ULF Waves/Fluctuations in the Distant Foreshock: Statistical Approach

A broad statistical study addresses for the first time an evolution of ultra-low frequency waves and/or fluctuations in the terrestrial foreshock around the Moon generated through the interaction between the back-streaming particles reflected from the bow shock and the incoming solar wind. It is supposed that the waves propagate sunward but they are convected by the solar wind flow back toward the bow shock and their amplitudes grow. However, our study shows that waves/fluctuations could be growing as well as decaying toward the bow shock under the quasi-radial interplanetary magnetic field. We demonstrate that the growth rate is positive and larger for compressive variations of the magnetic field strength and density than for components of the magnetic field. We show that even if a possible influence of the Moon and its wake is excluded, the growth rate is decreased by nonlinear effects. Plain Language Summary The paper presents an extensive statistical study of fluctuations in the distant foreshock. The study is based on observations of the ARTEMIS spacecraft pair orbiting around the Moon. The study is motivated by already published values of wave growth rate in this region that are in some sense contradictory. The analysis is based on ratios of standard deviations of the ion density and magnetic field magnitude and its components measured by two spacecraft. The growth rate was computed during intervals when both spacecraft were inside the foreshock in positions ensuring that the wave propagation from the upstream to downstream spacecraft cannot be influenced by the Moon or its wake. Although the determined growth rates can have different signs in individual events, we demonstrate that the growth rate is positive and larger for compressive variations of the magnetic field strength and density than for components of the magnetic field in a statistical sense. We also show that the growth rate is decreased by nonlinear effects.