Abstract
We investigate a pair creation cascade in the magnetosphere of a rapidly rotating neutron star. The charge depletion due to global flows of charged particles causes a large electric field along the magnetic field lines. Electrons and positrons are accelerated by this field to radiate gamma-rays via curvature process. Some of the gamma-rays collide with the X-rays emitted from the stellar surface to materialize as pairs in the gap. The replenished charges partially screen the original electric field. To take in to account of these physical processes self-consistently, we must solve the set of the Poisson equation for the electro-static potential and the Boltzmann equations for electrons, positrons, and gamma-ray photons simultaneously. In this thesis, we first examine the time-dependent nature of particle accelerators by solving the non-stationary Boltzmann equations on the twodimensional poloidal plane in which both the rotational and magnetic axes reside. Evaluating the temperature of the heated polar cap surface, which is located near the magnetic pole, by the bombardment of gap-accelerated particles, and applying the scheme to millisecond pulsar parameters, we demonstrate that the solution converges to a stationary solution of which pair-creation cascade is maintained by the heated polar-cap emission, in a wide range of three-dimensional parameter space (period, period derivative, magnetic inclination angle). We also examine the criterion for such a self-sustained particle accelerator to be maintained, and present the deathlines of millisecond pulsars on the (period, period derivative) plane for a few representative inclination angles.