Multi-spacecraft detection of kinetic Alfvén waves in the turbulent cusp region

Four Cluster spacecraft with inter-distance up to 127 km measured similar waves in the Earth´s mid-altitude cusp region during northward IMF B_z On April 13 2002. The magnetic field fluctuation spectrum resembles the classical Kolmogorov power law with the index f ^-1.67 under the proton gyrofrequency f_cp (~0.3 Hz), breaks and steepens near f_cp with a scaling f ^-2.45 down to 10 Hz. Using k-filtering technique, we have obtained the wave vector and dispersion relation of the waves. The propagation angle between the wave vector and the magnetic field ranges from 80° to 92°, meaning that the waves propagate quasi-perpendicular to the background magnetic field. By comparing the dispersion relation with the linear solution of the Vlasov kinetic theory obtained by WHAMP, we find the possible evidence of Kinetic Alfvén wave (KAW). The region of KAWs is characterized with strong density gradient and finite plasma β, but without apparent shear flows or field aligned ion beams. These results suggest that the KAW turbulence may be generated by the density inhomogeneity (and resulting ion drift) in the cusp region before being damped or dissipated in the scales below the proton gyroscales.