[1] ELF/VLF waves play a crucial role in the dynamics of the radiation belts and are partly responsible for the main losses and the acceleration of energetic electrons. Modeling wave-particle interactions requires detailed information of wave amplitudes and wave normal distribution over L-shells and over magnetic latitudes for different geomagnetic activity conditions. We performed a statistical study of ELF/VLF emissions using wave measurements in the whistler frequency range for 10 years (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010) aboard Cluster spacecraft. We utilized data from the STAFF-SA experiment, which spans the frequency range from 8 Hz to 4 kHz. We present distributions of wave magnetic and electric field amplitudes and wave normal directions as functions of magnetic latitude, magnetic local time, L-shell, and geomagnetic activity. We show that wave normals are directed approximately along the background magnetic field (with the mean value of  -the angle between the wave normal and the background magnetic field, about 10 ı -15 ı ) in the vicinity of the geomagnetic equator. The distribution changes with magnetic latitude: Plasmaspheric hiss normal angles increase with latitude to quasi-perpendicular direction at 35 ı -40 ı where hiss can be reflected; lower band chorus are observed as two wave populations: One population of wave normals tends toward the resonance cone and at latitudes of around 35 ı -45 ı wave normals become nearly perpendicular to the magnetic field; the other part remains quasi-parallel at latitudes up to 30 ı . The observed angular distribution is significantly different from Gaussian, and the width of the distribution increases with latitude. Due to the rapid increase of  , the wave mode becomes quasi-electrostatic, and the corresponding electric field increases with latitude and has a maximum near 30 ı . The magnetic field amplitude of the chorus in the day sector has a minimum at the magnetic equator but increases rapidly with latitude with a local maximum near 12 ı -15 ı . The wave magnetic field maximum is observed in the night sector at L > 7 during low geomagnetic activity (at L 5 for K p > 3). Our results confirm the strong dependence of wave amplitude on geomagnetic activity found in earlier studies.

Chorus waves are among the most important natural electromagnetic emissions in the magnetosphere as regards to their potential effects on electron dynamics. They can efficiently accelerate or precipitate electrons trapped in the outer radiation belt, producing either fast increases of relativistic particle fluxes or auroras at high latitudes. Accurately modeling their effects, however, requires detailed models of their wave power and obliquity distribution as a function of geomagnetic activity in a particularly wide spatial domain, rarely available based solely on the statistics obtained from only one satellite mission. Here we seize the opportunity of synthesizing data from the Van Allen Probes and Cluster spacecraft to provide a new comprehensive chorus wave model in the outer radiation belt. The respective spatial coverages of these two missions are shown to be especially complementary and further allow a good cross calibration in the overlap domain. We used 4 years (2012–2016) of Van Allen Probes VLF data in the chorus frequency range up to 12 kHz at latitudes lower than 20°, combined with 10 years of Cluster VLF measurements up to 4 kHz in order to provide a full coverage of geomagnetic latitudes up to 45° in the chorus frequency range 0.1fce–0.8fce. The resulting synthetic statistical model of chorus wave amplitude, obliquity, and frequency is presented in the form of analytical functions of latitude and Kp in three different magnetic local time sectors and for two ranges of L shells outside the plasmasphere. Such a synthetic and reliable chorus model is crucially important for accurately modeling global acceleration and loss of electrons over the long run in the outer radiation belt, allowing a comprehensive description of electron flux variations over a very wide energy range.