Relativistic Alfvén Waves Entering Charge-starvation in the Magnetospheres of Neutron Stars

Instabilities in a neutron star can generate Alfvén waves in its magnetosphere. Propagation along the curved magnetic field lines strongly shears the wave, boosting its electric current j A. We derive an analytic expression for the evolution of the wavevector k and the growth of j A. In the strongly sheared regime, j A may exceed the maximum current j 0 that can be supported by the background e ± plasma. We investigate these charge-starved waves, first using a simplified two-fluid analytic model, then with first-principles kinetic simulations. We find that the Alfvén wave is able to propagate successfully even when κ ≡ j A/j 0 ≫ 1. It sustains j A by compressing and advecting the plasma along the magnetic field lines with an increasing Lorentz factor, γ ≳ κ 1/2. The simulations show how plasma instabilities lead to gradual dissipation of the wave energy. Our results suggest that an extremely high charge-starvation parameter κ ≳ 104 may be required in order for this mechanism to power the observed fast radio bursts (FRBs) from SGR 1935+2154. However, cosmological FRBs with much higher luminosities are unlikely to be a result of charge-starvation.