Some conservation properties of linearized particle codes

Conservation laws are derived which are appropriate for use in linearized particle simulation codes. A continuity equation describing mass or charge conservation and an extended Poynting theorem describing energy flow are obtained for general curvilinear coordinate systems. These conservation equations are expressed in terms of quantities readily calculable in a particle code, serve to quantitatively assess the validity and precision of code results, and provide valuable insight into the physics being studied. A conserved quantity related to the system energy, rather than a Poynting theorem, is derived from a Lagrangian formulation. It is bilinear in first-order quantities but is not attractive for implementation as a diagnostic in a linearized particle simulation.