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In "Radiative Processes in Astrophysics" from Rybicki and Lightman there is a chapter called "6.9 The impossibility of a synchrotron maser in vacuum":

They prove that there can not be a synchrotron maser in vacuum. I understand the very little mathematics, which basically consists in showing that $\alpha_\nu$ – the absorption coefficient – is positive for this special case. But why does a positive absorption coefficient imply the impossibility of population inversion?

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The "MA" part of MASER is microwave amplification. A positive attenuation coefficient implies negative amplification (i.e. attenuation, or negative gain). MASER gain is symbolized by a negative attenuation coefficient in the medium.

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