Dipole model of the Earth's magnetic field

Abstract: Green function solution to Maxwell equations for interplanetary and coronal magnetic fields above photosphere, considering field at source surface

Abstract: Dipole representations of the earth's magnetic field have been found to have insufficient accuracy for the study of magnetically trapped particles. A coordinate system consisting of the magnitude of the magnetic field B, and the integral invariant I has been found to adequately organize, measurements made at different geographic locations. It is shown in the present paper, that a parameter L = f(B,I) can be defined which retains most of the desirable properties of I and which has the additional property of organizing measurements along lines of force. Since the parameter L is the analog of a physical distance in a dipole field (the equatorial radius of a magnetic shell), it is usually found to present fewer conceptual difficulties than the integral invariant I.

Abstract: [1] This work builds on and extends our previous effort (Tsyganenko et al, 2003) to develop a dynamical model of the storm-time geomagnetic field in the inner magnetosphere, using space magnetometer data taken during 37 major events in 1996–2000 and concurrent observations of the solar wind and interplanetary magnetic field (IMF) The essence of the approach is to derive from the data the temporal variation of all major current systems contributing to the distant geomagnetic field during the entire storm cycle, using a simple model of their growth and decay Each principal source of the external magnetic field (magnetopause, cross-tail current sheet, axisymmetric and partial ring currents, and Birkeland current systems) is driven by a separate variable, calculated as a time integral of a combination of geoeffective parameters NλVβBsγ, where N, V, and Bs are the solar wind density, speed, and the magnitude of the southward component of the IMF, respectively In this approach we assume that each source has its individual relaxation timescale and residual quiet-time strength, and its partial contribution to the total field depends on the entire history of the external driving of the magnetosphere during a storm In addition, the magnitudes of the principal field sources were assumed to saturate during extremely large storms with abnormally strong external driving All the parameters of the model field sources, including their magnitudes, geometrical characteristics, solar wind/IMF driving functions, decay timescales, and saturation thresholds, were treated as free variables, and their values were derived from the data As an independent consistency test, we calculated the expected Dst variation on the basis of the model output at Earth's surface and compared it with the actual observed Dst A good agreement (cumulative correlation coefficient R = 092) was found, in spite of the fact that ∼90% of the spacecraft data used in the fitting were taken at synchronous orbit and beyond, while only 37% of those data came from distances 25 ≤ R ≤ 4 RE The obtained results demonstrate the possibility to develop a truly dynamical model of the magnetic field, based on magnetospheric and interplanetary data and allowing one to reproduce and forecast the entire process of a geomagnetic storm, as it unfolds in time and space

Abstract: A hydromagnetic theory is presented which explains the average characteristics of geomagnetic storms. The magnetic storm is caused by a sudden increase in the intensity of the solar wind. Stresses are then set up in the geomagnetic field by the solar plasma impinging upon the geomagnetic field and becoming trapped in it. These stresses, which are propagated to the earth as hydromagnetic waves, account for the observed average magnetic storm variations. The sudden commencement of the magnetic storm is due to a hydromagnetic wave generated by the impact of the solar plasma on the geomagnetic field. The initial phase of the magnetic storm, during which the magnetic field is above average intensity, is due to the increased solar wind pressure. During the initial phase, instability causes small plasma clouds to become imbedded in the magnetic field. They break up and diffuse into the magnetic field to form a belt of trapped particles from the sun (principally protons and electrons). The trapped protons set up stresses, mainly due to centrifugal force, which account for the main phase of the magnetic storm. The recovery from the main phase is attributed to the relief of the stress on the geomagnetic field by the transfer of the energy of the trapped protons to neutral hydrogen by means of ion-atom charge exchange. The correct recovery time for the magnetic storm is predicted from the measured cross section of the ion-atom charge-exchange process and the hydrogen density values around the earth deduced from the scattering of solar Lyman-α radiation.

Abstract: We present a new analysis of the transport of cosmic rays in a turbulent magnetic field that varies in all three spatial dimensions. The analysis utilizes a numerical simulation that integrates the trajectories of an ensemble of test particles from which we obtain diffusion coefficients based on the particle motions. We find that the diffusion coefficient parallel to the mean magnetic field is consistent with values deduced from quasi-linear theory, in agreement with earlier work. The more interesting and less understood transport perpendicular to the average magnetic field is found to be enhanced (above the classical scattering result) by the random walk, or braiding, of the magnetic field. The value of κ⊥ obtained is generally larger than the classical scattering value but smaller than the quasi-linear value. The computed values of κ⊥/κ∥, for a representation of the interplanetary magnetic field, are 0.02-0.04; these values are of the same general magnitude as those assumed in recent numerical simulations of cosmic-ray modulation and transport in the heliosphere, and give reasonable agreement with spacecraft observations of cosmic rays. Some consequences of these results for the interpretation of heliospheric observations are discussed.