The latest Micromesh Gas Amplification Structures (Micromegas) are achieving outstanding energy resolution for low energy photons, with values as low as 11% FWHM for the 5.9 keV line of $^{55}$Fe in argon/isobutane mixtures at atmospheric pressure. At higher energies (MeV scale), these measurements are more complicated due to the difficulty in confining the events in the chamber, although there is no fundamental reason why resolutions of 1% FWHM or below could not be reached. There is much motivation to demonstrate experimentally this fact in Xe mixtures due to the possible application of Micromegas readouts to the Double Beta Decay search of $^{136}$Xe, or in other experiments needing calorimetry and topology in the same detector. In this paper, we report on systematic measurements of energy resolution with state-of-the-art Micromegas using a 5.5 MeV alpha source in high pressure Ar/isobutane mixtures. Values as low as 1.8% FWHM have been obtained, with possible evidence that better resolutions are achievable. Similar measurements in Xe, of which a preliminary result is also shown here, are under progress.
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