Quasi‐monochromatic ULF foreshock waves as observed by the four‐spacecraft Cluster mission: 1. Statistical properties

Cluster data are used to study the statistics of a particular type of foreshock wave: quasi‐monochromatic ultra‐low‐frequency (ULF) waves with characteristic periods of 30 s in the spacecraft frame. On the basis of a large set of foreshock observations made in 2001 with spacecraft separations ∼600 km, the intrinsic properties of the waves are found using a cross‐correlation timing analysis. This method, which allows the solar wind rest frame properties of the waves to be calculated with fewer assumptions when compared to previous dual spacecraft analysis, is described in detail. The performance of minimum variance analysis (MVA) as a wave analysis tool is investigated experimentally using this multispacecraft analysis. MVA estimates of propagation direction are shown to diverge from the multispacecraft estimate in the limit of linear wave polarization. Theoretical estimates of MVA error are also compared to the observations. Previously established wave properties derived from ISEE are independently tested; it is found that statistically, the waves propagate at frequencies an order of magnitude below the ion cyclotron frequency in the solar wind rest frame and have wavelengths of the order of an Earth radius. However, these statements mask the fact that there is significant variation about these average values that is physical in nature. The data are plotted in the ω − k plane and the average frequency and wave number are used to experimentally identify the “average” resonant beam speed. This beam speed is an order of magnitude greater than the local Alfvén speed in the solar wind rest frame. Furthermore, histograms of the inferred beam speed normalized to the solar wind speed are presented and compared to previously published plasma data. Finally, the spacecraft frame wave period is found to be proportional to the magnetic field strength in a manner consistent with previous analyses.