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# Magnetospheres

This module is designed to introduce you to some of the elementary properties of planetary magnetic fields.

## Planet

You can select to display the magnetic fields of the planets Earth, Mercury, Jupiter, Saturn, Uranus, and Neptune. The planets Venus and Mars have no intrinsic magnetic field detectable by orbiting spacecraft. There are currently no plans to measure the magnetic field of the dwarf planet Pluto.

## Magnetosphere

You can choose among the following magnetic field options: dipole, image dipole, spherical, elliptical, and the empirical model of Tsyganenko. These options are described below.

• Dipole
• This option shows the dipole magnetic field lines, the directions that one would follow with a three-dimensional compass for each of the planets that has a significant planetary magnetic field. The size of the region in which the magnetic field is drawn is proportional to the size of the magnetic cavity, or magnetosphere that the planet carves out of the solar wind. Thus tiny Mercury with its very weak magnetic field appears large because its magnetosphere is small, while the planet Jupiter appears very small because in comparison its magnetosphere is very large.

For these displays we have kept the magnetic axis of each planet vertical so that the rotation axis is tilted an amount equal to the angle between the magnetic dipole axis and the rotation axis. On Saturn this angle is zero, while on the Earth it is 11°. A dipole field is the simplest approximation to a planetary magnetic field. Actual planetary magnetic fields can be much more complex than this, especially near the planet’s surface.

The dipole magnetic field in a vacuum is the simplest magnetic configuration encountered in nature. It arises due to currents in a loop. The strength of such a current loop is called its magnetic moment and is proportional to the area of the loop times the current carried by the loop. The dipole magnetic moment is also numerically equal to the value of the magnetic field at any point in the equatorial plane times the cube of the distance from the center of the body. The magnetic moment of the Earth is approximately 8 x 1015 Tm3.

• Image dipole
• The magnetized plasma of the solar wind blows against the intrinsic magnetic fields of the planets, confining the planetary field to a cavity called the magnetosphere. In this and the other displays the solar wind blows from the left, confining the planetary field and stretching it out to the right. The lines emanating from each planet are called lines of magnetic force or magnetic field lines. They are displayed in the noon-midnight meridian.

The magnetosphere is a complex and dynamic system. In order to understand this system this module presents a series of approximations to the Earth’s magnetosphere of increasing complexity. The first model that displays some of the properties of a real magnetosphere is the image dipole model displayed here. The image dipole model was the first model of the Earth’s magnetosphere and it was proposed by S. Chapman and V.C.A. Ferraro in 1931. They correctly hypothesized that the solar wind was highly electrically conducting and would exclude the Earth’s field from its interior, compressing the field to the right-hand side of this diagram. If the interface with the solar wind were a flat plate, the distortion in the magnetic field on the right-hand side of the plate would be the same as if there were a dipole field on the left-hand side of the plate at the same distance from it and of the same strength (magnetic moment). This is equivalent to the Earth’s magnetic field being reflected in a mirror and is therefore called the image dipole model of the magnetosphere.

The magnetic field at the equator at the forward boundary of the magnetosphere, the interface with the solar wind is exactly double that of a pure dipole at the same location. The field component normal to the interface is zero. There are two null points where the total field is zero and above and below which the field points in opposite directions parallel to the plate. Bringing the image dipole closer to the Earth simulates the effect of an increase of the solar wind pressure. This model was developed by Chapman and Ferraro to explain the phenomenon called the geomagnetic storm.

• Spherical
• The interface between the solar wind and the magnetic field is not a flat plate but a curved surface. To examine the effect of the curvature of this surface on the magnetic field inside the magnetosphere, this option shows the situation in which the Earth’s dipole finds itself in a spherical superconductor. This resembles somewhat the situation in which the solar wind velocity dropped to zero but it retained sufficient thermal pressure (the extended solar corona) to confine the magnetosphere on all sides. It differs from this case because the pressure required to confine the magnetic field of a dipole within a spherical surface is not uniform over that surface.

As shown here the field is compressed and enhanced everywhere, but most noticeably in the outer reaches of the magnetosphere near the equator, where it is tripled in strength. This compares with the doubling of the field strength at the boundary, or magnetopause, in the case of the image dipole model.

• Ellipsoidal
• The ionized, extended, upper atmosphere of the Sun, called the solar corona, is not static but expands outward from the Sun. This confines the Earth’s magnetic field on the sunward, or dayside, of the magnetosphere, and stretches it out in the antisolar direction.

On the dayside of the Earth the magnetopause can be approximated by an ellipsoid of revolution symmetric about the Earth-Sun line with the Earth at one focus of the ellipsoid. This option lets us examine the magnetic structure of such a magnetosphere as first developed by N. Tsyganenko in 1989. The figure shows the magnetic field in the noon-midnight meridian plane for a dipole magnetic field enclosed by a ellipsoidal conductor. The nose of the magnetosphere is 10.0 REarth in front of the Earth and the end of the tail is 76.6 REarth behind the Earth. In this model the dayside magnetic field is more compressed than in the image dipole model but less than in the spherical model. The nightside field is weaker than in the image dipole and spherical models but not as weak as in the real magnetosphere, in which the plasma provides some of the pressure that balances the pressure applied by the solar wind.

• Empirical model of Tsyganenko
• The image dipole, spherical, and ellipsoidal magnetosphere options present the expected field configuration of a magnetosphere devoid of plasma. Thus, no electric currents could flow within the magnetosphere, either along or across the magnetic fields lines. The only electric currents that could flow were within the Earth and on the surface of the magnetosphere (i.e., the magnetopause). This option shows the model developed by Tsyganenko (1989) based on magnetic field observations that includes currents within the magnetosphere, and simulates more realistically the actual field configuration of the Earth’s magnetosphere. The figure shows the magnetic field in the noon-midnight meridian plane for the empirical model of Tsyganenko.

## Show

• Magnetic field lines
• Shows the planet’s magnetic field lines. A magnetic field line is a path through a magnetic field that is everywhere parallel to the local magnetic field.

• Isocontours
• Shows the contours along which magnetic field strength is constant.

For the image dipole magnetosphere, the solar wind acts to force the contours slightly closer to the Earth on the sunlit side (left) as opposed to the nightside (right). This difference in strength between noon and midnight can be observed (on the surface of the Earth) as a diurnal variation.

Because of the asymmetry of the magnetic field in the ellipsoidal and empirical models, a diurnal change is seen as the Earth turns. Because of the presence of plasma in the tail and the cross tail current, the diurnal variation is greater for the empirical model than other models in this module.

• Planet grid lines
• Displays a grid, with spacing between lines equal to the the displayed planet’s radius.

## Measuring the magnetic field using the mouse

To measure the planetary magnetic field, move the pointer across the screen and click the mouse. A small random component has been added to the location of the cursor so that repeated clicks at apparently the same location are in fact at slightly different locations and result in different measured fields. This overcomes limitations of the finite digitization of locations on the screen.

The coordinate system in which the measurements are made and written in the boxes on the left are aligned with the magnetic dipole axis (z) and the equatorial plane (x). The coordinate z-axis is upward in the diagram whether or not the magnetic dipole is aligned parallel or antiparallel to this direction. The coordinate x-axis is positive to the left. The origin of the coordinate system is the center of the planet.

The quantities in the boxes are as follows.

Pointer position (Cartesian)
Gives the x and z location of the measurement in planetary radii.
Magnetic field (Cartesian)
Gives the two components of the magnetic field in nanoTeslas (nT). A Tesla is a Wb/m2 or 10,000 Gauss.
Pointer position (Polar)
Gives the position of the pointer in polar coordinates. The Radius box gives the distance from the center of the planet in planetary radii. The Magnetic latitude box gives the angle in degrees that the radius vector makes with the equator, i.e., the latitude of the point of observation. The colatitude is 90° - θ.
Magnetic field (Polar)
Gives the two components of the magnetic field in a polar coordinate system. The BR component is radially outward. The BT component is tangential to the surface of the planet and in the direction of the colatitude, i.e., from the upward pole toward the equator. It is downward at the Earth’s equator.
Total field and invariant latitude
Gives the total magnetic field, which is the square root of the sum of the squares of BR and BT, and the invariant latitude, which is the magnetic latitude in degrees where the field line meets the surface of the planet. If L is the equatorial distance from the center of the planet to the field line, then the invariant latitude is the angle whose cosine is the reciprocal of the square root of L.