Method of the Particle-in-Cell Simulation for the Y-Point in the Pulsar Magnetosphere

Abstract

Abstract Recent observations in the X-ray and Gamma-ray suggest that the emission region of the pulsar magnetosphere can be multifold. In particular, the open-close boundary of the magnetic field, so-called the Y-point, can be a new candidate place where magnetic field energy converts into plasma heat and/or flow energy. Here, we present a new Particle-in-Cell code, which can be applied to the Y-point of the pulsar magnetosphere in axisymmetric geometry. The electromagnetic solver is used in two-dimensional grid points with cylindrical coordinates ($R$, $z$), while the particle solver operates in three-dimensional Cartesian coordinates ($x$, $y$, $z$), where the Buneman–Boris method is used. The particle motion is treated in special relativity. The inner boundary conditions are set up to generate rotation of the magnetosphere by use of the force-free semi-analytic solution given by Uzdensky (2003, ApJ, 598, 446). The code has been verified by dispersion relations of all wave modes in electron-positron plasmas. The initial test run is also presented to demonstrate the Y-shaped structure at the top of the dead zone on the light cylinder. We suggest that the structure is variable with quasi-periodicity with magnetic reconnection, and that plasma will be accelerated and/or heated. In a time-averaged point of view, the break up of the ideal-MHD (magneto-hydrodynamics) condition takes place in the vicinity of the Y-point.