Relativistic Alfven 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 jA. We derive an analytic expression for the evolution of the wavevector k and the growth of jA. In the strongly sheared regime, jA may exceed the maximum current j0 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 ≡ jA/j0 ≫ 1. It sustains jA by compressing and advecting the plasma along the magnetic field lines with an increasing Lorentz factor, γ ≳ κ1/2. 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