Recent observations in 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 the place where magnetic field energy converts into the plasma heat and/or flow energy. Here, we present a new Particlein-Cell code in axisymmetric geometry, which can be applied to the Y-point of the pulsar magnetosphere. The electromagnetic solver is used in the two-dimensional grid points with the cylindrical coordinate (R, z), while the particle solver operates in the three-dimensional Cartesian coordinate (x, y, z) by use of Buneman-Boris method. The particle motion can be relativistic. The inner boundary conditions are set up to generate rotation of the magnetosphere in 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 the wave modes in an electron-positron plasma.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 the time-averaged point of view, break up of the ideal-MHD condition takes place in the vicinity of the Y-point.

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