  Numerical schemes that preserve the structure of the kinetic equations can
provide stable simulation results over a long time. An electromagnetic
particle-in-cell solver for the Vlasov-Maxwell equations that preserves at the
discrete level the non-canonical Hamiltonian structure of the Vlasov-Maxwell
equations has been presented in [Kraus et al. 2017]. Whereas the original
formulation has been obtained for Cartesian coordinates, we extend the
formulation to curvilinear coordinates in this paper. For the discretisation in
time, we discuss several (semi-)implicit methods either based on a Hamiltonian
splitting or a discrete gradient method combined with an antisymmetric
splitting of the Poisson matrix and discuss their conservation properties and
computational efficiency.
