Pseudo-spectral Simulation Of Pulsar Magnetosphere And Its Application

The simulations of realistic pulsar magnetosphere have became one of impor-tant research fields in pulsar physics since the magnetosphere is the site of particle acceleration and radiation.In this thesis,the simulations of the pulsar magneto-sphere and its applications are studied.A code to solve a set of time-dependent Maxwell equations is independently developed and is applied to the pulsar mag-netosphere simulations and the calculations of light curves.Main results are as follows.At first,two-dimensional simulations of force-free pulsar magnetosphere for an aligned rotator are performed.In this method,both electric and magnetic fields are expanded in terms of the vector spherical harmonic(VSH)functions in spherical geometry and the divergence-free state of the magnetic field is enforced analytically by a projection method.Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be reproduced well by our pseudo-spectral code.Further,the method is used to present a 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 spin-down luminosity obtained in the steady state is in good agreement with the value given by Spitkovsky(2006).Next,an oblique pulsar magnetosphere with a plasma conductivity is studied by using a pseudo-spectral method.The pulsar magnetospheres in infinite(i.e.,force free approximation)and finite conductivities are simulated and a family of solutions that smoothly transition from the Deutsch vacuum solution to the force-free solution are obtained.The sin~2αdependence of the spin-down luminosity on the magnetic inclination angleαis retrieved in the force-free regime.Finally,emission patterns and light curves ofγ-ray pulsars in the terms of dissipation magnetospheres are studied,whereγ-ray light curves are produced by the geometric method and the particle trajectory method,respectively.As an example,the light curves predicted in the two methods are compared to observed light curve at>0.1 GeV energies for Vela pulsar observed by Fermi-LAT.For the geometric method,the magnetosphere with the lowσvalue provides a better match to the observed data.For the particle trajectory method,the magnetosphere with a near force-free regime within the light cylinder and a highσvalue outside the light cylinder can better reproduce the light curves of Vela pulsar.It is pointed that the ratios of stellar R_?and light-cylinder r_Lin the simulation is not realistic for Vela pulsar periods.Therefore,the results from the two methods can not be ruled out.