Magnetospheric equilibrium with anisotropic pressure

Abstract

Self-consistent magnetospheric equilibrium with .jnisotropic pressure is obtained by employing an iterative metric method for solving the inverse equilibrium equation in an optimal flux coordinate system. A method of determining plasma parallel and perpendicular pressures from either analytic particle distribution or particle distribution measured along the satellite's path is presented. The numerical results of axisymmetric magnetospheric equilibrium including the effects of finite beta, pressure anisotropy, and boundary conditions are presented for a bi-Maxwellian particle distribution. For the isotropic pressure cases, the finite beta effect produces an outward expansion of the constant magnetic flux surfaces in relation to the dipole field lines, and along the magnetic field the toroidal ring current is maximum at the magnetic equator. The effect of pressure anisotropy is found to further expand the flux surfaces outward. Along the magnetic field lines the westward ring current can be peak away from the equator due to an eastward current contribution resulting from pressure anisotropy. As pressure anisotropy increases, the peak westward current can become more singular. The outer boundary flux surface has significant effect on the magnetospheric equilibrium. For the outer flux boundary resembling dayside compressed flux surface due to solar wind pressure, the deformation of the magnetic field can be quite different from that for the outer flux boundary resembling the tail-like flux surface.

3-D Force-balanced Magnetospheric Configurations

“…10. The most interesting feature appears in Plot (a) of the figure, showing the fact that the azimuthal (toroidal) current is peaked away from the equator, a result previously obtained for the 2-D case by Cheng [1992]. The maximum transverse current appears in twin regions, above and below the plane, and thus the current is maximum in this case in regions which do not have the maximum field curvature.…”

“…(4) for ψ, again boundary conditions in the θ coordinate means knowing the value of ψ at both ends of a field line. If those are on the Earth surface and again consider the field there to be dipolar, their value of ψ is then analytically known [e.g., Stern, 1967;Cheng, 1992Cheng, , 1995:…”

“…9 shows contours in the equatorial plane of constant perpendicular pressure, P ⊥ . Once P ⊥ and P are known in the equatorial plane, their values along the field lines are uniquely determined from energy and magnetic moment conservation [e.g., Cheng, 1992].…”

Resonance frequency of stretched magnetic field lines based on a self‐consistent equilibrium magnetosphere model

“…A large abundance of magnetospheric heavy ions like oxygen is often invoked as the cause of the discrepancy, which is difficult to justify under normal conditions. A significant reduction was obtained by Bhattacharjee et al [1999] is quite general and can be applied to a more realistic magnetospheric equilibrium with any specified shape of field line stretching [Cheng, 1992]. This opens up the opportunity to examine the FLR frequencies without the limitation imposed by the cold plasma theory.…”

MHD Field Line Resonances and Global Modes in Three-Dimensional Magnetic Fields

“…With the magnetospheric magnetic field represented by two Euler potentials as B = ∇ψ × ∇α, where ψ is the poloidal flux and α is a toroidal angle-like variable, the plasma pressure can be written as P = P (ψ, α). By further assuming that the pressure is only a function of the poloidal flux, P = P (ψ), the continuous and discrete spectra of shear Alfvén wave and slow 4 magnetosonic wave for two-dimensional axisymmetric equilibrium magnetic field models [Cheng, 1992], where the magnetic field is nonuniform along and across the ambient magnetic field, have been studied [e.g., Cheng and Chance, 1986;Cheng et al, 1993].…”