Euler potentials and geomagnetic drift shells

The equation of drift surfaces, traced by the guiding center motion of charged particles moving in a magnetic field, is discussed in terms of Euler potentials α and β. Particular attention is given to fields deviating to a limited extent from a dipole configuration, for which it is shown that the result is related to the drift-shell parameter L, with an added ‘shell-splitting function’ G1, which can be approximately derived. Such an approximation is used to derive shell splitting in a model of the magnetosphere, and the results are compared to exact ones obtained numerically. An improved drift shell parameter L′, replacing McIlwain's L in this case, is also discussed.