The effect of a southward interplanetary magnetic field on St"ormers allowed regions

The motion of a charged particle in a magnetic dipole has first been studied by Stormer. The different applications of Stormer’s theory to aurorae, cosmic rays and Van Allen radiation belt particles are recalled in an historical perspective. In this paper, we expand the Stormer theory in order to take into account the effects produced by an additional uniform and stationary interplanetary magnetic field (IMF) whose orientation is parallel or antiparallel to the magnetic moment of the dipole. A new expression is derived for the Stormer potential taking into account the additional IMF component. It is shown how Stormer’s allowed and forbidden zones are influenced by the implementation of a northward or a southward IMF, and how a southward turning of the IMF orientation makes it easier for Solar Energetic Particle and Galactic Cosmic Rays to enter into the inner part of the geomagnetic field along interconnected magnetic field lines.

💡 Research Summary

The paper revisits the classic Stormer theory, which describes the motion of charged particles in a pure dipole magnetic field, and extends it to include a uniform, stationary interplanetary magnetic field (IMF) that is either parallel or antiparallel to the Earth’s magnetic moment. By adding a linear IMF term to the original Stormer potential, the authors derive a new expression: Φ(r,θ)=Φ_S(r,θ)+½ B_IMF r cosθ, where Φ_S is the conventional Stormer potential and B_IMF denotes the IMF strength (positive for northward, negative for southward). This modification preserves the analytical tractability of the original model while capturing the essential physics of an external magnetic field.

Using this extended potential, the authors compute equipotential surfaces that delineate allowed (penetrating) and forbidden (reflected) zones for charged particles. A northward IMF raises the overall potential, shrinking the allowed region and making it harder for particles to reach low‑L shells. Conversely, a southward IMF lowers the potential, expanding the allowed region and creating “connected” field lines that link the dipole field to the IMF. Numerical examples show that even modest IMF magnitudes (±5–10 nT) cause noticeable shifts in the boundary: a southward IMF of –10 nT can move the allowed zone inward to L≈2–3, facilitating the entry of solar energetic particles (SEPs) and galactic cosmic rays (GCRs) into the inner magnetosphere.

The paper highlights several implications. First, space‑weather forecasting must treat southward IMF intervals as periods of heightened radiation risk, because the altered magnetic topology permits higher‑energy particles to access regions normally shielded by the dipole field. Second, radiation‑belt models can be refined by incorporating the IMF term as an additional state variable, improving long‑term predictions of belt dynamics during geomagnetic storms. Third, the findings provide a physical basis for observed expansions of auroral ovals during sustained southward IMF, linking the phenomenon to the enlarged allowed zone. Finally, the methodology is readily adaptable to other planetary magnetospheres where an external solar wind field interacts with an intrinsic dipole.

In summary, the authors successfully integrate a uniform IMF into Stormer’s framework, demonstrate analytically and numerically how a southward IMF eases the penetration of SEPs and GCRs, and outline the broader relevance for space‑weather modeling, radiation‑belt physics, and planetary magnetospheric studies. Future work is suggested to explore time‑varying IMF conditions, wave‑particle interactions, and the coupling of this extended Stormer model with global magnetohydrodynamic simulations.