Alfvén waves in the foreshock propagating upstream in the plasma rest frame: statistics from Cluster observations

We statistically study various properties of low-frequency waves such as frequencies, wave numbers, phase velocities, and polarization in the plasma rest frame in the terrestrial foreshock. Using Cluster observations the wave telescope or k-filtering is applied to investigate wave numbers and rest frame frequencies. We find that most of the foreshock waves propagate upstream along the magnetic field at phase velocity close to the Alfvén velocity. We identify that frequencies are around 0.1xΩcp and wave numbers are around 0.1xΩcp/VA, where Ωcp is the proton cyclotron frequency and VA is the Alfvén velocity. Our results confirm the conclusions drawn from ISEE observations and strongly support the existence of Alfvén waves in the foreshock