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.