Variational formulation of plasma dynamics
| Autor: | G. O. Ludwig |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Cauchy distribution Equations of motion Eulerian path Invariant (physics) Condensed Matter Physics 01 natural sciences Virial theorem 010305 fluids & plasmas symbols.namesake Classical mechanics 0103 physical sciences symbols Covariant transformation Boundary value problem 010306 general physics Hamiltonian (quantum mechanics) |
| Zdroj: | Physics of Plasmas. 27:022110 |
| ISSN: | 1089-7674 1070-664X |
| DOI: | 10.1063/1.5139315 |
| Popis: | Hamilton's principle is applied to obtain the equations of motion for fully relativistic collision-free plasma. The variational treatment is presented in both the Eulerian and Lagrangian frameworks. A Clebsch representation of the plasma fluid equations shows the connection between the Lagrangian and Eulerian formulations, clarifying the meaning of the multiplier in Lin's constraint. The existence of a fully relativistic hydromagnetic Cauchy invariant is demonstrated. The Lagrangian approach allows a straightforward determination of the Hamiltonian density and energy integral. The definitions of momentum, stress, and energy densities allow one to write the conservation equations in a compact and covariant form. The conservation equations are also written in an integral form with an emphasis on a generalized virial theorem. The treatment of boundary conditions produces a general expression for energy density distribution in plasma fluid. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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