A direct analytic method of calculating the quadrupole parameters of a planetary magnetic field |
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| Authors: | D M Willis |
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| Institution: | Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, England |
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| Abstract: | Summary. Attention is drawn to a direct analytic method of calculating the quadrupole parameters of a planetary main magnetic field. Following a brief survey of the general theory of magnetic multipoles, an explicit algorithm is derived for calculating the quadrupole moment and the directions of the two quadrupole axes, given the five spherical harmonic coefficients of the second degree. It is shown that the direct analytic method of calculating the quadrupole parameters yield results for the geomagnetic quadrupole that are in exact agreement with those obtained by the more usual iterative procedure. Moreover, the direct analytic method has the distinct advantage that it does not require approximate values of the quadrupole parameters to be specified in advance. The direct analytic method of solution is used to calculate the quadrupole parameters for three different models of the main field of the Earth at epoch 1975; these computations provide some indication of the current uncertainties in the geomagnetic quadrupole parameters. It is also pointed out that a pseudo-quadrupole moment, which has been used to compare the quadrupole strengths of different planetary magnetic fields, is not strictly consistent with Maxwell's classical definition of a quadrupole moment. A precise physical definition of this pseudo-quadrupole moment is propounded. |
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