A particle in cell method with an unconditionally stable field solver

Summary form only given. A recently developed implicit wave solver, based on the Method of Lines Transpose, dimensional splitting and a fast 1D integral solution method, removes the CFL condition while maintaining computational cost comparable to explicit wave solvers^1,2. We present the application of this wave solver in a particle-in-cell (PIC) method for the simulation of plasmas in an approach that can handle both electrostatic and fully electromagnetic cases by formulating Maxwell´s equations as wave equations for potentials in the Lorenz gauge. We describe the coupling of the wave solver to particles, and show the results of some standard one- and two-dimensional electrostatic test problems, and discuss the extension to the fully electromagnetic case.