Recently, the availability of new high-spatial and -temporal resolution observations of the solar photosphere has allowed the study of the oscillations in small magnetic elements. Small magnetic elements have been found to host a rich variety of oscillations detectable as intensity, longitudinal or transverse velocity fluctuations which have been interpreted as MHD waves. Small magnetic elements, at or below the current spatial resolution achieved by modern solar telescopes, are though to play a relevant role in the energy budget of the upper layers of the Suns atmosphere, as they are found to cover a significant fraction of the solar photosphere. Unfortunately, the limited temporal length and/or cadence of the data sets, or the presence of seeing-induced effects have prevented, so far, the estimation of the power spectra of kink-like oscillations in small magnetic elements with good accuracy. Motivated by this, we studied kink-like oscillations in small magnetic elements, by exploiting very long duration and high-cadence data acquired with the Solar Optical Telescope on board the Hinode satellite. In this work we present the results of this analysis, by studying the power spectral density of kink-like oscillations on a statistical basis. We found that small magnetic elements exhibit a large number of spectral features in the range 1-12 mHz. More interestingly, most of these spectral features are not shared among magnetic elements but represent a unique signature of each magnetic element itself.
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