The geomagnetic components from eight low‐latitude ground stations and the ATS 1 satellite are studied for substorms occurring on December 24 and 25, 1967, and on August 15, 1968. A simple, four‐parameter, field‐aligned line current model is employed, and the linear inverse problem is constructed to determine the set of model parameters that best fit the data. A straightforward review of linear inversion theory is included in the theory section. The four model parameters are the magnitude of the current, the L shell on which the current flows, and the azimuthal positions of the eastern and western portions of the circuit. Both growth phases and expansion phases are treated. The best fits to the ground and satellite data are shown to be independent of the L parameter for values of L ≳ 3.5 when only ground data are treated and for values of L ≳ 8.5 when satellite data are included. The four‐parameter model, although it produces good qualitative fits to expansion phase data, is unable to fit the data within 2 standard deviations of the error in the observations. The model is able to fit the growth phase of one substorm within 1 standard deviation. In one substorm with an apparent growth phase a better fit of the data during the expansion phase was obtained by combining the line current model of the growth phase with an additional four‐parameter line current model.

An analytic solution is presented for the steady state electric and magnetic fields induced by the motional electric field of the solar wind in the atmosphere or interior of a planet that is asymmetrically surrounded by solar wind plasma. The electrically conducting ionosphere or interior must be in direct electrical contact with the solar wind over the day side of the planet. The conducting region of the planet is modeled by a sphere or a spherical shell of arbitrarily stratified electrical conductivity. A nonconducting cylindrical cavity is assumed to extend downstream on the night side of the planet. The solar wind is assumed to be highly conducting so that the induced fields are confined to the planet and cavity. Induced currents close as sheet currents at the solar wind‐cavity and solar wind‐planet interfaces. Numerical evaluation of the analytic formulas are carried out for a uniformly conducting spherical model. Among the quantities computed are (1) the induced electrical and magnetic fields, which are compared to those of the spherically symmetric theory, (2) the total current through the body and the total power dissipated in the planet, which are reduced 25% in comparison with those of the spherically symmetric theory, (3) the radial electromagnetic stress on the incident plasma, which is found to be asymmetric over the subsolar hemisphere and strongly dependent upon the spiral angle of the interplanetary magnetic field, and (4) the flow pattern of the sheet currents.

An analytic theory is developed for both the steady state and the time‐dependent electric and magnetic fields inside the moon and its downstream cavity for interplanetary electromagnetic field fluctuations incident at arbitrary angles to the cavity axis. The moon model has an electrical conductivity, electrical permittivity, and magnetic permeability which vary arbitrarily with radius. The cavity downstream of the moon in the solar wind is assumed to be an infinitely long nonconducting cylinder. If the interplanetary field fluctuations propagate parallel to the cavity, the far cavity field is a single cylindrical transverse electric mode propagating downstream with the same frequency, wavelength, and phase velocity as the interplanetary field. The far cavity field is the result of a forced surface wave on the cylindrical boundary of the void. When the interplanetary fluctuations are incident at an arbitrary angle to the cavity axis, the far cavity field is a superposition of an infinite number of cylindrical TE (transverse electric) and TM (transverse magnetic) modes. Each of these modes is a surface wave with the same frequency and downstream phase velocity (the ratio of the angular frequency to the magnitude of the component of the interplanetary wave vector parallel to the cavity axis) as the incident interplanetary field. If the magnetic perturbation vector of the incident wave is normal to the cavity axis, the far cavity field is a linear combination of cylindrical TE and TM modes for arbitrary angles of incidence. However, if the interplanetary electric field fluctuation is normal to the axis of the void, the far cavity field is pure TE independent of the incidence angle. Resonances can occur in the far cavity TE and TM forced surface waves if the apparent velocity of the interplanetary wave parallel to the void axis, i.e., the downstream phase velocity, coincides with one of the characteristic TE or TM wave guide speeds of the circular cylindrical void for waves of the same frequency as the interplanetary radiation. When the interplanetary waves travel parallel to the void axis, their downstream and actual phase velocities coincide; these phase speeds are smaller than the velocity of light in vacuum, c, so that no resonances in the far cavity field are possible, since characteristic wave guide phase velocities are greater than c. Particular TE and TM modes may be absent from the far cavity field for certain incidence angles and frequencies of the interplanetary radiation. At normal incidence the far cavity behaves as a forced electromagnetic oscillator. At frequencies greater than 50 and 105 Hz, for the TE and TM modes, respectively, the cavity is a cylindrical wave guide for electromagnetic field perturbations associated with the moon. For frequencies less than 50 Hz the cavity field perturbations due to the presence of the moon are attenuated downstream of the moon.