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 discuss chorus emissions measured by the four Cluster spacecraft at close separations during a geomagnetically disturbed period on 18 April 2002. We analyze the lower band of chorus below one half of the electron cyclotron frequency, measured at a radial distance of 4.4 Earth's radii, within a 2000 km long source region located close to the equator. The characteristic wave vector directions in this region are nearly parallel to the field lines and the multipoint measurement demonstrates the dynamic character of the chorus source region, changing the Poynting flux direction at time scales shorter than a few seconds. The electric field waveforms of the chorus wave packets (forming separate chorus elements on power spectrograms) show a fine structure consisting of subpackets with a maximum amplitude above 30 mV/m. To study this fine structure we have used a sine-wave parametric model with a variable amplitude. The subpackets typically start with an exponential growth phase, and after reaching the saturation amplitude they often show an exponential decay phase. The duration of subpackets is variable from a few milliseconds to a few tens of milliseconds, and they appear in the waveform randomly, with no clear periodicity. The obtained growth rate (ratio of the imaginary part to the real part of the wave frequency) is highly variable from case to case with values obtained between a few thousandths and a few hundredths. The same chorus wave packets simultaneously observed on the different closely separated spacecraft appear to have a different internal subpacket structure. The characteristic scale of the subpackets can thus be lower than tens of kilometers in the plane perpendicular to the field line, or hundreds of kilometers parallel to the field line (corresponding to a characteristic time scale of few milliseconds during the propagation of the entire wave packet). Using delays of time-frequency curves obtained on different spacecraft, we have found the same propagation direction as obtained from the simultaneous Poynting flux calculations. The delays roughly correspond to the whistler-mode group velocity estimated from the cold plasma theory. We have also observed delays corresponding to antiparallel propagation directions for two neighboring chorus wave packets, less than 0.1 s apart.

Although collisionless shocks primarily exist to mediate the flow of supermagnetosonic plasma, they also act as sites for particle acceleration. It is now well known that for certain magnetic field geometries, a portion of the inflowing plasma returns to the upstream region rather than being processed by the shock and passing irreversibly downstream. The combination of the inflowing plasma and this counterstreaming component upstream of the shock is subject to a number of plasma instabilities, leading to the generation of waves. These waves interact in a highly complex manner with the ions and electrons making up the plasma and can cause part of the plasma distribution to reach high energies.The region of space upstream of the bow shock, magnetically connected to the shock and filled with particles backstreaming from the shock is known as the foreshock. As discussed in Balogh et al. (2005), the bow shock can be classified into quasi-perpendicular and quasi-parallel shock regions according to the angle θ Bn between the shock normal n and the direction of the solar wind magnetic field B. For the quasi-perpendicular bow shock (θ Bn > 45 • ), the foreshock is restricted to the shock foot, while in the quasi-parallel part of the bow shock (θ Bn < 45 • ), it

[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.

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