Curvilinear Polyadic Moments of the Boltzmann Equation. I. Polyadic Hierarchy for An N-Species, Dilute, "Point" Plasma
Annals of Physics
The Maxwell transport equation is rederived, using a general curvilinear polyadic momentS(r, v, t) of the Boltzmann equation. When this moment is specified in turn to be the velocity polyads S = m, mv, mvv,···, mvv ··· v, the coupled hierarchy of velocity moments for an N species, dilute, point plasma is thereby obtained. For suitable choices of S and proper polyadic contractions, all of the dilute, point-plasma transport equations can be derived. Explicit results include: (1) The polyadic transport equation, with arbitrary acceleration a, for the l-th order poly-pressureΓl = ϱ〈ννν···ν〉 (l terms). (2) The first seven moment transport equations, for both arbitrary acceleration a and electromagnetic acceleration q(E + v × B), governing the flow of mass density ϱ, continuum velocity V, energy density e, heat flux vector q, pressure tensor P, heat flux tensor Q, and moment of momentum r × mV.
Included, also, is a brief outline of future papers in this series and an appendix summarizing the curvilinear polyadic calculus used throughout the series.
Hawkins, Lawrence Carl, "Curvilinear Polyadic Moments of the Boltzmann Equation. I. Polyadic Hierarchy for An N-Species, Dilute, "Point" Plasma" (1970). Mathematics Faculty Articles. 49.