  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 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.
