We develop the theory of spin light of neutrino in matter ($SL u$) and include the effect of plasma influence on the emitted photon. We use the special technique based on exact solutions of particles wave equations in matter to perform all the relevant calculations, and track how the plasmon mass enters the process characteristics including the neutrino energy spectrum, $SL u$ rate and power. The new feature it induces is the existence of the process threshold for which we have found the exact expression and the dependence of the rate and power on this threshold condition. The $SL u$ spatial distribution accounting for the above effects has been also obtained. These results might be of interest in connection with the recently reported hints of ultra-high energy neutrinos $E = 1 div 10$ PeV observed by IceCube.
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