Nonlinear self-focusing in strongly magnetized pair plasma

An intense radiation field can modify plasma properties and the corresponding refractive index and lead to nonlinear propagation effects such as self-focusing. We estimate the corresponding effects in pair plasmas for circularly polarized waves, in both unmagnetized and strongly magnetically dominated cases. 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 (FRBs)], where the cyclotron frequency ${\omega }_B$ dominates over the 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) the ponderomotive force is $F_p^{\left(B\right)}=-m_e{c}^2/4B_0^2\mathbf{\nabla }{E}^2$, which 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); and (iii) for a radiation beam propagating along a constant magnetic field in the pair plasma with density $n_{\pm }$, the ponderomotive force leads to the appearance of circular currents that lead to a decrease of the field within the beam by a factor $\mathrm{\Delta }B/B_0=2\pi n_{\pm }{m}_e{c}^2{E}^2/B_0^4$. Applications to the physics of FRBs are discussed; we conclude that for the parameters of FRBs, the dominant magnetic field completely suppresses nonlinear self-focusing or filamentation.

Figure 1

(a) View from the side. An intense radiation beam is propagating along the magnetic field. The gradients of the field intensity induce the ponderomotive force ${\mathbf{F}}_p^{\left(B\right)}$. In the high external magnetic field $B_0$ the ponderomotive force leads to azimuthal drift of charged particles $\pm {\mathbf{v}}_d$ that creates toroidal current and decreases the background magnetic field. (b) View along the direction of the beam. In the core the radiation energy density is high and it induces a ponderomotive force directed away from the center. In the external magnetic field (chosen to be out of the plane) the ponderomotive force leads to charge-dependent drift of particles and generation of the toroidal current (in the clockwise direction). The induced current produces a field counteraligned with the external field.