Neptune: An efficient time dependent 3D simulations of coherent radiation sources

NEPTUNE (Nonlinear Evolution of Particle Trajectories Under Non-stationary Excitation) is a new code under development for 3D time dependent large amplitude simulations of coherent radiation sources. The code deals mainly with the description of the beam tunnel where the interaction between the electron beam and the electromagnetic (EM) waves takes place. The EM fields are described by complex envelopes allowing several carrier frequencies which are all harmonics of some fundamental frequency. The fields are calculated self consistently with the electron beam as a source, using the ADI scheme. The ADI scheme is based on splitting the time step into two halves. In each sub-step Maxwell's equations are solved implicitly in one direction and explicitly in the perpendicular direction. The ADI scheme is unconditionally stable, thus the time step can be larger than the one imposed by the CFL condition. This allows, in principal, high spatial resolution required for high frequency cavities without extending the calculation time. Nevertheless, the ADI scheme requires a solution of six tri-diagonal equations for the electric field followed by derivation of the magnetic field. This increased complexity somewhat impairs the efficiency of the calculations. The boundary conditions on the six faces of the beam tunnel are general, and can be specified either as perfect conductor, symmetry boundary conditions or arbitrary external specification. The electron beam is described by a set of trajectories. The frozen-field approximation used for the solution of the equation of motion for these trajectories facilitates the calculations, but requires that the transit time of the electrons in the interaction domain is much shorter than the cavity fill time, as is the case in most of the coherent radiation sources. The resulting code is expected to be more efficient and requires modest computing power compared to conventional 3D particle-in-cell codes. Examples of the use of the code for dielectric loaded waveguide serving as a slow-wave amplifier are presented.