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The nonlinear interaction of an arbitrarily large-amplitude circularly polarized electromagnetic wave with an unmagnetized electron-positron plasma is considered, taking into account relativistic particle-mass variation as well as large-scale density perturbations created by radiation pressure. It is found that the interaction is governed by an equation for the electromagnetic wave envelope, which is coupled with a pair of equations describing fully nonlinear longitudinal plasma motions. The dynamics of the nonlinear electromagnetic wave packet is studied.

The theory of black-body radiation in thermal equilibrium with a homogeneous and isotropic plasma is presented. The relevant thermodynamic quantities of the radiation are obtained. The presence of the plasma changes qualitatively and often quantitatively the concept of black-body radiation, essentially through the effect of plasma density.

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A general quantum dispersion equation for electron-positron(hole)-ion quantum plasmas is derived and studied for some interesting cases. In an electron-positron degenerate Fermi gas, with or without the Madelung term, a new type of zero sound waves are found. Whereas in an electron-hole plasmas a new longitudinal quantum waves are revealed, which have no analogies in quantum electron-ion plasmas. The excitation of these quantum waves by a low-density monoenergetic straight electron beam is examined. Furthermore, the KdV equation for novel quantum waves is derived and the contribution of the Madelung term in the formation of the KdV solitons is discussed.

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An explanation is given for the fixed blueshift observed of an intense short pulse laser propagating in a gas chamber filled with helium. The observed shift is found to be independent of the laser power and gas pressure above some critical power. The results are explained by the formation of filaments, which occur due to nonlinear gas polarization effects. The blueshift is in qualitative agreement with a one dimensional particle-in-cell simulation including ionization of the gas.

Nonlinear interaction between intense photons and sound waves in a relativistically hot electron–positron plasma is considered. The modulational instability of a constant amplitude photon is investigated and the formation of polarons (localized photon envelopes trapped in a self-created density cavity) is discussed. The relevance of this investigation to astrophysical plasmas is pointed out.