Time Evolution of Pulsar Magnetosphere: An Implicit Approach
We apply a computationally efficient technique to validate the global structure of the pulsarmagnetosphere. This is achieved by implementing a three dimensional, computationally intense,implicit Crank-Nicolson finite-difference scheme. We are particularly interested in the magneti-cally dominated region around a neutron star. This region of magnetic influence, called the mag-netosphere is evolved under the approximation of force-free electrodynamics (FFE). The mainobjective of this dissertation is to present our code and use it to demonstrate and verify the nowwidely accepted global features of a pulsar magnetosphere. Our implicit approach is tested for thetwo extreme conditions of the magnetosphere: vacuum and FFE. Our results qualitatively agreewith previously developed time-dependent models for an oblique rotator. The current density cor-responding to the FF approximation is first evolved using the advection/perpendicular term andthen by allowing a non-zero parallel component. We also demonstrate, in line with previous stud-ies, that our simulations can run steadily for several stellar rotations. Further study is howeverrequired to understand the structure of the magnetosphere when a non-zero parallel componentof the current density is incorporated. With better spatial and time resolution implementing animplicit method is important as the approach can be treated efficiently towards dissipative termswithin a current density equation. In addition, the approach can be useful to investigate magneto-spheres filled with resistive plasma, achieve better resolution current sheets and in developing anefficient Particle-In-Cell (PIC) technique.