  Most plasmas are only partially ionized. To better understand the dynamics of
these plasmas, the behaviors of a mixture of neutral species and plasma in
ideal magnetohydrodynamic states are investigated. The current approach is
about the construction of coupled kinetic models for the neutral gas, electron,
and proton, and the development of the corresponding gas-kinetic scheme (GKS)
for the solution in the continuum flow regime. The scheme is validated in the
1D Riemann problem for an enlarged system with the interaction from the Euler
waves of the neutral gas and magnetohydrodynamic ones of the plasma.
Additionally, the Orszag-Tang vortex problem across different ionized states is
tested to examine the influence of neutrals on the MHD wave evolution. These
tests demonstrate that the proposed scheme can capture the fundamental features
of ideal partially ionized plasma, and a transition in the wave structure from
the ideal MHD solution of the fully ionized plasma to the Euler solution of the
neutral gas is obtained.
