Archimedean Spiral Distribution of Energetic Particles in Earth's Inner Radiation Belt

Archimedean spirals are common in various fields such as biology, engineering, astronomy, and space physics. Here we report the discovery of patterns resembling the general Archimedean spirals in particle distributions in the Earth radiation belt. Our analytic theory and numerical simulations demonstrate that electrons with initially asymmetric spatial distributions form such spirals in the inner magnetosphere, where particles at smaller radial distances move more slowly in angular velocity. These spirals result in time-varying peaks and valleys in particle fluxes, referred to as "zebra stripes," which are well consistent with Van Allen Probes measurements. Although the initial asymmetric distribution may be seeded by the electric field in the magnetosphere, the spiral formation does not require them. Furthermore, we show that, due to the same fundamental motion of charged particles in regions dominated by dipole fields, this spiral phenomenon may also appear in the proton distributions, as well as in planetary magnetospheres. The Archimedean spiral is named after the 3rd-century BC Greek mathematician Archimedes. Such spirals have been seen from the sunflower head, Iridogorgia to galactic arms. Throughout the solar system, the average configuration of the background magnetic field also aligns with Archimedean spirals, as it is dragged by charged particles that are ejected radially from the surface of the rotating Sun, a fundamental discovery made by E. N. Parker. However, it remains unknown whether an Archimedean spiral exists in the near-Earth space. Here we report for the first time the discovery of patterns similar to the general Archimedean spirals in particle distributions in the radiation belt, a region filled with energetic charged particles surrounding Earth. This happens because electrons closer to the Earth move slower in the angular direction. These spirals manifest as time-varying peaks and valleys in the electron spectagrams, named as "zebra stripes." Our theory and simulation results are well consistent with the measurements of the Van Allen Probes. Besides, our theory predicts that these spirals could occur on protons and other planets with similar magnetic fields. The first known discussion and discovery of Archimedean spiral structures in Earth's magnetosphere Electrons' general Archimedean spiral-like distribution results in the formation of "zebra stripes" in the inner radiation belt Our findings hold exciting implications for understanding magnetospheric physics beyond our planet