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

We study the propagation of a strong, low frequency, linearly polarized fast magnetosonic wave inside the magnetosphere of a neutron star. The relative strength $\delta B/B$ of the wave grows as a function of radius before it reaches the light cylinder, and what starts as a small perturbation can grow to become nonlinear before it escapes the magnetosphere. Using first-principles Particle-in-Cell (PIC) simulations, we study in detail the evolution of the wave as it becomes nonlinear. We find that an initially sinusoidal wave becomes strongly distorted as $\delta B/B$ approaches order unity. The wave steepens into a shock in each wavelength. The plasma particles drift into the shock and undergo coherent gyration in the rest of the wave, and subsequently become thermalized. This process quickly dissipates the energy of an FRB emitted deep within the magnetosphere of magnetar, effectively preventing GHz waves produced in the closed field line zone from escaping. This mechanism may also provide an effective way to launch shocks in the magnetosphere from kHz fast magnetosonic waves without requiring a relativistic ejecta. The resulting shock can propagate to large distances and may produce FRBs as a synchrotron maser.