Three-dimensional simple conformal symplectic particle-in-cell method for simulations of high power microwave devices

To overcome the staircase error in traditional particle-in-cell (PIC) method, simple conformal (SC) symplectic PIC method is presented. The SC symplectic finite-difference time-domain (FDTD) scheme is used to advance electromagnetic fields without reduction of time step. Particles are emitted from conformal boundaries with the charge conserving emission scheme and moved using the relativistic Newton-Lorentz force equation. The electromagnetic field and particles are coupled through the current term in Maxwell´s equations. One numerical example is used to verify the algorithms.