Stokes Representation for the Solutions of Maxwell-Vlasov

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DOI: 10.4236/jemaa.2011.31002   PDF   HTML     4,346 Downloads   7,450 Views  

Abstract

Maxwell-Vlasov PDEs system describes the dynamics of plasma consisting of charged particles with long-range inter-action. Their solutions can be written using some Stokes potentials. Section 1 presents the experimental devices which can produce a magnetic trap. Magnetic geometric dynamic provides mathematical tools for describing the magnetic flow (see [1-7]). Stokes representation for the solutions of PDEs as Maxwell PDEs or Maxwell-Vlasov PDEs are used analyzing electromagnetic energy in magnetic traps. Section 2 studies Maxwell-Vlasov PDEs system. Stokes represen-tation of its solutions, using Maximum Principle for a multitime optimal control problem, is obtained. Section 3 dis-cusses a method for changing a given ODEs system into a geodesic motion under a gyroscopic field of forces (geomet-ric dynamics). Section 4 proposes a modified form for Maxwell-Vlasov PDEs, by replacing the classical gyroscopic force with the one appearing in geometric dynamics. Stokes representation for the solutions of modified Max-well-Vlasov PDEs is also obtained.

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M. Pîrvan and C. Udrişte, "Stokes Representation for the Solutions of Maxwell-Vlasov," Journal of Electromagnetic Analysis and Applications, Vol. 3 No. 1, 2011, pp. 7-12. doi: 10.4236/jemaa.2011.31002.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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