Full simulation of the open field lines above pulsar's polar cap - Part I

Abstract

We have programmed a full simulation of the open field lines above the polar cap of a magnetized pulsar, using time dependent Particle In Cell (PIC) numerical code (Birdsall and Langdon 1991). We consider the case of free ejection of electrons from the star surface, a Space Charge Limited Flow (SCLF) model. We report here the first results of the simulation. Electrons are accelerating along the open field lines to the flat space-time SCLF maximum Lorentz factor prediction, with oscillation pattern. Than we add the General Relativistic Frame Dragging correction that provide the particles the high Lorentz factor (10^6 - 10^7) needed to initiate pair production. The electrons accelerate according to the analytic expressions given in Muslimov and Tsygan 1992, and Muslimov and Harding 1997, with oscillation pattern. Electron-positron pair production is now being programmed, using the cross sections appears in the literature, and Monte-Carlo code. After completing this stage, we will automatically get: a) the positron return current (thus we could calculate the polar cap heating and the X-ray emission). b). The photons and electrons observed spectrum (photons and electrons that escape the magnetosphere after the cascade). c). The pulsar death line (pulsars with not enough pair production). d). The PFF height (pair formation front location). Those results will be report in a different paper.