Boundary conditions for the Darwin model of approximation to Maxwell´s equations

Summary form only given. An approach for finding boundary conditions for the Darwin model, which is commonly used as an approximation of Maxwell equations in electron beam simulations, has been developed. These conditions guarantee the uniqueness of the decomposition and are compatible with the perfectly conducting wall boundary condition for the overall electric field. Furthermore, it can be proved, on rigorous mathematical grounds, that the resulting Darwin model is well posed (i.e., its solution exists and is unique) and that, under suitable compatibility conditions on the initial data, it approximates the Maxwell system up to the order (V/C)³, where V is the characteristic velocity scale in the problem. The same approach can also be used for the quasielectrostatic model