Analysis of the local wave vector orientation of plasma waves in the Earth’s Magnetosheath observed by spacecraft in the tetrahedral formation

Spacecraft architecture that places the spacecraft in a tetrahedral arrangement rather than in the same plane has been taken into consideration in this analysis. The combination of the empirical mode technique and the simple Hilbert transform have been used on the real-valued signal observed aimed at analyzing the local wave vector orientation of plasma waves in the Earth’s Magnetosheath observed by spacecraft in the tetrahedral formation. The real-valued signal is decomposed into intrinsic mode functions (imf). The tetrahedral geometry of the four Cluster satellite on February 18, 2002, observed at 5: 27: 30 UT, yielded average values of tetrahedron elongation E = 0.070 and planarity P = 0.040 for a scale of 20.000km: 1.000cm. Since the values of E and P for a regular tetrahedron are close to zero, these values are small enough to ensure good results of the 3-D measurement. This produced results in three dimensions along the separation of each satellite pair. The result reveals at some points, a non-dispersive wave. The projections of the wave vector that make angles with the spacecraft separation line enabled the determination of wave orientation with respect to the sun using the solar wind coordinate system. In addition, these angles specify the wave vector's direction. The average minimum and maximum spacecraft separation, according to the results, were 88 and 108 km, respectively. The average value of the plasma bulk velocity during the chosen period is [−175,52, 112] kms−1 in x, y and z directions respectively. The local wave vector projection has been plotted along the spacecraft separation. As a reference satellite, we used Cluster satellite C3. This made it possible to pair, and Sat13, Sat23, and Sat43 were used. The wave's wavelength is between 1030.2 and 1366.1 kilometers. Between the separation line of the Sat13 pair and the projection of each wave vector component, there is an angle that ranges from 87 to 91 degrees. With the use of tetrahedral formation of spacecraft to analyze the local wave vector orientation of plasma waves in the Earth’s Magnetosheath, we believe the wave to be spiral-shaped wave.