Abstract
We propose a conservative prescription for perfect-conductor boundary conditions for a Darwin particle-in-cell (PIC) model on curvilinear meshes and arbitrarily shaped boundaries. The Darwin model is a subset of Maxwell's equation in which the electromagnetic mode (light wave) has been analytically removed. This renders the Darwin formulation elliptic, instead of hyperbolic. Historically, Darwin-PIC practitioners have had difficulty implementing a well-posed set of boundary conditions for realistic applications. In this study, we demonstrate the well-posedness and effectiveness of a simple boundary-condition prescription for perfect conductors of specified potential and of arbitrary shape in multiple dimensions, using a recently developed conservative, implicit Darwin-PIC algorithm. The boundary conditions conserve the electromagnetic energy, and preserve the Coulomb gauge of the vector potential, ∇⋅A=0 exactly. We demonstrate that global energy is exactly conserved in curvilinear, simply-connected domains in the specific case of particles reflecting off perfect conductors.
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