FRB coherent emission from decay of Alfven waves

We present a model for fast radio bursts (FRBs) where a large-amplitude Alfven wave packet is launched by a disturbance near the surface of a magnetar, and a substantial fraction of the wave energy is converted to coherent radio waves at a distance of a few tens of neutron star radii. The wave amplitude at the magnetar surface should be about 10(11) G in order to produce an FRB of isotropic luminosity 10(44) erg s(-1). An electric current along the static magnetic field is required by Alfven waves with non-zero component of transverse wave vector. The current is supplied by counter-streaming electron-positron pairs, which have to move at nearly the speed of light at larger radii as the plasma density decreases with distance from the magnetar surface. The counter-streaming pairs are subject to two-stream instability, which leads to formation of particle bunches of size of the order of c/omega(p), where omega(p) is the plasma frequency. A strong electric field develops along the static magnetic field when the wave packet arrives at a radius where electron-positron density is insufficient to supply the current required by the wave. The electric field accelerates particle bunches along the curved magnetic field lines, and that produces the coherent FRB radiation. We provide a number of predictions of this model.