Compressive plasma turbulence is investigated at sub-ion scales in the solar wind using both the Fast Plasma Investigation (FPI) instrument on the Magnetospheric MultiScale mission (MMS), as well as using calibrated spacecraft potential data from the Spin Plane Double Probe (SDP) instrument. The data from FPI allow a measurement down to the sub-ion scale region ($f_{sc}gtrsim 1$ Hz) to be investigated before the instrumental noise becomes significant at a spacecraft frame frequency of $f_{sc}approx 3$Hz, whereas calibrated spacecraft potential allows a measurement up to $f_{sc}approx 40$Hz. In this work, we give a detailed description of density estimation in the solar wind using the spacecraft potential measurement from the SDP instrument on MMS. Several intervals of solar wind plasma have been processed using the methodology described which are made available. One of the intervals is investigated in more detail and the power spectral density of the compressive fluctuations is measured from the inertial range to the sub-ion range. The morphology of the density spectra can be explained by either a cascade of Alfven waves and slow waves at large scales and kinetic Alfven waves at sub-ion scales, or more generally by the Hall effect. Using electric field measurements the two hypotheses are discussed.
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