An iterative method is developed by which one can 
calculate approximately the boundary of a magnetic field 
confined by a plasma. This method consists essentially of 
varying an assumed surface until the magnetic multipole 
moments of the currents, which would flow on that surface 
to balance the plasma pressure, cancel the corresponding 
moments of the magnetic sources within the surface. The 
method is applied to two problems. For a dipole source of moment M emu in a plasma of 
uniform pressure p dynes/cm^2 that does not penetrate the 
magnetic field, the approximate equation of the surface 
is r = 0.82615 M^(1/3) p^(-1/6)(1-0.120039α^2 - .004180α^4 - .001085α^6 + .000200α^8 - .000597α^(10) + .000326α^(12) - .000094α^(14)) cm, where α is the latitude in radians from the plane normal to M. The surface formed by a cold plasma of density N_0 and pair mass velocity M_t moving past a dipole of moment Me_y with a velocity –U_oe_z extends to infinity downwind. In a coordinate system (x, y, z) centered at the dipole, neutral points, where the surface is parallel to the wind direction, occur at the points (0, ±R_n, .27R_n), and other points on the surface are (0, 0, 1.02R_n), (0, ±2R_n, -∞) and (±1.97R_n, 0, -∞). R_n = 1.0035 (M/(M_tN_oU^2_o)^(-1/2)^(1/3) is about 9 earth radii for the solar wind case.

Calculation by a Moment Technique of the Perturbation of the Geomagnetic Field by the Solar Wind.

This paper describes the structure and the magnetic-field, electric-field, and plasma properties of the ISEE-1 magnetopause crossing on November 5, 1978, which occurred near the subsolar point when the IMF was strongly northward. It was found that the magnetopause was composed of three layers: (1) a sheath transition layer, in which there is a gradual density decrease without a change in temperature and which occurs totally within the magnetosheath plasma; (2) an outer boundary layer, which is dominated by magnetosheath particles; (3) and an inner boundary layer dominated by magnetospheric particles. No significnt heating or cooling was seen across the magnetopause during this crossing. The plasma within each of the layers was quite uniform, and their boundaries were sharp, suggesting that there was very little diffusion present.

Structure and properties of the subsolar magnetopause for northward IMF: ISEE observations

The three-dimensional shape of the magnetopause

The solar wind-magnetosphere interaction for northward interplanetary magnetic field (IMF) is studied using a newly developed three-dimensional adaptive mesh refinement (AMR) global MHD simulation model. The simulations show that for north-ward IMF the magnetosphere is essentially closed. Reconnection between the IMF and magnetospheric field is limited to finite regions near the cusps. When the reconnection process forms newly closed magnetic field lines on the day side, the solar wind plasma trapped on these reconnected magnetic field lines becomes part of the low-latitude boundary layer (LLBL) plasma and it convects to the nightside along the magnetopause. The last closed magnetic field line marks the topological boundary of the magnetospheric domain. When the last closed magnetic field line disconnects at the cusps and reconnects to the IMF, its plasma content becomes part of the solar wind. Plasma convection in the outer magnetosphere does not directly contribute to the reconnection process. On the dayside the topological boundary between the solar wind and the magnetosphere is located at the inner edge of the magnetopause current layer. At the same time, multiple current layers are observed in the high-altitude cusp region. Our convergence study and diagnostic analysis indicate that the details of the diffusion and the viscous interaction do not play a significant role in controlling the large-scale configuration of the simulated magnetosphere. It is sufficient that these dissipation mechanisms exist in the simulations. In our series of simulations the length of the magnetotail is primarily determined by the balance between the boundary layer driving forces and the drag forces. With a parametric study, we find that the tail length is proportional to the magnetosheath plasma beta near the magnetopause at local noon. A higher solar wind density, weaker IMF, and larger solar wind Mach number results in a longer tail. On the nightside downstream of the last closed magnetic field line the plasma characteristics are similar to that in the magnetotail, posing an observational challenge for identification of the topological status of the corresponding field lines.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JA900378

A numerical study of solar wind—magnetosphere interaction for northward interplanetary magnetic field

Sunward convection in the polar cap has long been given as evidence of convection cells that close within the polar cap. These are called “lobe cells” because they are confined to the open field lines that form the tail lobes. Whether lobe-cell convection is physically possible, however, has been seriously questioned. In support of lobe cells, we demonstrate their existence in an MHD model and illustrate the geometry of their circulating magnetic field lines for merging with a purely azimuthal (+By) interplanetary magnetic field (IMF). We find that the ratio of flux circulating in lobe cells compared with merging cells increases with decreasing Alfven Mach number and that sunward flow in the polar cap occurs both in lobe cells and on newly opened field lines in normal or “merging” cells. Although at any given time the sunward moving fields are configured in an overdraped pattern similar to that associated with northward IMF, the concept of sunward motion driven by electric field mapping or, equivalently, tugging on these overturned field lines does not apply, at least for the azimuthal IMF case. The overdraped fields and the null points to which they converge are immersed in a diffusion region at the magnetopause and support field-aligned potential drops so that in the course of time, the field lines lose their identity by changing partners. Thus the sunward flowing fields in the ionosphere are decoupled from their magnetopause counterparts and move in response to the ionospheric potential, which has been modified from the applied solar wind potential by diffusion effects. These MHD model results both support and elucidate concepts deduced from primitive superposition and phenomenological models.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JA03393

MHD model merging with IMF By : Lobe cells, sunward polar cap convection, and overdraped lobes

Magnetic fields deflect charged particles and the fields are somewhat impervious to charged particles not already trapped within them Thus, as we should expect, the Earth’s magnetic field makes a bubble in the supersonic plasma flowing outward from the Sun and called the solar wind This bubble in which the Earth’s magnetic field is largely confined and compressed is called the magnetosphere and the boundary between the Earth’s magnetic field on the inside and the turbulent interplanetary plasma and magnetic field on the outside is called magnetopause The magnetopause is very thin when compared to its radius of curvature (about 10−3 to 10−5) and can be regarded as infinitesimally thin Within this thin boundary layer electric currents flow which are created by the magnetically deflected plasma The effect of these currents is to cancel or terminate the geomagnetic field outside the magnetosphere and to augment the geomagnetic dipole field inside since the effect of the outside pressure is to compress the geomagnetic field

J. Y. Choe

Papers

The Magnetospheric Boundary