Experimental Determination of Ion Acoustic Wave Dispersion Relation With Interferometric Analysis

In this paper we study electrostatic waves with time-dependent frequency features in the terrestrial foreshock. These short (0.1-0.3 s) duration waves are characterized by a significant frequency drift where the peak wave power shifts from a few hundred Hz to 2-4,000 Hz in a few hundred milliseconds. Based on the electric field data from the Magnetospheric Multiscale Mission (MMS) we have identified 46 of these wave packets. Using four spacecraft timing approach we find that these waves have a propagation direction pointing upstream. However, their plasma frame velocity is less than the solar wind speed, therefore they are eventually convected downstream toward the bow shock. We use the double-probes of MMS and present an interferometric analysis, which allows us to obtain the dispersion relation of these waves and directly compare them to theoretical ones. We show that the measured dispersion relations are in good agreement with Doppler shifted ion acoustic waves and discuss potential mechanisms related to impulsive reflected ions that may allow the growth of these waves and cause time-dependent frequency features.