Mode Identification of Terrestrial Foreshock ULF Waves Observed by Cluster

ULF waves in the terrestrial foreshock observed simultaneously by the four Cluster satellites were analyzed to identify the plasma wave modes and to study the effect of plasma beta on the intrinsic wave properties. The wave properties in the spacecraft and solar wind frames such as the wave frequency, total wave number, phase speed and wave polarization are experimentally derived using the Minimum Variance Analysis (MVA) for the case study and the Phase Differencing (MVA-free) technique for the statistical study. Both studies indicate that the waves with a 30 second period propagate in the upstream direction at a finite angle with respect to the background magnetic field in the plasma rest frame but are then convected downstream in the spacecraft frame. It is shown that these waves propagate in the fast magnetosonic mode. A similar analysis of the 3 second period waves shows them to be propagating in the upstream direction in the Alfvén / Ion Cyclotron mode. The measured wave properties in the plasma rest frame are in good agreement with theoretical kinetic dispersion relation with a different plasma beta, which has rather significant deviation from fluid model especially for the high plasma beta. In conclusion it is found that the experimentally derived foreshock ULF wave properties are basically in good agreement with previous results but the effect of plasma beta is indispensable to choose the correct wave mode branch especially for the high plasma beta condition.