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Abstract

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 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 ≡ j_A/j₀ ≫ 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.