  We introduce an extensible multi-fluid moment model in the context of
collisionless magnetic reconnection. This model evolves full Maxwell equations,
and simultaneously moments of the Vlasov-Maxwell equation for each species in
the plasma. Effects like electron inertia and pressure gradient are
self-consistently embedded in the resulting multi-fluid moment equations,
without the need to explicitly solving a generalized Ohms's law. Two limits of
the multi-fluid moment model are discussed, namely, the five-moment limit that
evolves a scalar pressures for each species, and the ten-moment limit that
evolves the full anisotropic, non-gyrotropic pressure tensor for each species.
We first demonstrate, analytically and numerically, that the five-moment model
reduces to the widely used Hall Magnetohydrodynamics (Hall MHD) model under the
assumptions of vanishing electron inertia, infinite speed of light, and
quasi-neutrality. Then, we compare ten-moment and fully kinetic
Particle-In-Cell (PIC) simulations of a large scale Harris sheet reconnection
problem, where the ten-moment equations are closed with a local linear
collisionless approximation for the heat flux. The ten-moment simulation gives
reasonable agreement with the PIC results regarding the structures and
magnitudes of the electron flows, the polarities and magnitudes of elements of
the electron pressure tensor, and the decomposition of the generalized Ohm's
law. Possible ways to improve the simple local closure towards a nonlocal fully
three-dimensional closure are also discussed.
