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Intense radiation field can modify plasma properties, the correspondingrefractive index, and lead to such nonlinear propagation effects asself-focusing. We estimate the corresponding effects in pair plasma, both inunmagnetized and strongly magnetically dominated case. First, in theunmagnetized pair plasma the ponderomotive force does not lead to chargeseparation, but to density depletion. Second, for astrophysically relevantplasmas of pulsar magnetospheres, (and possible loci of Fast Radio Bursts),where cyclotron frequency $\omega_B$ dominates over plasma frequency $\omega_p$and the frequency of the electromagnetic wave, $\omega_B \gg \omega_p,\,\omega$, we show that (i) there is virtually no nonlinearity due to changingeffective mass in the field of the wave; (ii) ponderomotive force is $F_p^{(B)}=- {m_e c^2}/({4 B_0^2}) \nabla E^2$; it is reduced by a factor$(\omega/\omega_B)^2$ if compared to the unmagnetized case ($B_0$ is theexternal magnetic field and $E$ is the electric field of the wave); (iii) forradiation beam propagating along constant magnetic field in pair plasma withdensity $n_\pm$, the ponderomotive force leads to appearance of circularcurrents that lead to the decrease of the field within the beam by a factor$\Delta B/B_0 = 2\pi n_\pm m_e c^2 {E^2}/{B_0^4}$. Applications to the physicsof FRBs are discussed; we conclude that for parameters of FRB's the dominantmagnetic field completely suppresses nonlinear radiation effects.

Nonlinear optics in strongly magnetized pair plasma, with applications to FRBs