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 ${\omega }_{\mathrm{B}}/a_0<\omega <a_0{\omega }_{\mathrm{B}}$, 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 ${\omega }_{\mathrm{B}}/a_0<\omega <a_0{\omega }_{\mathrm{B}}$ is essentially a generalization of the cyclotron resonance to strong electromagnetic pulses with $a_0>1$. When ${\omega }_{\mathrm{B}}/a_0<\omega <a_0{\omega }_{\mathrm{B}}$, 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 nonlinear. 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 the implications of our results for constraining emission models of fast radio bursts.

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• Electromagnetic waves & oscillations
• Space & astrophysical plasma
• Electron-positron plasmas
• Magnetized plasma
• Test-particle methods
• Two-fluid & multi-fluid model