Multi-spacecraft observations of earthward flow bursts

On the basis of the plasma, electric and magnetic fields jointly observed by Cluster and the Double Star TC-1 spacecraft in the Earth's magnetotail, we have investigated the earthward flow bursts by introducing the momentum equation in the X-direction in the ideal conditions of magneto hydrodynamics (MHD). One earthward flow burst with a peak in excess of 500 km/s was selected, when the four spacecraft of Cluster were located around -16 R_E and TC-1 was located around -10 R_E in the X-direction. The inter-spacecraft distances in Y and Z directions were smaller than the statistical spatial scales of the bursty bulk flows. When the Y components of E and -V×B were compared, there was no clear breakdown of the frozen-in condition during the earthward flow burst. With the measured plasma and magnetic parameters from two spacecraft at different positions in the magnetotail, the X component of the pressure gradient was calculated. Magnetic tension was calculated using the magnetic field measured at four points, which could be compared with the assumed constant in the past research with single satellite. When the pressure gradient and the magnetic tension were put into the MHD momentum equation, some samples of the earthward flow bursts were accelerated and some were decelerated. The braking process of the earthward flow burst was more complicated than what the past results had shown. The accelerated samples accounted for about one third of the whole earthward flow bursts and discontinuously located among the decelerated elements. The original single earthward flow burst event might be split into several short flow bursts when it was moving to the Earth. Our results may partly illustrate that the duration of fast flows during three phases of substorm becomes short near the Earth. The results are consistent with the past results that fast flows intrude to places earthward the typical braking region.