A structure-preserving algorithm for Vlasov–Darwin system conserving charge, canonical momentum, and Hamiltonian

Abstract

In this paper, a conservative numerical method for the Vlasov–Darwin system is proposed. The Darwin model was assumed to be valid only in the Coulomb gauge, but recently this model has also been extended to the Lorenz gauge [1]. The Darwin model, based on the Lorenz gauge, exhibits a good symmetry between scalar and vector potentials, making the proofs of physical constraints relatively easy. In addition, the total energy was believed to be one of the conservative quantities of the Vlasov–Darwin system. However, the improved theory suggests that the Hamiltonian is the conservative quantity rather than the total energy. The structure-preserving scheme proposed in this paper exactly maintains the Lorenz gauge and the conservation laws of charge, canonical momentum, and Hamiltonian in discrete form.