The spectral simulations of axisymmetric force-free pulsar magnetosphere

A pseudo-spectral method with an absorbing outer boundary is used to solve a set of the time-dependent force-free equations. In the method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergencelessness of magnetic field is analytically enforced by a projection method. Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be well reproduced by our pseudo-spectral code. Further the method is used to present the time-dependent simulation of the force-free pulsar magnetosphere for an aligned rotator. The simulations show that the current sheet in the equatorial plane can be resolved well, and the obtained spin-down luminosity in the steady state is in good agreement with the value given by Spitkovsky (2006).