Archimedean Spiral Distribution of Electrons in Earth Inner Magnetosphere

We present an analytic theory to demonstrate that electrons with an initially asymmetric spatial distribution would form an Archimedean spiral distribution in the inner magnetosphere. Such evolution is a result of the gradient/curvature drift, whose angular velocity decreases with radial distance. It has been known for a long time that spectrograms of energetic electrons in Earth's inner radiation belt exhibit time-varying organized peaks and valleys. Recent observations from Van Allen Probes have shown that such regular patterns are ubiquitous and are referred to as “zebra stripes”. Our theory can predict zebra stripes accurately. We also use the Rice Convection Model (RCM) to simulate zebra stripes. For the simplest situation with the dipolar magnetic field model, the analytic theory perfectly matches with the RCM simulation. In a realistic simulation, the RCM reproduces the time-dependent structures and evolution of the zebra stripes, which are in good consistency with Van Allen Probes observations.