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Macroscopic Lagrangian description of warm plasmas: 1. Formulation of the Lagrangian
Author(s) -
Peng Y.K. M.,
Crawford F. W.
Publication year - 1983
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs018i006p01355
Subject(s) - classical mechanics , physics , lagrangian and eulerian specification of the flow field , lagrangian , euler–lagrange equation , eulerian path , thermal conduction , nonlinear system , hamiltonian (control theory) , hamiltonian mechanics , maxwell's equations , plasma , mathematics , quantum mechanics , mathematical physics , mathematical optimization , phase space
A macroscopic Lagrangian is derived which includes a pressure tensor, heat conduction, and elastic collisions. Its Euler‐Lagrange equations are shown to be the Maxwell equations and the macroscopic force law. The corresponding Hamiltonian is derived, and Hamilton's canonical equations are also demonstrated to lead to the Maxwell equations and the macroscopic force law. The treatment is facilitated by working in a mixture of Eulerian coordinates (for the fields) and Lagrangian coordinates (for the particle motions), and the introduction of a macroscopic potential expressed in terms of the plasma thermal energy and the energy losses by heat conduction. In paper 2 the macroscopic Lagrangian is applied to the description of nonlinear three‐wave interactions.