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We consider the effects of collective plasma processes on synchrotronemission from highly relativistic electrons. We find, in agreement with Sazonov(1970), that strong effects are possible also in the absence of anon-relativistic plasma component, due to the relativistic electrons (andprotons) themselves. In contrast with Sazonov, who infers strong effects onlyin cases where the ratio of plasma frequency to cyclotron frequency is muchlarger than the square of the characteristic electron Lorentz factor, nu_p/nu_B>> gamma^2, we find strong effects also for 1 << nu_p/nu_B << gamma^2. Themodification of the spectrum is prominent at frequencies nu < nu_{R*} = nu_pmin[gamma, (nu_p/nu_B)^(1/2)], where nu_{R*} generalizes the Razin-Tsytovichfrequency, nu_R = gamma nu_p, to the regime nu_p/nu_B << gamma^2. Applying ourresults to gamma-ray burst (GRB) plasmas, we predict a strong modification ofthe radio spectrum on minute time scale following the GRB, at the onset offireball interaction with its surrounding medium, in cases where the ratio ofthe energy carried by the relativistic electrons to the energy carried by themagnetic field exceeds ~ 10^5. Plausible electron distribution functions maylead to negative synchrotron reabsorption, i.e to coherent radio emission,which is characterized by a low degree of circular polarization. Detection ofthese effects would constrain the fraction of energy in the magnetic field,which is currently poorly determined by observations, and, moreover, wouldprovide a novel handle on the properties of the environment into which thefireball expands.Comment: 28 pages, 1 figure, submitted to Ap

Collective Processes in Relativistic Plasma and Their Implications for Gamma‐Ray Burst Afterglows