Investigations of the magnetospheric plasma distribution in the vicinity   of a pulsar - I Basic formulation
  The magnetospheric plasma distribution in the vicinity of a pulsar at various inclination angles is investigated using a new relativistic, parallel 3D Particle-In-Cell (PIC) code DYMPHNA3D. DYMPHNA3D uses a superposition of the electromagnetic fields associated with a rotating magnetised conducting sphere in a vacuum (the pulsar fields) and the electromagnetic fields due to the presence of the magnetospheric plasma surrounding the pulsar (the plasma fields), as the total fields. The plasma is moved self-consistently through the magnetosphere using the PIC methodology. Our initial simulation results are presented here. These show similar solutions to those obtained from previous numerical simulations, which show the fundamental plasma distribution in the vicinity of an aligned rotating neutron star to consist of two polar domes and an equatorial torus of trapped non-neutral plasma of opposite sign. The aligned case being the case in which the inclination angle between the magnetic dipole moment and the rotation axis of the star is zero. Furthermore, our code allows for off-axis simulations and we have found that this plasma distribution collapses into a Quad-Lobe charge-separated non-neutral magnetospheric plasma distribution in the case of an orthogonal rotator, i.e., the case in which the magnetic dipole moment is oriented at right angles to the rotation axis of the neutron star, with the plasma remaining trapped close to the stellar surface by the force-free surfaces. We find that if initialised with a Goldreich-Julian type distribution, the system is seen to collapse rapidly into these stable Dome-Torus structures. 
John Mc Donald and Andrew Shearer