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.

Three‐component dynamic spectrograms (0–80 mHz) of AMPTE/CCE magnetic field data from August 24, 1984, through December 7, 1985, have been used to survey ULF pulsation activity occurring from L = 5 to 9 in the equatorial magnetosphere (±16° magnetic latitude) at all local times. The data were scanned visually, and each half‐hour interval was categorized by spectral type, approximate polarization, spectral intensity, and spacecraft location to produce a data base representing 7231 hours of observations. Coherent pulsations are divided into nine categories which fall into four basic classes: (1) harmonic toroidal resonances (17.9% of the data), (2) fundamental mode toroidal resonances (11.0%), (3) radially polarized pulsations (5.2%), and (4) compressional low‐frequency pulsations (10.6%). Classes (1) and (2) are not mutually exclusive. Intervals devoid of coherent pulsations are divided into five levels according to noise intensity and account for 56.8% of the observations. Uncategorized events represented 4.2% of the data. The spatial occurrence distributions of each pulsation category and the latitude distribution of selected categories have been examined. The basic conclusions of the study are as follows: (1) Harmonic toroidal resonances are found to be the dominant coherent activity on the dayside, particularly in the prenoon hours, where they occur 60% of the time. Their region of excitation is uniformly distributed in radial distance and extends in local time from 0600 to 1600 but cuts off sharply at the local time boundaries. The pattern is consistent with excitation by a dayside energy source, possibly upstream waves, but the spatial distribution places constraints on models of energy transmission. (2) Fundamental toroidal resonances are observed with an occurrence rate of 40% to 50% for L > 8 at dawn but were observed less than 10% of the time at dusk for L > 8. Dusk is also the site of several types of pulsations of sufficient average intensity to obscure fundamental mode resonances, so this trend may be exaggerated by masking effects. Nonetheless, the dawn/dusk asymmetry is sufficiently remarkable to warrant further study. The occurrence distribution exhibits a pronounced node at the magnetic equator, and the occurrence rate for MLAT > 13° at dawn is ≈80%, suggesting that the fundamental mode resonances are present continually at the dawn flank. The preference for occurrence at the flank suggests that the Kelvin‐Helmholtz instability is ultimately responsible for driving the resonances. (3) Radially polarized pulsations are observed ≈10% of the time except in the 0400–1100 MLT, sector where their occurrence rate is less than 5%. The occurrence distribution of radially polarized waves suggests that they are driven by wave‐particle interactions but not by freshly injected particles. (4) Storm time Pc 5 type waves were observed most often at dusk for L > 8 where they occurred ≈30% of the time. A secondary maximum in storm time Pc 5 type occurrence near dawn was also found. The spatial distribution of storm...

[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.

Abstract. We have calculated the integrated ULF wave power in the Pc5 band at two stations, Kevo (part of the International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometer array in Scandinavia, at auroral zone latitudes), and Cape Dorset (part of the Magnetometer Array for Cusp and Cleft Studies (MACCS) in Arctic Canada, at cusp latitudes), and compared this power against the solar wind velocity for the last six months of 1993, a period characterized by two persistent high-speed solar wind streams. We find for both local noon at Cape Dorset, and for local morning at Kevo, the Pc5 band power (0.002 -0.010 Hz) integrated over a six-hour period exhibits a clear power-law dependence on the solar wind velocity. At Cape Dorset we found power c• Vsw 4, with a correlation coefficient r = 0.73, and at Kevo we found power c• Vsw 6'5, with r = 0.74. Much of the remaining variation in Pc5 power is due to temporal patterns evident at both stations in response to recurrent high speed streams. Power was strongest at the leading edge of each high speed stream and subsequently decreased more quickly than Vsw. Our observations suggest that it is insufficient to make estimates of Pc5-range ULF wave power on the basis of Vsw alone' one must consider other physical factors, either intrinsic to the solar wind or related to its interaction with Earth's magnetosphere. The Kelvin-Helmholtz instability is often considered to play a dominant role in this interaction, and the level of instability depends on both velocity and density. By means of a simple simulation using typical density and velocity values during the passage of a high speed stream, we were able to obtain good agreement with the t.emporal variations we observed. Finally, this study indicates that ground-based pulsation observations can provide reliable proxies of the initial passage of high speed solar wind streams past Earth.

The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes.