Steady state magnetic field configurations for the Earth's magnetotail

Abstract

We present a two‐dimensional, force‐balanced magnetic field model in which flux tubes have constant pVγ throughout an extended region of the nightside plasma sheet, between approximately 36 RE geocentric distance and the region of the inner edge of the plasma sheet. We have thus demonstrated the theoretical existence of a steady state magnetic field configuration that is force‐balanced and also consistent with slow, lossless, adiabatic, earthward convection within the limit of the ideal MHD (isotropic pressure, perfect conductivity). The numerical solution was constructed for a two‐dimensional magnetosphere with a rectangular magnetopause and nonflaring tail. The primary characteristics of our steady state convection solution are (1) a pressure maximum just tailward of the inner edge of the plasma sheet and (2) a deep, broad minimum in equatorial magnetic field strength Bze, also just tailward of the inner edge. Our results are consistent with Erickson's (1985) convection time sequences, which exhibited analogous pressure peaks and Bze minima. Observations do not indicate the existence of a Bze minimum, on the average. We suggest that the configurations with such deep minima in Bze may be tearing‐mode unstable, thus leading to substorm onset in the inner plasma sheet.

Stationary magnetospheric convection on November 24, 1981. 1. A case study of "pressure gradient/minimum-<i>B</i>" auroral arc generation

“…This relation is valid in the MHD tail approximation when magnetic tension f Árf is negligible. Indeed, solutions of the Grad-Shafranov equation for stationary magnetospheric con®gurations with a MFM lead to quite dierent radial pressure pro®les (see, for example, Hau et al, 1989). However, there are several aspects of the magnetospheric neutral sheet structure in the``wall region'' that are not taken into account in the static Grad-Shafranov equation.…”

“…Evidently, for the isotropic pressure case, a more rigorous treatment is possible, in comparison with that in GVZ92, of the magnetic ®eld structure in equilibrium with plasma pressure with the use of magnetic vectorpotential A(r 0 ,z) and Grad-Shafranov equation. Its solution, with the given B Z (r 0 ) as a boundary condition, can be sought in a way described in Hau et al (1989), andHau (1991). For an adiabatic lossless convection, Hau et al (1989) show that to avoid the``pressure balance inconsistency'', a minimum must appear in the magnetic ®eld B Z (r 0 ) pro®le.…”

“…For an adiabatic lossless convection, Hau et al (1989) show that to avoid the``pressure balance inconsistency'', a minimum must appear in the magnetic ®eld B Z (r 0 ) pro®le. We must note that the steady-state B Z (r 0 ) pro®les deduced in GVZ92 and in SPP96 are very similar to those deduced in Hau et al (1989), and Hau (1991), as was noted in the two former papers. However, it was stated in Sect.…”

Self‐organized criticality in the substorm phenomenon and its relation to localized reconnection in the magnetospheric plasma sheet

“…Steady magnetospheric convection, as the name implies, has been explained in terms of convection in the plasma sheet [Hau et al, 1989], but to our knowledge, the deep minimum in the tail magnetic field required by this explanation has not been found. IN Figure 2d for R4.…”

Structure, force balance, and evolution of incompressible cross-tail current sheet thinning

“…Since such pressures are not observed, it was concluded that sunward convection must be an unsteady process. Later, Hau et al [1989] and Hau [1991] constructed a steady force-balanced MHD model in which the magnetotail has a broad minimum in the equatorial magnetic field strength in the near-Earth plasma sheet. In such a model, steady convection becomes possible.…”