Polar caps and auroral zones under idealized axisymmetric magnetic fields

The geomagnetic field, modified by the solar wind, determines the shape, area and location of polar caps and auroral zones, among other magnetosphere and upper atmosphere characteristics. Since the field varies greatly with time it is of interest to analyze polar caps and auroral zones variations linked to magnetic field variations of intensity and pattern. Polar caps and auroral zones locations and areas for various single harmonic axial field configurations are obtained analytically assuming a simple magnetopause model. As the axial degree n increases, the polar caps and auroral zones total number, given by n + 1 and 2n respectively, also increase. However, their total areas decrease from a larger value in the case of an axial dipole to a minimum for an axial octupole (n = 3), and then increase for increasing degrees. The increasing rate is much higher in the auroral zones case to the point that it exceeds the dipolar value at n = 5 while in the polar caps case this occurs at n = 8. The absolute latitudes of the auroral zones and polar caps that reside around the geographical poles increase with axial degree. Our results represent an end-member case of the evolution of auroral zones and polar caps during polarity reversals if the transition involves axial dipole energy cascade to higher axial degrees. Evidence for such an energy transfer is found in the historical record of the geomagnetic secular variation.