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We study the propagation of a strong, low frequency, linearly polarized fastmagnetosonic wave inside the magnetosphere of a neutron star. The relativestrength $\delta B/B$ of the wave grows as a function of radius before itreaches the light cylinder, and what starts as a small perturbation can grow tobecome nonlinear before it escapes the magnetosphere. Using first-principlesParticle-in-Cell (PIC) simulations, we study in detail the evolution of thewave as it becomes nonlinear. We find that an initially sinusoidal wave becomesstrongly distorted as $\delta B/B$ approaches order unity. The wave steepensinto a shock in each wavelength. The plasma particles drift into the shock andundergo coherent gyration in the rest of the wave, and subsequently becomethermalized. This process quickly dissipates the energy of an FRB emitted deepwithin the magnetosphere of magnetar, effectively preventing GHz waves producedin the closed field line zone from escaping. This mechanism may also provide aneffective way to launch shocks in the magnetosphere from kHz fast magnetosonicwaves without requiring a relativistic ejecta. The resulting shock canpropagate to large distances and may produce FRBs as a synchrotron maser.

Propagation of a Strong Fast Magnetosonic Wave in the Magnetosphere of a Neutron Star