Size and shape of ULF waves in the terrestrial foreshock

Using simultaneous four spacecraft data, estimates of the size and shape of ULF waves in the terrestrial foreshock are presented. Estimates of the size of the waves in different directions are obtained by calculating the spatial autocorrelation function of the magnetic field in the wave frame using cross‐correlations of magnetic field measurements between the four Cluster spacecraft. The correlation length along the wave vector, its wavelength, is typically 1–3 R E , consistent with previous estimates. The correlation length perpendicular to the wave vector, however, is typically 3–8 times the wavelength, between 8 and 18 R E . The shape of the waves can be approximated as an oblate spheroid, symmetric around the wave vector. However, the wave front tends to be significantly more planar than a spheroid, implying planarity of the waves over several R E and hence a coherent periodic variation of the magnetic field at the bow shock on these scales. There is some evidence that at least during one extended interval of ULF waves, their finite perpendicular extent results in an additional quasi‐periodic enhancement and modulation of the waves, with a period of several minutes, at the spacecraft.