Structure of magnetic field lines

In this paper the Hamiltonian structure of magnetic lines is studied in many ways. First it is used vector analysis for defining the Poisson bracket and Casimir variable for this system. Second it is derived Pfaffian equations for magnetic field lines. Third, Lie derivative and derivative of Poisson bracket is used to show structure of this system. Finally, it is shown Nambu structure of the magnetic field lines.

► We have studied structure of magnetic field lines using Pfaffian Hamilton equations.
► Magnetic field lines has Hamiltonian structure.
► It is shown that they also have Nambu structure.