A multi-dimensional particle-in-cell code KLAP is introduced. Field ionization, impact ionization and two body collision are considered in a one-dimensional code. Moving window technology is used in a three-dimensional code to study laser wakefield acceleration in GeV region. Terahertz radiation, laser propagation in neutral gas medium, surface electron acceleration as well as GeV electron generation in laser wakefield acceleration are studied.

A numerical scheme for the Fokker-Planck equation is proposed with a finite element method,which is relatively simple for implementation and physically clear. It assures a positive distribution function and particle-number conservation without specific requirement on grid and time step.The scheme is confirmed in one-dimensional simulations.It can be extended easily to multi-dimensional cases.