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The production mechanism and radio spectra of synchrotron radiation from relativistic electrons in winds of massive stars are investigated in detail to account for the non-thermal radio emission observed in some early-type stars. The synchrotron emitting electrons must be accelerated in situ at the radio emitting region to explain the observed radio luminosity and spectra because of severe inverse Compton cooling of the relativistic electrons. Strong shocks generated inside the winds by line-driven instabilities are believed to be responsible for the acceleration of high energy particles; thus they must be able to propagate to very large radii (more than one hundred stellar radii) into the radio emitting region. A simple snow-plough theory is developed for the shock propagation in winds. We have also taken into account the large free-free optical depth and the Razin effects of the dense winds. The calculated radio spectra match well the observations, which also put severe constraints on our model parameters.
