Investigation of the Magnetosphere of Ganymede with Galileo's Energetic Particle Detector

Ph.D. dissertation by Shawn M. Stone, University of Kansas, 1999.

Copyright 1999 by Shawn M. Stone.  Used with permission.

1.1 Anatomy of a Magnetosphere

The solar system is extensively populated with charged particles and electromagnetic fields. The discipline of Space Plasma Physics is concerned with the interaction of these energetic charged particles with the electromagnetic field in space, especially of those at the Earth and other planets. The greatest source of energetic charged particles in the interplanetary medium is the sun’s outwardly expanding solar corona called the solar wind [Parker, 1958, 1959]. The solar wind is a plasma, made of primarily equal number of protons and electrons, whose properties vary with time and distance from the sun. At the orbit of the Earth (1 AU) the average properties of the solar wind plasma are number density n~=5-10 cm^-3, velocity v~=400 km/s, and thermal temperature T~=1x10⁵°K [Wolffe et al., 1966; Neugebauer and Snyder, 1966; Formisano et al., 1974]. As the solar wind flows outward, it encounters the magnetic fields of the planets such as the Earth or Jupiter. The interaction induces large-scale currents that confine the planetary magnetic field, diverting the solar wind around it forming a magnetic cavity called the magnetosphere [Gold, 1959; Beard, 1964]. Figure 1.1 shows a schematic diagram of the Earth's magnetosphere.

Figure 1. A schematic diagram of the magnetosphere of the Earth. The incident solar wind plasma encounters the magnetic field of the Earth which acts as an obstacle diverting plasma around it. The other planets in the solar system with intrinsic magnetic fields have a magnetosphere with similar structure [Parks, 1991].

1.1.1 Magnetospheric Boundaries

The Earth is an obstacle to the solar wind flow with a velocity of U_o= 400 km/s in the solar wind frame. The speed that information travels in a plasma is given by the sonic speed

and the Alfven speed

where γ is the polytropic index, T_e and T_i are the electron and ion temperatures, k_B is Boltzmann's constant, m_i is the ion mass, B_o is the magnetic field strength, μ_o is the permeability of free space, and ρ_o is the mass density of the plasma. Using the parameters for the solar wind given in the previous paragraph and γ=5/3 yields

The Mach numbers for the solar wind plasma at the Earth are then given by

where M_S and M_A are the sonic and Alfvén Mach numbers respectively. The result is a supersonic (M_S>1) and super-Alfvénic (M_A>1) plasma flow. The consequence of this is when the solar wind impacts the planetary magnetic field of the Earth, the waves are not fast enough to tell the incoming plasma to turn. A bow shock is then formed upstream towards the sun [Sonett and Abrams, 1963; Freeman, 1964; Tidman, 1967; Kaufmann, 1968]. A bow shock is analogous to the shock wave that exists detached ahead of a bullet as it moves through the air [Axford, 1962; Kellogg, 1962] but is different in nature because the plasma is collisionless [Sonett et al., 1964].

The boundary that separates the solar wind plasma from the magnetosphere is called the magnetopause. The location of the magnetopause boundary is determined by the hydromagnetic pressure balance between the plasma pressure of the solar wind and the magnetic pressure of the geomagnetic field:

where B is the magnitude of the geomagnetic field at the equatorial standoff distance of the magnetopause. The average pressure of the plasma at the standoff distance (subsolar point) is given by

and if the dipole model for the geomagnetic field is used (discussed in Chapter 3):

where B_E is the equatorial surface strength of the Earth's field, r_o is the standoff distance in Earth radii (1 R_e=6.38 x 10³ km), and the factor of 2 comes from the fact that the field is compressed at the boundary [Beard, 1964, 1973]. Putting Equations [1.5] through [1.7] together and solving for r_o yields

Using the parameters given above for the Earth (B_E= 3 x 10⁴ nT) , the offset distance of the magnetopause is approximately 10 R_E.

Magnetospheres also have long tails called magnetotails. Magnetotails are produced by the interaction of the magnetized solar wind with the planet's magnetic field. Although this interaction is collisionless, it transfers part of the solar wind momentum and energy to the planetary magnetic field, stretching it in the anti-solar direction [Ness, 1965]. The length of the tail depends on the magnetic moment of the planet. For the Earth, the tail stretches out to approximately 200 Earth radii (1 R_e=6.38 x 10³ km). Jupiter's magnetotail is believed to extend all the way to Saturn's orbit [Parks,1991].

1.1.2 Trapped Radiation, Ring Currents, and Corotational Plasma

Magnetospheres are populated with charged particles. The configuration of the inner magnetosphere of the Earth is such that charged particles are trapped in a magnetic bottle (Chapter 2). This fact was first discovered by the Explorer I satellite in 1958 and was dubbed the Van Allen Radiation Belts [Van Allen, 1959, 1983]. The sources of these charged particles are both external to the magnetosphere and local. The solar wind, planetary ionospheres, satellite sputtering, and cosmic ray albedo neutron decay (CRAND) all contribute [Hess, 1968].

The trapped particles in planetary magnetospheres obey the Lorentz force. They gyrate around the magnetic field lines as well as bounce in a longitudinal motion (North-South direction). In addition, due to the inhomogeneity and the bending of magnetic field lines, forces arise that cause the particles to drift in an azimuthal direction. This drift motion is charge-dependent, and electrons and ions move in an opposing manner, producing a net current called a ring current. A considerable amount of energy is contained in the ring current during geomagnetic storms [Frank, 1967; Berko et al., 1975].

Another azimuthal motion of charged particles is produced by the electric field that is induced by a rotating planetary magnetic field called the corotational electric field [Taylor and Hones, 1965]. The motion is not charge dependent; both species of particles corotate with the planet in a corotational plasma. The speed of corotation depends on the angular velocity of the planet, on the distance from the planet, and on the local magnetic field strength. This is discussed in Chapter 2.

Next: 1.2 Satellites Embedded Within Magnetospheres 

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