Quite a number of empirical models have been developed for the Earth's magnetic
field. The internal source field models represent the Earth's main (core)
magnetic field for magnetically quiet conditions (Kp <= 1). As shown by Gauss in
1839, the potential of the geomagnetic field can be represented by a spherical
harmonic series, the first term being the simple dipole term. The gradient of
the potential determines the magnetic vector field. The Earth's real magnetic
field is the sum of several contributions including the main (core) field, the
crustal (anomaly) field, and external source fields. The core contribution
dominates the field from the Earth's surface up to about four Earth radii. The
principal data sources for main field modeling are
The main field models listed on the following pages differ in the data base used, in the number of coefficients (i.e., degree/order of Legendre polynomials and Taylor series expansion), and in the epoch represented. All coefficient sets are based on the usual Schmidt quasi-normalized form of associated Legendre functions. It is recommended in all cases to use a specific model only for the time period covered by the data base on which the specific model is based.
The main field software package consists in most cases of the coefficients only. Programs to calculate geomagnetic parameters from these sets of coefficients are also available from the National Space Science Data Center (NSSDC) (see below).
Beyond four Earth radii, the Earth's magnetic field is increasingly affected by
the impinging solar wind. The distortions can be described by several external
source fields caused by current systems. One can identify three main current
systems in the undisturbed outer magnetosphere:
This section also lists several computer programs related to geomagnetic models including software (1) to compute the geomagnetic field strength B and its vector components and the L-shell value, (2) to convert between different coordinate systems (see also Appendix B), and (3) for magnetic field-line tracing. L is McIlwain's (1961) shell parameter, which at the magnetic equator corresponds to the radial distance from the Earth's center expressed in units of Earth radii. In the case of a dipole magnetic field (no multipole terms), the parameter L labels the dipole field lines. In the case of the real field, however, L varies along a field line, although the variation is less than 1% in the inner magnetosphere. L is defined as a function of the adiabatic invariant I; I is the curve integral over the particle momentum (parallel to the magnetic field) integrating along the field line between conjugate points. The functional dependence between L and I was determined for a pure dipole field and was then also used for the real field.
The widely used and recommended International Geomagnetic Reference Field (main field only) and Tsyganenko Magnetic Field Model (with external sources) packages include software for B, L calculation and field-line tracing, and an interactive driver, which simplifies access to these models.
The flux of trapped electrons and protons in the Earth's radiation belt has been measured by a large number of satellites over the last three decades. Knowledge of the particle environment is essential for estimates of the radiation exposure of humans and materials in space. J. Vette and his colleagues at NSSDC have developed and improved empirical models for the trapped particle fluxes since the mid-sixties. The particle fluxes can best be described in terms of the coordinates B/Bo and L; Bo is the magnetic field strength at the magnetic equator (minimum value). Application of these models requires, therefore, the use of a geomagnetic field model.
Go to the Magnetospheric Models index Go to the Space Physics Models page
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