The Geomagnetic Field

To obtain an understanding of the magnetosphere, we must first examine the geomagnetic Field. The earth's magnetic field is an important feature since it generally prevents a direct encounter between the ionosphere and energetic particles of solar origin, and especially solar wind. Mars, for example, does not have a magnetosphere, and it is widely held that solar wind "erosion" has eliminated a good portion of the Martian atmosphere. A geographically localized region that does not afford this protection is found in the neighborhood of the magnetic pole. Since the geomagnetic field is an efficient deflector of the solar wind, why are parameters of the solar wind significant in the morphology of the magnetosphere and the ionosphere beneath it?

The magnetic field of the earth resembles a bar magnetic in many respects. The longitudinal field lines are aligned with the axis of a hypothetical magnet at the ends (poles), and the transverse field lines define an equatorial plane that bisects the magnet. If the field around this bar magnetic were to represent the first-order field of the earth, then we see that the polar field line orientation is nearly vertical while the equatorial field lines are horizontal. This is a good model but there are some differences. First, the geomagnetic field is not purely dipolar, and secondly, the axis of the best-fit dipole does not correspond precisely to the rotational axis of the earth. The geomagnetic field is generated by several sources and current systems located within the earth, the ionosphere, and the magnetosphere. The internal sources include a field produced by currents flowing near the earth's core at a depth of about 3000 km. This component dominates all other sources below about five earth radii. The geomagnetic field may be adequately represented by a magnetic dipole tilted with respect to the earth's rotational axis. Some local anomalies result from direct magnetization of crustal material, but these are generally averaged-out at ionospheric heights. The effects of ionospheric/magnetospheric current system sources depend upon the heights being analyzed, but these components are usually small below a few earth radii.

The simplest approximation to the geomagnetic field is an earth-centered dipole directed southward and inclined at about 11.5 degrees to the earth's rotational axis. Thus the North Pole is 78.5°N, 291°E, and the South pole is 78.5°S, 111°E. This model can be improved by displacing the dipole a distance equal to 0.0685 Re toward 15.6° N and 150.9°E, where Rc is the earth radius. This modification places the North Pole at 81°N, 84. 7°W, and the South Pole at 75°S, 120.4°E. However, there is considerable wander in the precise coordinate placement if the model is slightly changed because of longitude sensitivity at high latitudes. There are also secular variations of the field associated with gradual reduction in the dipole field strength, a migration of regional anomalies, a northward movement of the dipole, and other variations. Some approximation methods have been based upon the fact that the geomagnetic field decreases in intensity with the inverse cube of geocentric distance, and these methods extrapolate surface values to ionospheric heights. Such approximations tend to emphasize local effects, but the availability of surface magnetic field properties makes the use of such approaches very tempting. Maps of surface values of the total magnetic field, the azimuthal variation of the compass (declination), and the inclination of the magnetic field from the horizontal (dip) may be found in a number of sources. Figure 2-15 shows the conventions associated with measurements of the geomagnetic field. Units vary depending upon application. The primary transformations are given in Table 2-6.

Geomagnetic Coordinates

F: total field H: horizontal X: northward y: eastward z: vertical

D: declination I: inclination

Figure 2-15: Conventions used in Geomagnetic Field Measurements

Table 2-6: Magnetic Field Units and Conversions

Magnetic Induction (B)

1 gamma = I0"5 Gauss = 10"9 Tesla = 1 nanoTesla

Magnetic Intensity (H)

1 gamma = 10"5 Oersted [cgs units] 1 gamma = 10"2 (4^cy, ampere turns/meter [mks units]

The gamma unit (i.e., y) is employed in some of the older literature, but it is equivalent to the nanoTesla unit (i.e., nT or 10"9 Telsa). Table 2-7 is a listing of various field amplitudes of interest.

Table 2-7: Amplitudes of Selected Magnetic Fields

Earth Surface

~ '/2 Gauss

5 x 104 nT

Benign Solar Field

-1.0 Gauss

105 nT

Disturbed Solar Field

~104 Gauss

109 nT

Solar Wind

~ 6 nT

Secular Field Decay at the Equator

~ 16 nT/yr

Sq Field Variations from Equatorial Currents

0-50 nT

Lunar-Solar Tidal Variations

~3nT

Geomagnetic Storms at Mid-Latitudes (Kp=9)

~ 103 nT

There are a number of representations of the geomagnetic field. A description of the methods is given by Knecht and Shuman [1985]. One of the methods that is most physically attractive for demonstrating ionospheric-magnetospheric interactions is one for which the field is modeled in a so-called B-L coordinate frame (see Fig. 2-16). In this system, the field may be exhibited in curves of constant magnetic field intensity B and curves of constant L. In the B-L system, a particular magnetic shell is characterized by a unique L value corresponding to the normalized geocentric distance of the field Vector over the equator. Thus, L = 2 corresponds to a field line that reaches its maximum height over the geomagnetic equator at 2 Re, where Re is the earth radius and a convenient normalization factor. This system is quite useful in the study of particles trapped in the magnetosphere such as those found in the Van Allen radiation belts. The terrestrial footprint of a specified field line will occur at two points. These are called conjugate points.

Ionospheric plasma disturbances and resultant telecommunication phenomena are best characterized in terms of geomagnetic rather than geographic coordinates. Accordingly, emphasis should be given to the specification of geomagnetic coordinates for telecommunication terminals, for purposes of space weather assessment.

The dipole method leads to a coordinate system of Geomagnetic Latitudes and Longitudes (i.e., the Geomagnetic Coordinate System). Figure 2-16 depicts a family of Geomagnetic Latitude lines on a Geographic coordinate grid. It is based upon the 1965 IGRF (i.e., International Geomagnetic Reference Field). Other methods include those that replace Geomagnetic Latitude with either Dip Latitude or Invariant Latitude [Jensen et al., I960], The Corrected Geomagnetic Coordinate System (CGCS) is a refinement of the Geomagnetic Coordinate system, and like the B-L system, is useful in studies of conjugate effects and other high latitude phenomena.

North Latitude (deg)

Figure 2-16: The B-L Coordinate System. The curves depicted are in the magnetic meridian plane. The L parameter is related to the height of the field line over the magnetic equator. B is the magnetic field intensity in Oersteds. From Jursa [1985],

North Latitude (deg)

Figure 2-16: The B-L Coordinate System. The curves depicted are in the magnetic meridian plane. The L parameter is related to the height of the field line over the magnetic equator. B is the magnetic field intensity in Oersteds. From Jursa [1985],

Current Methodology uses a representation of the field in terms of a multipole expansion of the magnetic scalar potential function in which the coefficients are based upon a least squares approach to provide a best fit to the field data. This method is now well established and the model, and coefficients, for computing the field are widely available. The internationally accepted model of the geomagnetic field is the IGRF (mentioned above) with the 1985 version being the most accurate. Previous models have been developed at 5-year intervals beginning in 1965. Coefficients for these models are available from the World Data Center A for Rockets and Satellites at Beltsville, Maryland.

From Figure 2-17, we see that the geomagnetic latitude lines are shifted equatorward in the American sector, relative to Europe and Asia. Knecht and Shuman [1985] have portrayed this situation in a way that gets your attention. They have plotted identifiable land masses in a mercator format, but use Geomagnetic Coordinates for registration (see Figure 2-18).

Longitude

Figure 2-17: Geomagnetic Latitudes (From CCIR [1980]).

Longitude

Figure 2-17: Geomagnetic Latitudes (From CCIR [1980]).

Another useful coordinate is the Magnetic Latitude, as opposed to Geomagnetic Latitude. This might be more properly called the Dip Latitude since it is based upon a transformation of observed dip angles by the following formula:

where © is the Magnetic Latitude and / is the Dip angle.

Figured 2-18: Mecator representation of the world using Geomagnetic Latitudes as the registration format. (From Knecht and Shuman [1985])

Figure 2-19 is a plot of Magnetic (Dip) Latitude. Notice that the magnetic latitude lines passing through the United Kingdom and northern Europe cut through the middle of the continental United States.

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