EARTH: MAGNETIC FIELD AND MAGNETOSPHERE

 

C. T. RUSSELL AND J. G. LUHMANN

Originally published in:
Encyclopedia of Planetary Sciences, edited by J. H. Shirley and R. W. Fainbridge,
208-211, Chapman and Hall, New York, 1997.

 

Earth is the most important planet for the study of the generation of planetary magnetic fields and the physics of planetary magnetospheres, not because of any special property of its magnetic field or its magnetosphere but simply because we have been able to study the magnetic field over a very long period of time. Understanding the temporal behavior of both interior and exterior sources of magnetic fields is the key to understanding the physics of those source regions. Continuous measurements of the Earth's magnetic field have now been taken for over a century and a half from observatories on the surface of the Earth and for about 3 decades from spacecraft above the surface of the Earth. These data have been supplemented with less precise data based on inferred values of the magnetic field deduced from remanent magnetic fields in rocks, pottery, and similar objects that can become magnetized as they cool.

 

Planet and Interior

The Earth is the most rapid rotator of the planets of the inner solar system. It rotates once on its axis relative to the stars every 23 hours and 56 minutes (and every 24 hours relative to the Sun). It has a crust and a mantle surrounding a liquid metallic core which in turn encloses a solid metal core. The average radius of the Earth is 6371 km. Seismic evidence shows that the mantle is about 2886 km thick and the metallic core about 3485 km. By volume, 16% of the planet consists of core and 84% of mantle. The inner solid core is created by the solidification of the outer core as the Earth cools. Thus the inner core is believed to be still growing in size. At present it is about 1221 km in radius and occupies about 4% of the volume of the core. Thus it is still quite small. The energy released by the freezing of the inner core (both latent heat of fusion and gravitational settling) is thought to provide the source of energy for driving the Earth's magnetic dynamo. The density of the inner core, deduced from long period gravimeters which can detect the pendulum-like motion of the inner core, rocking back and forth within the fluid core, is 13 gcm-3. The outer liquid core density is thought to be about 0.5 gcm-3 less. Thus while the liquid core occupies only about 16% of the volume of the planet, it contains about 36% of the mass.

The heat released in the interior of the planet by the solidification of the core, by radiative decay and by the general cooling of the Earth, is transmitted to the surface of the planet by a combination of convection and conduction. Convection requires the motion of the material. In a fluid this results in the familiar cells of hot liquid rising, cooling at the top of the cell and sinking back down to the source of the heat, only to be heated and repeat the cycle. In a rotating fluid this motion becomes much more complex. The addition of a magnetic field whose strength is expected to be large enough to be dynamically significant will further complicate the motion. As a result of this complexity, progress in understanding the generation of the Earth's magnetic field has been slow (See Dynamo Theory).

Convection occurs even in the solid mantle above the core. In turn this convection drives plate motions which drive tectonic activity on the surface of the Earth. However, it is difficult to deduce the interior processes from their surface manifestations in tectonic activity. In order to probe the interior, seismic waves are being used to create tomographs of the horizontal as well as radial structure. This field is in its infancy but it promises to allow us to measure the inhomogeneity of the mantle and thereby gain greater insight into how convection in the mantle is taking place.

 

Magnetic Field

It has been known at least since W. Gilbert's "De Magnete," written in the reign of Elizabeth I at the end of the 16th century, that the Earth was a giant magnet with a dipolar magnetic field. It was realized not long afterward that the internal magnetic field varied with time. While at present the principal variation is a westward drift, the field undergoes notable other variations including reversals. Today the magnetic pole that is in the northern hemisphere is a south pole. It attracts the north pole of a magnet. In earlier times the pole in the northern hemisphere has been a north pole, and compasses, had they been available at that time, would have pointed in the opposite direction. The frequencies of these reversals are themselves functions of time. For example, 60 million years ago reversals occurred about once every 500,000 years, whereas 10 million years ago reversals occurred 3 times as often, about every 150,000 years [Barton, 1989].

The magnetic field is generally represented by a spherical harmonic expansion which is a solution of Laplace's equation. Contributions to the field on the surface of the Earth arise from both internal and external sources. In the following discussion we will concern ourselves with only the interior sources. The spherical harmonic expansion expresses a scalar potential, V, whose gradients are the three vector components of the magnetic field.

 

where and are the Earth's longitude and latitude, a is the radius of the Earth and r is the distance from the center of the Earth. The index n is the degree of the term and the index m is the order. The function Pnm(cos ) is the associated Legendre function with Schmidt normalization. There are three normalizations encountered in practice: Schmidt, abbreviated Pnm; Gauss, abbreviated Pn,m; and Neumann, abbreviated Pn,m. The Schmidt normalization is standard for published coefficients. The coefficients gnm and hnm are called the Gauss coefficients. Table 1 gives the Gauss coefficients for the Earth's magnetic field to degree and order 4 [IAGA, Division I Working Group 1, 1987].

 

Table 1. Spherical Harmonic Coefficient (in nT) of Terrestrial Magnetic Field (IGRF 1985)


Coefficient Degree (m) Order (n)
1 2 3 4
______________________________________________________
4 169
gnm 3 835 -426
2 1691 1244 363
______________________________________________________
1 -1903 2045 -2208 780
gno 0 -29877 -2073 1300 937
1 5497 -2191 -312 233
______________________________________________________
2 -309 284 -250
hnm 3 -296 68
4 -298


The dipole term g1o is the dominant term of the spherical harmonic expansion. This coefficient gives the size of the effective dipole moment along the Earth's rotation axis. We can combine the three degree 1 terms to create a tilted dipole moment, M, whose magnetic moment is given by

 

M = a3 (g102 + g112 + h112)0/00

This moment would have a pole at a latitude

 

= tan-1[g10 / (g112 + h112)0/00]

and at a longitude given by

 

= tan-1 ( h11 / g11)

 

Table 2 gives the co-latitude, east longitude and magnitude of the magnetic moment of the Earth's dipole at selected times over the last four centuries [Barton, 1989]. This table clearly shows that the strength of the dipole moment has been monotonically decreasing over the last 400 years, and has diminished almost 20% in that time. The pole has drifted 45o westward or about 0.1o degree per year and the co-latitude has varied from a low of 3.1o to 11.5o and now is decreasing rapidly again at a rate of about 0.02o per year, a rate similar to the maximum rate of change in co-latitude seen in the historical record. Thus, it is no longer appropriate to quote 11.5o as the tilt of the dipole axis, as is widely done.

 

Table 2. Location and Strength of the Centered Tilted Magnetic Dipole
Year Dipole Moment x 1015Tm3
(degrees)
Co-latitude
(degrees)
East Longitude
(degrees)
1990 7.84 10.8 289.0
1980 7.91 11.2 289.2
1970 7.97 11.4 289.8
1960 8.02 11.5 290.5
1950 8.07 11.5 291.1
1900 8.27 11.5 292.0
1850 8.47 11.5 295.6
1800 8.61 10.8 301.0
1750 8.84 10.1 305.4
1700 9.00 8.3 314.6
1650 9.18 7.0 322.3
1600 9.36 5.4 330.3
1550 9.54 3.1 334.1

 

Another means of obtaining insight into how rapidly the Earth's magnetic field is evolving is to examine the secular variation, the time rate of change of each of the terms in Table 1. We can obtain a characteristic time by dividing the secular variation into the value of the coefficient. These characteristic times are given in Table 3. The minimum times of about 20 years are overestimates of the rapidity of the change because these represent coefficients passing near zero, but the median values of close to 200 years are meaningful. The interior field of the Earth is varying sufficiently rapidly that it must be remeasured on decadal time scales to be accurate enough for most research purposes. The most accurate way to do this is with low altitude polar satellites, but no such program is planned by any of the major space agencies.

Secular variation is not just important for determining the most accurate magnetic field model at all times. The secular variation also provides a means of determining the behavior of the dynamo, because the magnetic field is to a high degree of approximation frozen into the fluid motions of the core. Thus, to understand the interior of the Earth, we need a vigorous program of space-borne measurements, in addition to the seismic networks. Finally, while the seismic studies depend on event-oriented studies, the magnetic surveys require long baselines of the highest accuracy measurements. Thus there are basically two quite different styles of observation in these two disciplines, despite quite similar objectives.

 

Table 3. Characteristic Times (in Years) for Spherical Harmonic Coefficients of Terrestrial Magnetic Field (IGRF 1985)


Coefficient Degree (m) Order (n)
1 2 3 4
______________________________________________________
4 25
gnm 3 8350 304
2 242 2073 47
______________________________________________________
1 190 601 480 1300
gno 0 1288 151 255 9370
1 244 191 59 61
______________________________________________________
2 15 123 114
hnm 3 27 27
4 331
Median Characteristic Time: 224 191 255 114


 

Magnetosphere

The magnetic field of the Earth acts as an obstacle to the magnetized flowing plasma from the Sun, called the solar wind (q.v.). The typical dynamic pressure exerted by the solar wind on the Earth's magnetic cavity, or magnetosphere as it is now called, is about 1.7 nPa. The point where the solar wind dynamic pressure and the pressure exerted by the Earth's magnetic field are in balance is at about 10 Earth radii in the sunward direction along the Earth-Sun line. As shown in Figure 1, the Earth's magnetic field forms a cavity in the shape of a blunt body with its "nose" at this position and an extended "tail". The cavity flares to about 15 Earth radii on either side of the Earth above the dawn-dusk terminators, and the solar wind stretches the terrestrial magnetic field for perhaps 1000 Earth radii in the antisolar direction. Since the solar wind is traveling relative to the Earth at speeds greater than the speed of compressional waves that are needed to divert the solar wind around the Earth's magnetosphere, a bow shock is formed in the solar wind upstream which slows the flow to "subsonic" velocities, diverts it around the obstacle, and heats the downstream solar wind plasma. The nose of the bow shock is about 13 Earth radii in front of the Earth. The properties of the bow shock determine the nature of the flow that interacts with the magnetosphere; these properties are thus important in the transfer of energy from the solar wind to the magnetosphere.

Fig. 1. Cut away drawing of the Earth's magnetosphere showing the major plasma regimes, current systems and flows.

The magnetosphere in Figure 1 is cut away to reveal the different regions of charged particles in the magnetosphere and the electrical currents flowing therein. The region of least energetic plasma is the plasmasphere in the innermost region of the magnetosphere which is the high altitude extension of the ionosphere. This cold, dense plasma is caused by the ionization of the neutral atmosphere by solar ultraviolet and extreme ultraviolet radiation. The tenuous plasma mantle at high altitudes is formed by the entry of solar wind along the boundary of the magnetosphere. These charged particles reach the center of the tail where processes can accelerate them to even higher energies. The dashed lines illustrate the flow of the average low energy particles outside and inside the magnetosphere. The flow on the outside is away from the Sun and on the inside toward the Sun. The electric fields associated with these flows can accelerate the charged particles to very high energies and help populate the radiation belts, also known as the Van Allen belts, both inside and outside the plasmasphere.

The thick, dark lines in Figure 1 show the major electrical current systems. The magnetopause current is that which flows due to the pressure gradient in the shocked solar wind plasma when it reaches the magnetic field of the Earth. The tail current is the part of this current which connects to the current flowing across the center of the tail, dividing it into two lobes with oppositely directed magnetic fields. This current is often called the neutral sheet current. The current associated with the energetic particles in the radiation belts which encircle the planet is called the ring current. Finally, there are currents that move along magnetic field lines rather than across them. These field-aligned currents transmit stresses from the outer magnetosphere to the ionosphere. Thus, if one were to push on the plasmas in the outer reaches of the magnetosphere, a current would flow along the magnetic field to the ionosphere. As the current flowed across magnetic fields in the ionosphere, it would exert a force on the ionosphere. Thus, the force on the outer magnetosphere ultimately is transmitted to the ionosphere and thence to the atmosphere.

Fig. 2. The near Earth neutral point model of substorms. In the top panel is sketched the magnetic topology of the magnetosphere shortly after the interplanetary magnetic field turns southward. The newly connected magnetic flux is carried into the tail as it is merged on the dayside at rate M. The magnetic flux on the dayside Day decreases and the magnetic flux in the tail Lobe increases until tail reconnection begins at rate R. This removes flux from the lobe that is convected to the dayside at rate C [R. L. McPherron, EOS, 55, 994, 1974, copyright by the American Geophysical Union].

This energy transfer also depends greatly on the direction of the interplanetary magnetic field (q.v.). If the interplanetary magnetic field points northward, parallel to the Earth's magnetic field at the stand-off point in the equatorial plane, there is minimal energy transfer. The interaction is not completely non-viscous but under normal conditions the magnetosphere remains in a quiescent state. When the interplanetary magnetic field turns southward, the process known as reconnection begins near the subsolar point as illustrated in Figure 2. The magnetic field lines of the magnetosphere and the solar wind become linked and maximal energy transfer ensues. If the rate of energy transfer is sufficiently small, this energy can be stored for some time through a buildup of magnetic flux in the tail. Eventually, this storage region becomes unstable and releases the magnetic flux and its associated energy. In this example, M measures the rate at which the interplanetary magnetic field is connected to the magnetosphere's magnetic field and the rate at which magnetic flux is carried into the magnetotail. At this time the reconnection rate, R, in the tail increases and flux is returned from the lobes to the closed field line region. This process is known as a substorm; it provides the energy for auroral displays and ionospheric disturbances observed on the surface of the Earth. If the southward interplanetary magnetic field is strong and remains southward for a prolonged period (hours), then energetic plasma moves deep into the magnetosphere, circling the Earth in a ring current. When the ring current causes a depression in the surface magnetic field of more than about 50 nT, then a geomagnetic storm (q.v.) is said to have occurred.

The classical geomagnetic storm begins with a sudden jump in the Earth's magnetic field followed within hours by a large depression of the magnetic field as the ring current builds up. Then after several days the ring current returns to quiet values. We now know that this period of storminess is initiated when a large bubble of magnetized plasma is ejected from the Sun in a process known as a coronal mass ejection (q.v.). This plasma bubble plows through the solar wind causing a shock wave in front of it. The bubble itself has large magnetic components parallel and anti-parallel to the Earth's field. When the leading shock wave hits the Earth, the magnetosphere is compressed and the surface field jumps. When the region of anti-parallel magnetic field encounters the Earth, strong reconnection begins and much energy flows into the magnetosphere from the solar wind, powering the geomagnetic storm and building up the ring current.

The arrival of the interplanetary shock can cause disruption of terrestrial power and communication systems. Power distribution systems and communication systems employ long (continent and ocean-wide) electrical conductors. When the shock wave strikes, the rapid rate of change of the magnetic field induces voltages in these conductors which may cause parts of them to fail. Historically, major power blackouts have often been the result of solar disturbances. Thus the solar-terrestrial environment has a very direct affect on our increasingly technological society.

 

Acknowledgments

The preparation of this review was supported by the National Sciences Foundation under grant ATM 90-16900.

 

References

Barton, C. E. 1989, "Geomagnetic secular variation," in The Encyclopedia of Solid Earth Geophysics edited by D. E. James, 560-577, Van Nostrand Reinhold, New York.

Chapman, S. and J. Bartels, 1940, "Geomagnetism," Oxford University Press.

IAGA Division I Working Group 1, 1987. "The International Geomagnetic Reference Field revision, 1985," J. Geomag. Geoelect., 39, 773-779.

Jacobs, J. A., 1975, "The Earth's Core," London, Academic Press.

Merrill, R. T. and M. W. McElhinny, 1983, "The Earth's Magnetic Field: It's History, Origin and Planetary Perspective," London, Academic Press.

Russell, C. T. and R. L. McPherron, 1973, "The magnetotail and substorms," Space Sci Rev., 15, 205-266.

Stacey, R. D., 1977, "Physics of the Earth," New York, Wiley and Sons.


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