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

Intense radiation field can modify plasma properties, the corresponding refractive index, and lead to such nonlinear propagation effects as self-focusing. We estimate the corresponding effects in pair plasma, both in unmagnetized and strongly magnetically dominated case. First, in the unmagnetized pair plasma the ponderomotive force does not lead to charge separation, but to density depletion. Second, for astrophysically relevant plasmas 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 changing effective 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 the external magnetic field and $E$ is the electric field of the wave); (iii) for radiation beam propagating along constant magnetic field in pair plasma with density $n_\pm$, the ponderomotive force leads to appearance of circular currents 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 physics of FRBs are discussed; we conclude that for parameters of FRB's the dominant magnetic field completely suppresses nonlinear radiation effects.