Dipole model of Earth's magnetic field
[Image:l shell global dipole.png|thumb|Plot showing field lines (which, in three dimensions would describe "shells") for L-values 1.5, 2, 3, 4 and 5 using a dipole model of Earth's magnetic field]
The dipole model of Earth's magnetic field is a first order approximation of the rather complex true Earth's magnetic field. Due to effects of the interplanetary magnetic field, and the solar wind, the dipole model is particularly inaccurate at high L-shells, but may be a good approximation for lower L-shells. For more precise work, or for any work at higher L-shells, a more accurate model that incorporates solar effects, such as the Tsyganenko magnetic field model, is recommended.
Formulation
The following equations describe the dipole magnetic field.First, define as the mean value of the magnetic field at the magnetic equator on Earth's surface. Typically.
Then, the radial and latitudinal fields can be described as
where is the mean radius of Earth, is the radial distance from the center of Earth, and is the colatitude measured from the north magnetic pole.
Alternative formulation
[Image:Mplwp earth-magnetic-field.svg|thumb|Magnetic field components vs. latitude]It is sometimes more convenient to express the magnetic field in terms of magnetic latitude and distance in Earth radii. The magnetic latitude, or geomagnetic latitude, is measured northwards from the equator and is related to the colatitude by
In this case, the radial and latitudinal components of the magnetic field are given by
where in this case has units of Earth radii.
Invariant latitude
Invariant latitude is a parameter that describes where a particular magnetic field line touches the surface of Earth. It is given byor
where is the invariant latitude and is the L-shell describing the magnetic field line in question.
On the surface of Earth, the invariant latitude is equal to the magnetic latitude.