  The space-filter approach has proved a fundamental tool in studying
turbulence in neutral fluids, providing the ability to analyze scale-to-scale
energy transfer in configuration space. It is well known that turbulence in
plasma presents challenges different from neutral fluids, especially when the
scale of interests include kinetic effects. The space-filter approach is still
largely unexplored for kinetic plasma. Here we derive the space-filtered (or,
equivalently "coarse-grained") equations in configuration space for a
quasi-neutral hybrid-kinetic plasma model, in which ions are fully kinetic and
electrons are a neutralizing fluid. Different models and closures for the
electron fluid are considered, including finite electron-inertia effects and
full electrons' pressure-tensor dynamics. Implications for the cascade of
turbulent fluctuations in real space depending on different approximations are
discussed.
