Magnetosphere of Oscillating Neutron Star. Nonvacuum Treatment

We generalize a formula for the Goldreich-Julian charge density (\rho), originally derived for rotating neutron star, for arbitrary oscillations of a neutron star with arbitrary magnetic field configuration under assumption of low current density in the inner parts of the magnetosphere. As an application we consider toroidal oscillation of a neutron star with dipole magnetic field and calculate energy losses. For some oscillation modes the longitudinal electric field can not be canceled by putting charged particles in the magnetosphere without a presence of strong electric current j = (c/(\omega r))\rho c. It is shown that the energy losses are strongly affected by plasma in the magnetosphere, and cannot be described by vacuum formulas.