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We investigate a pair creation cascade in the magnetosphere of a rapidly rotating neutron star. We 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 paper, we first examine the time-dependent nature of particle accelerators by solving the non-stationary Boltzmann equations on the two-dimensional 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 present the deathlines of millisecond pulsars.
We consider magnetospheric structure of rotating neutron stars with internally twisted axisymmetric magnetic fields. The twist-induced and rotation-induced toroidal magnetic fields align/counter-align in different hemispheres. Using analytical and nu
This paper deals with the Crab Nebula problem to suggest that particle acceleration takes place not only at the inner shock but also over a larger region in the nebula with disordered magnetic field. Kennel and Cornoniti (1984) constructed a spheri
We discuss the role of particle-in-cell (PIC) simulations in unveiling the origin of the emitting particles in PWNe. After describing the basics of the PIC technique, we summarize its implications for the quiescent and the flaring emission of the Cra
A self-consistent electrodynamics of a particle accelerator in a rotating neutron-star magnetosphere is investigated on the two-dimensional poloidal plane. Solving the Poisson equation for the electrostatic potential together with the Boltzmann equat
We continue our investigation of particle acceleration in the pulsar equatorial current sheet (ECS) that began with Contopoulos (2019) and Contopoulos & Stefanou (2019). Our basic premise has been that the charge carriers in the current sheet origina