TITLE:
Stokes Representation for the Solutions of Maxwell-Vlasov
AUTHORS:
Monica Pîrvan, Constantin Udrişte
KEYWORDS:
Maxwell-Vlasov PDEs, Magnetic Traps, Dynamics of Plasma, Gyroscopic Field of Forces, Dynamic Systems
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.3 No.1,
January
21,
2011
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.