(206) |

(207) |

The rearrangement of the flow term is, of course, trivial, since is independent of .

The th moment of the ensemble-average kinetic equation is obtained by multiplying the above equation by powers of and integrating over velocity space. The flow term is simplified by pulling the divergence outside the velocity integral. The acceleration term is treated by partial integration. Note that these two terms couple the th moment to the th and th moments, respectively.

Making use of the collisional conservation laws, the zeroth moment of Eq. (208)
yields the *continuity equation* for species :

Finally, the contracted second moment yields the

The interpretation of Eqs. (209)-(211) as *conservation laws* is
straightforward. Suppose that is some physical quantity (*e.g.*,
total number of particles, total energy, ...), and
is its density:

(212) |

(213) |

Applying this reasoning to Eq. (209), we see that
is indeed the
species- particle flux density, and that there are no local sources or sinks of
species- particles.^{} From Eq. (210), we
see that the stress tensor is the species- momentum flux density, and that
the species- momentum is changed locally by the Lorentz force and by collisional
friction with other species. Finally, from Eq. (211), we see that
is indeed the species- energy flux density, and that the
species- energy is changed locally by electrical work, energy exchange with
other species, and frictional heating.