Vacuum Outer-Gap Structure in Pulsar Outer Magnetospheres

We study the vacuum outer-gap structure in the outer magnetosphere of rotation-powered pulsars by considering the limit of trans-field height through a pair production process. In this case, the trans-field height is limited by the photon-photon pair production process and the outer boundary of the outer gap can be extended outside the light cylinder. By solving self-consistently the Poisson equation for electrical potential and the Boltzmann equations of electrons/positrons and γ-rays in a vacuum outer gap for the parameters of Vela pulsar, we obtain an approximate geometry of the outer gap, i.e. the trans-field height is limited by the pair-production process and increases with the radial distance to the star and the width of the outer gap starts at the inner boundary (near the null charge surface) and ends at the outer boundary which locates inside or outside the light cylinder depending on the inclination angle.