Dipole Model Of The Earth's Magnetic Field
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The dipole model of the Earth's magnetic field is a first order approximation of the rather complex true
Earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from structure of Earth, Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from ...
. Due to effects of the
interplanetary magnetic field The interplanetary magnetic field (IMF), also commonly referred to as the heliospheric magnetic field (HMF), is the component of the solar magnetic field that is dragged out from the solar corona by the solar wind flow to fill the Solar System ...
(IMF), and the
solar wind The solar wind is a stream of charged particles released from the Sun's outermost atmospheric layer, the Stellar corona, corona. This Plasma (physics), plasma mostly consists of electrons, protons and alpha particles with kinetic energy betwee ...
, the dipole model is particularly inaccurate at high
L-shell The L-shell, L-value, or McIlwain L-parameter (after Carl E. McIlwain) is a parameter describing a particular set of planetary magnetic field lines. Colloquially, L-value often describes the set of magnetic field lines which cross the Earth's ...
s (e.g., above L=3), 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 B_0 as the mean value of the magnetic field at the magnetic equator on the Earth's surface. Typically B_0=3.12\times10^\ \textrm. Then, the radial and latitudinal fields can be described as :B_r = -2B_0\left(\frac\right)^3\cos\theta :B_\theta = -B_0\left(\frac\right)^3\sin\theta :, B, = B_0\left(\frac\right)^3 \sqrt where R_E is the mean
radius of the Earth Earth radius (denoted as ''R''🜨 or ''R''E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatoria ...
(approximately 6370 km), r is the radial distance from the center of the Earth (using the same units as used for R_E), and \theta is the
colatitude In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude. In geography, Southern latitudes are defined to be negative, and as a result the colatitude ...
measured from the north magnetic pole (or
geomagnetic pole The geomagnetic poles are antipodal points where the axis of a best-fitting dipole intersects the surface of Earth. This ''theoretical'' dipole is equivalent to a powerful bar magnet at the center of Earth, and comes closer than any other poi ...
).


Alternative formulation

It is sometimes more convenient to express the magnetic field in terms of magnetic latitude and distance in Earth radii. The magnetic latitude (MLAT), or
geomagnetic latitude Geomagnetic latitude, or magnetic latitude (MLAT), is a parameter analogous to geographic latitude, except that, instead of being defined relative to the geographic poles, it is defined by the axis of the geomagnetic dipole, which can be accurat ...
, \lambda is measured northwards from the equator (analogous to
geographic latitude In geography, latitude is a geographic coordinate that specifies the north-south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the ...
) and is related to the colatitude \theta by :\lambda = \pi/2 - \theta. In this case, the radial and latitudinal components of the magnetic field (the latter still in the \theta direction, measured from the axis of the north pole) are given by :B_r = -\frac\sin\lambda :B_\theta = \frac\cos\lambda :, B, = \frac \sqrt where R in this case has units of Earth radii (R = r/R_E).


Invariant latitude

Invariant latitude is a parameter that describes where a particular magnetic field line touches the surface of the Earth. It is given by :\Lambda = \arccos\left(\sqrt\right) or :L = 1/\cos^2\left(\Lambda\right) where \Lambda is the invariant latitude and L is the L-shell describing the magnetic field line in question. On the surface of the earth, the invariant latitude (\Lambda) is equal to the magnetic latitude (\lambda).


See also

*
Geomagnetic pole The geomagnetic poles are antipodal points where the axis of a best-fitting dipole intersects the surface of Earth. This ''theoretical'' dipole is equivalent to a powerful bar magnet at the center of Earth, and comes closer than any other poi ...
*
Dipole In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: * An electric dipole moment, electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple ...
*
International Geomagnetic Reference Field The International Geomagnetic Reference Field (IGRF) is a standard mathematical description of the large-scale structure of the Earth's main magnetic field and its secular variation. It was created by fitting parameters of a mathematical model o ...
(IGRF) *
Magnetosphere In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior Dynamo ...
*
World Magnetic Model The World Magnetic Model (WMM) is a large spatial-scale representation of the Earth's magnetic field. It was developed jointly by the US National Geophysical Data Center and the British Geological Survey. The data and updates are issued by the U ...
(WMM) *
Dynamo theory In physics, the dynamo theory proposes a mechanism by which a celestial body such as Earth or a star generates a magnetic field. The dynamo theory describes the process through which a rotating, convection, convecting, and electrically conductin ...


References


External links


Instant run of Tsyganenko magnetic field model
from NASA CCMC

including Tsyganenko model source code {{DEFAULTSORT:Dipole Model Of The Earth's Magnetic Field Geomagnetism Magnetic field of the Earth Space physics