Density response to magnetic field fluctuation in the foreshock plasma

The foreshock plasma exhibits large-amplitude disturbance in the plasma density and the magnetic field. The question of the density response to the magnetic field fluctuation is addressed and studied observationally and statistically using the in situ Cluster spacecraft data of the foreshock plasma. Three major findings are obtained. First, the density response is unique to the magnetic field fluctuation and is of the fast magnetosonic mode type. Second, the density response to the total magnetic energy density (simply subtracting by the mean field) exhibits a clear scaling to the beta-tilde parameter defined as the squared ratio of the sound speed to the Alfvén speed. We interpret that the total fluctuations mostly represent linear-mode waves, and the scaling law has a potential application to estimate the plasma parameter beta using the fluctuation data of the density and the magnetic field only. Third, the density response to the nonlinear (or large-amplitude) magnetic field fluctuation has a weak agreement with the theoretical expectation from the quasi-static balance with a larger degree of scattering in the data. We conclude that the foreshock plasma overall exhibits the linear-mode waves (fast mode) and a moderate degree of nonlinear fluctuations. The concept of the quasi-static balance is partly justified and applicable in the foreshock plasma. [Figure not available: see fulltext.].