Modeling of Bound Electron Effects in Particle-in-Cell

To include the bound electron effects in particle-in-cell(PIC)simulation,we propose a model in which the response of the dipole components of partially ionized ions to external electromagnetic fields can be included.Instead of treating the macroion particle as a single particle without an internal structure,the ions are considered to have a structure composed of a central nucleus and a bounded electron cloud in our model.The two parts experience the interactions of both the external electromagnetic fields and the internal Coulomb fields.In this way,the laser scattering effects by a partially ionized medium can be modeled properly in the PIC simulation.The laser propagation in a neutral medium and the Bragg scattering of the laser in crystal structure have been simulated with a PIC code modified based on our model as the benchmark.Our model may find applications to study some interesting problems,such as the x-ray laser-driven wakefield acceleration in crystals,the x-ray laser-driven high energy density physics,and intense laser propagation in partially ionized nonlinear optical materials,etc.