  The hybrid kinetic-ion fluid-electron plasma model is widely used to study
challenging multi-scale problems in space and laboratory plasma physics. Here,
a novel conservative scheme for this model employing implicit particle-in-cell
techniques is extended to arbitrary coordinate systems via curvilinear maps
from logical to physical space. The scheme features a fully non-linear
electromagnetic formulation with a multi-rate time advance - including
sub-cycling and orbit-averaging for the kinetic ions. By careful choice of
compatible particle-based kinetic-ion and mesh-based fluid-electron
discretizations in curvilinear coordinates, as well as particle-mesh
interpolations and implicit midpoint time advance, the scheme is proven to
conserve total energy for arbitrary curvilinear meshes. In the electrostatic
limit, the method is also proven to conserve total momentum for arbitrary
curvilinear meshes. Although momentum is not conserved for arbitrary
curvilinear meshes in the electromagnetic case, it is for an important subset
of Cartesian tensor-packed meshes. The scheme and its novel conservation
properties are demonstrated for several challenging numerical problems using
different curvilinear meshes, including a merging flux-rope simulation for a
space weather application, and a helical $m=1$ mode simulation for magnetic
fusion energy application.
