This module allows you to explore the magnetic field configurations of multipolar magnatic fields of different order and degree.
There are three coefficients that describe a dipole magnetic field in the spherical harmonic expansion g10, g11, and h11. These correspond to the projection of the dipole moment along the z-axis (rotation), the x-axis, and the y-axis (in the rotational equator).
There are five coefficients that describe a quadrupole magnetic field in a spherical harmonic expansion. The five coefficients correspond to quadrupoles constructed from antiparallel, separated dipole moments. g20 corresponds to a separation along the rotation axis. This is called a zonal (rotationally symmetric) moment. The other four are planar with separation of the dipoles perpendicular to the dipole direction. g21 has the dipole moment along z and separated in y; h21 has the dipole moment along z and separated in x; h22 has the dipole moment along y and separated in x; g22 has the dipole moment along a direction at 45° to the x- and y-axes and a separation along a line at 45° to the x- and y-directions. That these five configurations provide all possible quadrupole fields (separated dipole pairs) can be shown by expressing the dipoles as separated monopoles and comparing.
That there are seven coefficients that describe an octupole magnetic field can be shown by expressing the dipoles as separated monopoles and comparing the spherical harmonic expansion g30, g31, h31, g32, h32, g33, and h33. These correspond to octupoles created by separating two quadrupoles. The g30 is a zonal moment created by separating two oppositely directed zonal quadrupoles along the z-azis (rotational). Two planar octupoles, g31 and h31, are constructed from linear quadrupoles; two planar types, g33 and h33, are constructed from planar quadrupoles and there are two cubic types, g32 and h32. That these seven octupole configurations provide all possible octupole fields (separated quadrupole pairs) can be seen by expressing the moments as distributed monopoles and comparing.