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We investigate compressive turbulence at sub-ion scales with measurementsfrom the Magnetospheric MultiScale Mission. The tetrahedral configuration andhigh time resolution density data obtained by calibrating spacecraft potentialallow an investigation of the turbulent density fluctuations in the solar windand their three-dimensional structure in the sub-ion range. The wave-vectorassociated with the highest energy density at each spacecraft frequency isobtained by application of the Multi-point signal resonator technique to thefour-point density data. The fluctuations show a strong wave-vector anisotropy$k_{\perp}\gg k_{\parallel}$ where the parallel and perpendicular symbols arewith respect to the mean magnetic field direction. The plasma frame frequenciesshow two populations, one below the proton cyclotron frequency$\omega<\Omega_{ci}$ consistent with kinetic Alfv\'en wave (KAW) turbulence.The second component has higher frequencies $\omega > \Omega_{ci}$ consistentwith ion Bernstein wave (IBW) turbulence. Alternatively, these fluctuations mayconstitute KAWs that have undergone multiple wave-wave interactions causing abroadening in the plasma frame frequencies. The scale-dependent kurtosis inthis wave-vector region shows a reduction in intermittency at the small scaleswhich can also be explained by the presence of wave activity. Our resultssuggest that small-scale turbulence exhibits linear-wave properties of kineticAlfv\'en and possibly ion-Bernstein/magnetosonic waves. Based on our results,we speculate that these waves may play a role in describing the observedreduction in intermittency at sub ion scales.

Possible coexistence of kinetic Alfv\'en and ion Bernstein modes in sub-ion scale compressive turbulence in the solar wind