Absorption of strong electromagnetic waves in magnetized pair plasmas

We discuss synchrotron absorption of a short electromagnetic pulse that propagates in a cold magnetized pair plasma. We show that the pulse can be absorbed when ${\omega }_{\mathrm{B}}\mathrm{/}{a}_0<\omega <a_0{\omega }_{\mathrm{B}}$, where $a_0>1$ is the strength parameter of the pulse, and $\omega$ and ${\omega }_{\mathrm{B}}$ respectively are the frequency of the wave and the cyclotron frequency in the background magnetic field (all quantities are defined in the reference frame where the particles are at rest before being illuminated by the pulse). The condition ${\omega }_{\mathrm{B}}\mathrm{/}{a}_0<\omega <a_0{\omega }_{\mathrm{B}}$ is essentially a generalization of the cyclotron resonance to strong electromagnetic pulses with $a_0>1$. When ${\omega }_{\mathrm{B}}\mathrm{/}{a}_0<\omega <a_0{\omega }_{\mathrm{B}}$, the propagation of electromagnetic waves in a plasma can be very different with respect to the propagation in vacuum because the wave equation is strongly non-linear. Then it is unclear whether the particles are heated stochastically due to synchrotron absorption, as found by studying the motion of a test particle in the field of a vacuum electromagnetic wave. We discuss implications of our results for constraining emission models of fast radio bursts.