Models of the earth's electric field

Detailed models of the electric field of the magnetosphere are derived in several stages. For all, the conductivity along field lines is assumed to be high enough to ensure the vanishing of E B everywhere except in the ionosphere. At first the rotation of the earth is ignored completely and a simple model is constructed which fits certain observed properties. Next, the rotation of the earth is taken into account, but the field is assumed to be that of a magnetic dipole rotating around its symmetry axis. This allows the concept of the electric potential to be retained, which permits the derivation of interesting properties including the use of a conjugate potential which paces the drift of charged particles in the field. Finally, the general case involving asymmetrical rotation is briefly discussed

An Introduction to Magnetospheric Physics by Means of Simple Models

The large scale structure and behavior of the Earth's magnetosphere is discussed. The model is suitable for inclusion in courses on space physics, plasmas, astrophysics or the Earth's environment, as well as for self-study. Nine quantitative problems, dealing with properties of linear superpositions of a dipole and a constant field are presented. Topics covered include: open and closed models of the magnetosphere; field line motion; the role of magnetic merging (reconnection); magnetospheric convection; and the origin of the magnetopause, polar cusps, and high latitude lobes

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift

Solar Terrestrial programs: A five year plan

Major projects to be initiated in the 1980-1985 period, designed to study the Sun, the heliosphere, Earth's magnetosphere, and the upper atmosphere involve the use of spacelab as well as free flying spacecraft. Current and recent investigations in these areas are reviewed and the guiding principles followed in planning future missions are examined. The implementation strategy, the planning process, and supporting research and technology are discussed

Unipolar induction in the magnetosphere

A theory is described for the production of electric currents in the magnetosphere and for the transfer of energy from the solar wind to the magnetosphere. Assuming that the magnetosheath has ohmic-type conduction properties, it is shown that unipolar induction can energize several current flows, explaining the correlation of the east-west component of the interplanetary magnetic field with polar electric fields and polar magnetic variations. In the tail region, unipolar induction can account for effects correlated with the north-south component of the interplanetary magnetic field

Euler potentials and their application in the Hamiltonian formulation of guiding center motion

Scalar analysis and Euler potentials for Hamiltonian formulation of charged particle motion in magnetic fiel

A study of the electric field in an open magnetospheric model

The qualitative properties of an open magnetosphere and its electric field are examined and compared to a simple model of a dipole in a constant field and to actual observations. Many of these properties are found to depend on the separatrix, a curve connecting neutral points and separating different field-line regimes. In the simple model, the electric field in the central polar cap tends to point from dawn to dusk for a wide choice of external fields. Near the boundary of the polar cap electric equipotentials curve and become crescent-shaped, which may explain the correlation of polar magnetic variations with the azimuthal component of the interplanetary magnetic field, reported by Svalgaard. Modifications expected to occur in the actual magnetosphere are also investigated: in particular, it appears that bending of equipotentials may be reduced by cross-field flow during the merging of field lines and that open field lines connected to the polar caps emerge from a long and narrow slot extending along the tail

Classical adiabatic perturbation theory

Adiabatic perturbation theory in celestial mechanic

Quantitative models of magnetic and electric fields in the magnetosphere

In order to represent the magnetic field B in the magnetosphere various auxiliary functions can be used: the current density, the scalar potential, toroidal and poloidal potentials, and Euler potentials -- or else, the components of B may be expanded directly. The most versatile among the linear representations is the one based on toroidal and poloidal potentials; it has seen relatively little use in the past but appears to be the most promising one for future work. Other classifications of models include simple testbed models vs. comprehensive ones and analytical vs. numerical representations. The electric field E in the magnetosphere is generally assumed to vary only slowly and to be orthogonal to B, allowing the use of a scalar potential which may be deduced from observations in the ionosphere, from the shape of the plasmapause, or from particle observations in synchronous orbits

The motion of a proton in the equatorial magnetosphere

A proton of low energy moving in the equatorial plane of the earth will experience drift motions due to both the magnetic field (magnetic gradient drift only, if the field is assumed to be that of a dipole) and the electric field. The electric drift again separates into two parts - the drift due to the main electric field (or convection electric field) existing in the frame of the earth, and that due to the earth's rotation. One result indicated by this work is that at distances of 4 - 6 earth radii, a transition from trapped proton orbits to open trajectories leading to the tail occurs at about 10 kev, the precise value depending upon local time. Such a transition also seems to be indicated by particle observations using Explorer 45. The energy spectrum (at magnetically quiet times) of equatorial protons above this energy can be explained by charge exchange but increased flux observed below it seems to be related to the influx of particles on open orbits from the tail