SIMBAD references

We re-examine the one-dimensional (1D) vacuum and nonvacuum accelerators in the outer magnetosphere of rotation-powered pulsars by considering the limit of trans-field height through pair-production process. In the original 1D nonvacuum outer gap model, both the Poisson equation for electrical potential and the Boltzmann equations of particles and γ-rays are solved self-consistently by assuming the trans-field height as a free parameter, usually resulting in a narrow outer gap (i.e., gap length along magnetic field lines is short). In the modified 1D nonvacuum outer gap model, two improvements have been made: the trans-field height is limited by photon-photon pair production process and the outer boundary of the outer gap can be extended outside the light cylinder. Under the above assumptions, we self-consistently solve the Poisson equation for electrical potential, and the Boltzmann equations of electrons/positrons and γ-rays in both vacuum and nonvacuum outer gaps for the parameters of both Vela and Geminga pulsars. 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 in the vacuum case) and ends at the outer boundary which is located inside or outside the light cylinder depending on the inclination angle. Our calculated results also indicate that γ-ray spectrum from a wide outer gap is flatter than the one from a narrow outer gap and the relation between the electric field and trans-field height has an important effect on the structure of the outer gap.