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Steady state self-consistent model for pulsar magnetospheres Leahy, Denis Alan

Abstract

A steady state self-consistent model for a pulsar magnetosphere is developed. It is shown that the central neutron star of a pulsar should possess a magnetosphere. In the first approximation, the inertia of the magnetospheric particles is neglected. Steady state corotating models are developed to calculate the structure of the magnetosphere for the axisymmetric case and the case of the arbitrarily oriented dipole. Two results are that charge density is proportional to the z component of the magnetic field and that the z component of the magnetic field vanishes at the light cylinder. The light cylinder is where the corotation velocity reaches the speed of light. The pulsar spin axis is aligned with the z axis. Illustrations of the fields are presented for the cases of magnetic dipole axis parallel and perpendicular to the spin axis. Next these models are altered to take into account the nonzero mass of the particles in the magnetosphere. An extra electric field is required to hold the particles in corotation. Charge separation is assumed. The following results are found: 1) Field lines which previously were horizontal inside the light cylinder, now have a cusp in them where they were horizontal. This cusp increases in size as its location approaches the light cylinder. 2) Field lines no longer are horizontal at the light cylinder but ertical, and divide into two groups those with positive B[sub z] (carrying negative charge) and those with negative (carrying positive charge). We next cease to require that the particles be fixed in the corotating frame. First the single particle motion is calculated for arbitrary fields, assuming small velocities in the rotating frame. We find that the motion can be separated into a slow drift along streamlines(which very nearly follow magnetic field lines) and a spiraling about these streamlines. The energy is conserved, and can be separated into a longitudinal and a transverse energy associated with the two types of motion. The transverse energy divided by the frequency of spiraling is an adiabatic invariant. For the axisymmetric case, a model is developed from which the fields, charge density, and velocities can be computed. With a restriction on the boundary conditions, an analytical model is outlined for the case of arbitrary magnetic multipoles.

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