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4.8.2 Solving and Mapping the Boundary

The external multipole model given in Section 4.3 is unphysical outside the magnetopause boundary, as unphysical as an image dipole, since the terms are directly proportional to r.  It is essential, then, to map the boundary of the magnetopause and tail field so that it can be turned off when the particles exit the magnetosphere of Ganymede.  The ideal method to approach this problem would have been to propose a boundary and then impose currents upon this boundary and integrate via the Biot-Savart law. Unfortunately, the magnetic field geometry of Ganymede is more complicated than a dipole. However, it is satisfactory to take the solution in Tables 4.8 and 4.9 and trace field lines until a balance is reached between the internal and external field lines, thus tracing out the boundary where the tangential components of the magnetic field vanish. The first guess boundary is based on a dipole with magnetic moment of the g₁⁰ of the respective encounter.  Figure 4.27 shows a trace for the G2 model. The function that is used for the fit is

where z_o is the offset distance of the boundary on an axis where the boundary is completely axially symmetric, denoted here as axial coordinates. This boundary is then rotated about the GSII X axis by a and GSII Z axis by b (Figure 4.28) until the inbound and outbound crossings reach a minimum, thus attaining the preliminary abberation angles from corotation.  The boundary is then refit in the same manner as above and the process repeated until there is no significant change in the aberration angles (less than a degree).  Table 4.10 lists the coefficients of Equation [4.35] for G2 and G7 along with the aberration angles that were derived from this process.

Figure 4.27 Magnetic line trace for the G2 encounter where r_o=2.0 R_g. The magnetic field from the internal Ganymede sources and the external Jovian field combine to define the boundary which is then sampled, and the data gathered from this sampling is fit to Equation [4.35].

Figure 4.28 Diagram representing the variation of the preliminary boundary by the aberration angles a and b.

Table 4.10 The boundary parameters for G2 and G7 derived from the fit of Equation [4.35]. The offset distance r_o was defined as 2.0 R_g for the G2 encounter.

Next: 4.8.3 Adding Finite Thickness to the Boundary

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Updated 10/22/02, T. Hunt-Ward
tizby@ftecs.com