Microscopic And Macroscopic Models in Plasma Physics
Microscopic And Macroscopic Models in Plasma Physics
Harold Grad
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Whereas the charge -neutral formulation is con- sistently Galilean-invariant, the alternative system has no invariance properties at all and shows rather awkward behavior in ordinary magneto-fluid dynamics. The only proper way to cover the entire range of densities is by a completely rela- tivistic treatment, but this has not yet been done. The guiding-center treatment of the plasma is seen to be essentially macroscopic with regard to the motion of the magnetic field lines, but it is microscopi...c with regard to the particle motion along the lines. This is consistent with our original heuristic argument regarding the preservation of the identity of a fluid element. The value chosen for p-E, viz. , (42), is such as to guarantee u = u_ provided that 16. A. A. Blank and H. Grad, "Fluid Magnetic Equations", Institute of Mathematical Sciences Report, NY0-6846-VI July 1958. - 32 - this holds initially; in other words there is a single macro- scopic fluid velocity. Prom the constraint equation (^l) and the moment equation for d/dt, one obtains exactly the same momentum equation as in the fluid theory (21).
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