Relativistic parametric instabilities in extended extragalactic radio sources

A general discussion is presented of parametric instabilities of electromagnetic waves in cold plasmas. Previous results for $$\textit f \equiv eE/m_\text e c\omega_0 \gg 1$$ and ≪ 1 are extended and the intermediate range $$\textit f\sim 1$$, which could be relevant in some astrophysical applications, is analysed by numerical techniques. In the final section a model for particle acceleration and radiation emission by turbulent plasma modes excited in extended radiosources by parametric absorption of strong electromagnetic waves is tentatively discussed.