2005ApJ...630..454M

We propose an analytical three-dimensional model of the open field line region of a neutron star (NS) magnetosphere. We construct an explicit analytic solution for arbitrary obliquity (angle between the rotation and magnetic axes) incorporating the effects of magnetospheric rotation, relativistic flow of charges (e.g., primary electron beam) along the open field lines, and E×B drift of these charges. Our solution employs the space-charge-limited longitudinal current calculated in the electrodynamic model of Muslimov and Tsygan and is valid up to very high altitudes nearly approaching the light cylinder. We assume that in the innermost magnetosphere, the NS magnetic field can be well represented by a static magnetic dipole configuration. At high altitudes the open magnetic field lines significantly deviate from those of a static dipole and tend to focus into a cylindrical bundle, swept back in the direction opposite the rotation and bent toward the rotational equator. We briefly discuss some implications of our study to spin-powered pulsars.