CM4 Toroidal Field (Ionospheric Coupling Currents)
When establishing the form of the basis functions used to represent ionospheric fields, it was assumed that the source currents flowed in a region that was entirely below the Magsat and POGO satellite sampling shells. In addition, a relationship was assumed between the external and internal fields from these currents based upon the concept of an equivalent sheet current flowing on a sphere at r = a + 110 km. If displacement currents are neglected, then the source currents are solenoidal, and these assumptions may be used for current loops or circuits which do not pierce the sampling shell, which is true for the E-region. However, in reality, these ionospheric currents are coupled to the magnetospheric and ionospheric E-region currents at the geomagnetic conjugate point through coupling currents which flow along the field lines of the Earth s magnetic field. This means, for instance, that the Magsat sampling region between 350 km and 550 km will be penetrated by F-region current whose associated magnetic field will not be curl-free, and hence, will not be expressible as the gradient of a potential. It should also be noted that in general only vector, as opposed to scalar, samples can detect these fields, since they are almost always perpendicular to the main field. Hence, only measurements from the Magsat satellite will be considered here.
Perhaps the largest difference between CM3 and CM4 is the resolution of toroidal fields generated by in situ F-region currents in the satellite sampling shells.
