Powerful parametric instability of Alfven waves in astrophysical pair plasma

We demonstrate that in highly magnetized pair plasmas, nonlinear Alfven waves with wave-number $k\le k_0={\omega }_p^2\mathrm{/}(\delta {\omega }_B)$ ($\delta =(\delta B)\mathrm{/}{B}_0$ are relative fluctuations of the magnetic field) experience powerful modulational instability. In the two-fluid approximation, we develop an analytic set-up for circularly polarized (CP) Alfven mode in its frame (where the initial configuration is stationary; it is moving with relativistic, amplitude-dependent Alfven velocity $v_A(\sigma ,\delta )$, while both charges experience different, amplitude-dependent, synchrotron gyration). PIC simulations using EPOCH code demonstrate that for Alfven waves with $k$ near $k_0$, large, parametrically-driven density fluctuations develop, and lead to fast modulational instability. Charge separation effects, for a CP wave in magnetized pair plasma, might be temporarily important; on longer time-scales the density fluctuations are charge neutral and in symmetric pair plasma quickly grow to large amplitudes. In highly magnetized plasma, $\sigma \gg 1$, high frequency modes $k\mathrm{/}{k}_0\sim (2-3)\times \sigma \gg 1$ are quickly generated; for smaller plasma magnetization, the dominant mode is at the Bragg’s condition $k=2k_0$. Long term behavior of CP and LP modes is similar. We discuss application of the results to the physics of Fast Radio Bursts generated/propagating in the magnetospheres of magnetars.