Statistical study of substorm recovery phases in the inner magnetosphere and magnetotail

Magnetospheric substorm is recognized as an important mechanism for transferring and dissipating solar wind energy to the ionosphere and near-Earth regions. A substorm is generally thought to consist of three phases: growth phase, expansion phase, and the recovery phase, and the total duration of a substorm is about 2–4 hour. In this work, we present a statistical study of the magnetotail state during different phases of substorms, recovery phase in particular, for a period of 5 years from 2016-2020 using multi-spacecraft and ground magnetic measurements. For best spatial and temporal coverage of the inner magnetosphere and magnetotail, we use THEMIS, RBSP, MMS mission observations complemented by the SuperMAG database of measurements from ground-based magnetometers. To examine the duration of substorm expansion and recovery phases in the ionosphere, inner magnetosphere and magnetotail, we first find the substorm peak and end times from a list of substorm onsets available on the SuperMAG website. Substorm peak corresponds to the peak intensity of the westward electrojet provided by the SML (SuperMAG AL) index. For the current analysis period, we obtain a few thousand events when there are at least two spacecraft in the tail, which provides good statistics. To determine the time scales of expansion and recovery phases in the inner magnetosphere and magnetotail, we divide the observations into different bins based on X and Y position of the spacecraft. Keeping focus at the center of the tail, i. e., -5 < Y < 8 RE, the bins are chosen to be -4 to -7 RE, -7 to -10 RE, -10 to -15 RE, and -15 to -25 RE. A superposed epoch analysis is performed on the IGRF field subtracted ($ \Delta Bz =Bz_{Measured}- Bz_{IGRF}$) $Bz$ component of observed magnetic field for complete period of analysis. To find the time scale for recovery phase, we center the superposed epoch around the peak time. Our results show that the timescale of the field recovery is  more than an hour near the geostationary orbit (-4 to -7 RE), 30 min to less than an hour in the range -7 to -10 RE and even shorter as we go beyond -10 RE. The results presented in this work will help understand the spatial and temporal evolution of substorms in the magnetotail, and will significantly improve our understanding of space physics.