Linear Wave Beams in the Crust of a Neutron Star

The propagation of axially symmetric wave beams near the equatorial plane of a neutron star is studied. These waves are excited by a spatially bounded perturbation in the form of a transverse magnetic field applied to the inner boundary of the crust of the star. For a small ratio of the perturbed to the unperturbed magnetic field, a linear theory can be employed to solve the evolution equation. This condition is satisfied in the crust plasma of a neutron star for typical radio luminosities of pulsars. The resulting simple, exact solution in the form of linear gaussian beams exists without additional conditions on the dissipation, dispersion, and narrowness of the beams, if the velocity c_n of these waves is constant. The latter requirement is well satisfied for the plasma in neutron star crusts. The width of the gaussian beam also depends weakly on position.