Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian

We investigate hybrid kinetic-MHD models, where a hot plasma (obeying kinetic theory) interacts with a fluid bulk (obeying MHD). Different nonlinear schemes are reviewed, including the pressure-coupling scheme (PCS) used in modern simulations. This latter scheme suffers from being non-Hamiltonian and to not exactly conserve total energy. Upon adopting Vlasov kinetics, the non-Hamiltonian PCS and a Hamiltonian variant are compared. At high frequency, the non-Hamiltonian version exhibits a spurious instability, which is removed in the Hamiltonian version.