[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.

[1] The Cluster spacecraft were favorably positioned on the nightside near the equatorial plasmapause of Earth at L ∼ 4.3 on 30 March 2002 to observe electromagnetic ion cyclotron (EMIC) rising tone emissions in association with Pc1 waves at 1.5 Hz. The EMIC rising tone emissions were found to be left-hand, circularly polarized, dispersive, and propagating away from the equator. Their burstiness and dispersion of ∼30s/Hz rising out of the 1.5 Hz Pc1 waves are consistent with their identification as EMIC triggered chorus emissions, the first to be reported through in situ observations near the plasmapause. Along with the expected H + ring current ions seen at higher energies (>300 eV), lower energy ions (300 eV and less) were observed during the most intense EMIC triggered emission events. Nonlinear wave-particle interactions via cyclotron resonance between the ∼2-10 keV H + ions with temperature anisotropy and the linearly-amplified Pc1 waves are suggested as a possible generation mechanism for the EMIC triggered emissions. Citation: Pickett, J. S., et al. (2010), Cluster observations of EMIC triggered emissions in association with Pc1 waves near Earth's plasmapause, Geophys.

International audienceWe report on quasi-parallel whistler emissions detected by the near-earth satellites of the THEMIS mission before, during, and after local dipolarization. These emissions are associated with an electron temperature anisotropy alpha=T_⊥e/T_||e>1 consistent with the linear theory of whistler mode anisotropy instability. When the whistler mode emissions are observed the measured electron anisotropy varies inversely with beta_||e (the ratio of the electron parallel pressure to the magnetic pressure) as predicted by Gary and Wang (1996). Narrow band whistler emissions correspond to the small alpha existing before dipolarization whereas the broad band emissions correspond to large alpha observed during and after dipolarization. The energy in the whistler mode is leaving the current sheet and is propagating along the background magnetic field, towards the Earth. A simple time-independent description based on the Liouville's theorem indicates that the electron temperature anisotropy decreases with the distance along the magnetic field from the equator. Once this variation of alpha is taken into account, the linear theory predicts an equatorial origin for the whistler mode. The linear theory is also consistent with the observed bandwidth of wave emissions. Yet, the anisotropy required to be fully consistent with the observations is somewhat larger than the measured one. Although the discrepancy remains within the instrumental error bars, this could be due to time-dependent effects which have been neglected. The possible role of the whistler waves in the substorm process is discussed