations suggest that the magnetotail structure associated with adiabatic earthward convection is intrinsically unstable even if the solar wind condition is precisely steady, which may explain why magnetospheric substorms should occur and why the neutral line associated with the substorm should occur in the near-earth plasma sheet.