Testing linear theory of EMIC waves in the inner magnetosphere: Cluster observations

In this paper, we test whether time periods with hot proton temperature anisotropy are associated with electromagnetic ion cyclotron (EMIC) waves and whether the plasma conditions during the observed waves satisfy the linear theory threshold condition. We identify 865 events observed by the Composition Distribution Function instrument onboard Cluster spacecraft 4 during 1 January 2001 to 1 January 2011 that exhibit a positive temperature anisotropy (Ahp = T⊥ h/T∥ h − 1) in the 10–40 keV protons. The events occur over an L range from 4 to 10 in all magnetic local times and at magnetic latitudes (MLATs) within ±50°. Of these hot proton temperature anisotropy (HPTA) events, only 68 events have electromagnetic ion cyclotron (EMIC) waves. In these 68 HPTA events, for those at 3.81.0 nT2/Hz mainly appear in the region with fEMIC/fH,eq 0.45 × fEMIC/fH,lo, and Ahp/(Ahp + 1) 0.25. By testing a threshold equation for the EMIC instability based on linear theory, we find that for EMIC waves with |MLAT| ≤ 10° in the He, H, and >H bands, the percentages that satisfy the predicted conditions for wave growth by the threshold equation are 15.2%, 24.6%, and 25.6%. For the EMIC waves with |MLAT| > 10° the percentages that satisfy the wave growth predicted conditions are only 2.8%, 2.6%, and 0.0%. Finally, possible reasons for the low forecast accuracies of EMIC waves are suggested. Key Points We do the statistical analysis of EMIC waves from a 10 year Cluster observation We test the A_hp versus EMIC wave frequency formula of Kennel and Petschek (1966) We test the linear theory derived by Blum et al. (2009)