Temporal particle-in-cell in Beam Optics Analyzer

Abstract

(This paper will describe the new feature, temporal particle-in-cell analysis in Beam Optics Analyzer in detail. Algorithms for pushing particles and field solution will be discussed. Numerical results for a diode as well as a gridded electron gun will demonstrate the implementation. BOA is a 3D particle trajectory code that solves the relativistic Lorentz equation of motion in the presence of static electromagnetic fields. It includes both Poisson and nonlinear Curl-Curl, finite element solvers to determine electrostatic and magnetostatic fields. It has a robust mesher with fine-grained controls, adaptive mesh refinement and routines to maximize performance by optimizing both geometric and parametric variables. In the previous versions, BOA iterates to a self consistent solution for the electromagnetic fields and particle trajectories to obtain a steady state solution. In the latest version, temporal analysis has been added. Here, all particles must be pushed synchronically in time necessitates a global time step calculation after each step. This involves an efficient search for the smallest element on the paths of all particles. Since this time step is typically small and several steps may be required for a particle to pass through an element, a highly accurate integrator with adaptive time step is not needed. Furthermore, higher order methods require either storage of additional temporal phase space data or evaluation of E and B at times other than integer or half-integer multiples of the time step with the same order of accuracy, leading to significant storage or computational expense. A more efficient integrator requiring fewer operations, such as the leapfrog method, is more desirable. The leapfrog method is accurate to second order and is a two-step formula, because data from the last two steps are required. It is very efficient because, unlike other two-step methods, it requires only one evaluation of the Lorentz force. It can be made even more efficient when implemented in conjunction with Boris scheme to efficiently evaluate the Lorentz force. For temporal PIC analysis, BOA also needs to provide the interface for users to prescribe time-dependent boundary conditions. A formula parser has been implemented to enter the electrode potentials as functions of time. BOA will also have the option using a series RLC circuit with driving potential or current for RF modulation. Given examples including a multiple beam electron gun with RF modulating modanode and a gridded gun will be presented.