Mathematics Faculty Articles

Title

Curvilinear Polyadic Moments of the Boltzmann Equation. I. Polyadic Hierarchy for An N-Species, Dilute, "Point" Plasma

Document Type

Article

Publication Date

5-1-1970

Publication Title

Annals of Physics

ISSN

0003-4916

Volume

58

Issue/No.

1

First Page

157

Last Page

175

Abstract

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 = ϱννν···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.

DOI

10.1016/0003-4916(70)90242-3

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