Yet another caveat to using the Dessler‐Parker‐Sckopke relation

The analytical formulation of the Dessler‐Parker‐Sckopke (DPS) equation relating the energy content of the ring current to the magnetic field depression at the Earth's center is examined. To conduct this study, a method is presented for numerically integrating inner magnetospheric pressure distributions according to the Biot‐Savart law to obtain magnetic field perturbations at an arbitrary location. It is found that the implicit assumption of the DPS relation requiring that all of the particle pressure is included in the integration can generate large errors relative to the true perturbation. When there is a nonzero pressure just inside the outer boundary of the integration volume, the DPS relation implicitly includes large azimuthal currents at this pressure discontinuity. By including ghost cells of adiabatically decreasing pressure beyond the outer boundary, a “true” perturbation from the currents within the simulation is obtained. The ratio of this corrected value to the DPS value systematically varies according to a simple pressure ratio. Other aspects of the DPS relation are also confirmed with this code, including the validity criterion imposed by the plasma pressure anisotropy and the validity of the relation for any local time asymmetry. The inclusion of closure currents in the perturbation calculation, which were not part of the DPS derivation, changes the local time profile of the perturbation and can make either a negligible or a substantial contribution in either a positive or a negative sense to the globally averaged perturbation.