The Van Allen radiation belts are two regions encircling the Earth in which energetic charged particles are trapped inside the Earth's magnetic field. Their properties vary according to solar activity and they represent a hazard to satellites and humans in space. An important challenge has been to explain how the charged particles within these belts are accelerated to very high energies of several million electron volts. Here we show, on the basis of the analysis of a rare event where the outer radiation belt was depleted and then re-formed closer to the Earth, that the long established theory of acceleration by radial diffusion is inadequate; the electrons are accelerated more effectively by electromagnetic waves at frequencies of a few kilohertz. Wave acceleration can increase the electron flux by more than three orders of magnitude over the observed timescale of one to two days, more than sufficient to explain the new radiation belt. Wave acceleration could also be important for Jupiter, Saturn and other astrophysical objects with magnetic fields.

[1] We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.

Magnetic reconnection leads to energy conversion in large volumes in space but is initiated in small diffusion regions. Because of the small sizes of the diffusion regions, their crossings by spacecraft are rare. We report four-spacecraft observations of a diffusion region encounter at the Earth's magnetopause that allow us to reliably distinguish spatial from temporal features. We find that the diffusion region is stable on ion time and length scales in agreement with numerical simulations. The electric field normal to the current sheet is balanced by the Hall term in the generalized Ohm's law, E(n) approximately jxB/ne.n, thus establishing that Hall physics is dominating inside the diffusion region. The reconnection rate is fast, approximately 0.1. We show that strong parallel currents flow along the separatrices; they are correlated with observations of high-frequency Langmuir/upper hybrid waves.