Observations of powerful radio waves from neutron star magnetospheres raise the question of how strong waves interact with particles in a strong background magnetic field $B_{bg}$. This problem is examined by solving the particle motion in the wave. Remarkably, waves with amplitudes $E_0>B_{bg}$ pump particle energy via repeating resonance events, quickly reaching the radiation reaction limit. As a result, the wave is scattered with a huge cross section. This fact has great implications for models of fast radio bursts and magnetars. Particles accelerated in the wave emit gamma-rays, which can trigger an $e^pm$ avalanche and, instead of silent escape, the wave will produce X-ray fireworks.
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