Magnetic energy distribution in the four-dimensional frequency and wave vector domain in the solar wind

Abstract

We present a measurement of the energy distribution in the four-dimensional (4-D) frequency and wave vector domain of magnetic field fluctuations in the solar wind. The measurement makes use of the wave telescope technique that has been developed particularly for multispacecraft data analysis. We review briefly the theoretical background and then present a numerical test using synthetic data; the technique is then applied to magnetic field data obtained while the Cluster spacecraft was in the solar wind. The energy distribution is determined in the flow rest frame in the frequency range below 0.2 rad/s and the wave number range below 0.0015 rad/km, corrected for the Doppler shift. We find the following properties in the energy distribution in the rest frame: (1) a double anisotropy in the wave vector domain associated with the mean magnetic field and the flow directions, (2) a symmetric distribution with respect to the sign of wave vector, and (3) no evidence for a linear dispersion relation in the frequency and wave number domain. Since the flow direction in the analyzed time interval is close to the normal direction to the bow shock, the anisotropy may well be associated with the bow shock. These results suggest that the solar wind is in a state of well-developed strong turbulence and justifies the theoretical picture of quasi-two-dimensional turbulence that obtains in the presence of a (relatively) strong DC magnetic field. However, the fluctuations are not axisymmetric around the mean field and the energy distribution is extended in the perpendicular direction to the flow or shock normal. Anisotropy associated with the boundary is reminiscent of previously reported magnetosheath turbulence. This study opens a way to investigate solar wind turbulence in the full 4-D frequency and wave vector space.