Classification of magnetic shells

A new method of calculating the magnetic shell parameter L, based on Pennington's perturbation method for calculating the shape of magnetic shells, is presented. In this approach the shell passing a given point is characterized by two parameters, L and a function αm of the local pitch angle. The dependence on θm is shown to be very weak, however, so that it may be neglected to a good approximation. Auxiliary functions necessary for this method are tabulated, including a 48-coefficient expansion of the geomagnetic potential in tilted-dipole coordinates, and the results are compared with those derived by McIlwain's method. The results are found to be, in general, within several per cent of those numerically integrated by McIlwain.