Finite conductivity boundary condition for FDTD PIC

Abstract

Summary form only given. The simplest boundary condition to implement in a finite difference time domain (FDTD) code is that of the perfect conductor where the tangential electric field and the normal magnetic field are set to zero. However, many problems require a lossy boundary. This is often implemented with the creation of a layer of cells within the metal that are given a finite conductivity. Resolving the skin depth in these cells may require using cells that are much smaller than those in the rest of the problem domain. This may reduce performance by requiring a smaller time step to satisfy the Courant condition. It also adds complexity to the code and to required input. Using a surface boundary condition (rather than a volume boundary condition) is potentially more efficient and easier to implement and use. This type of boundary often suffers the difficulty of requiring a time history of the magnetic field which for problems with large boundaries and/or many time cycles can lead to prohibitively large memory requirements. We propose a finite conductivity surface boundary condition that is easy to implement and has very little computational overhead. Preliminary tests show the method to be stable and to damp fields in a predictable way. However, quantitative agreement with analytic theory for simple test problems requires the use of a non-physical problem-specific parameter by the user.