Turbulence in the Earth's cusp region: The k-filtering analysis

On 13 April 2002, four Cluster spacecraft with separations up to 127 km measured similar turbulence in the exterior cusp during northward interplanetary magnetic field (IMF) B_z. Both the power spectra of magnetic and electric field fluctuations resemble the classical Kolmogorov power law, with the scaling f^-1.7 under the proton gyrofrequency f_cp (∼0.3 Hz), breaks near f_cp, and then steepens with the scalings f^-2.8 and f^-2.0 up to 10 Hz, respectively. The observed ratio of the electric to magnetic field is in agreement with the theoretical values of |δE/δB| for the quasi-perpendicular kinetic Alfvén waves (KAWs), which reflects the features of Alfvén turbulence. The wave vector and dispersion relation of the turbulence are obtained using k-filtering technique. The results show that the waves propagate quasi-perpendicularly to the background magnetic field. The similarity between the experimental and the theoretical dispersion relations indicates that the measured waves are kinetic Alfvén wave. The waves have right-handed elliptical polarization in the plane perpendicular to k. The main axis of polarization ellipse is perpendicular to the average magnetic field. These features furthermore indicate that the turbulence properties agree well with those of KAW mode. The observed KAW is much possibly produced through resonance mode conversion. We calculate the density gradient vector using multipoint density data and found that the waves propagate basically toward high-density region. The density gradient in the exterior cusp provides a favorable condition for the resonance converted KAW.