Hamiltonian description for magnetic field lines in fusion plasmas: A tutorial
Ricardo L. Viana, Michele Mugnaine, Iberê L. Caldas
Abstract
Under certain circumstances, the equations for the magnetic field lines can be recast in a canonical form after defining a suitable field line Hamiltonian. This analogy is extremely useful for dealing with a variety of problems involving magnetically confined plasmas, like in tokamaks and other toroidal devices, where there is usually one symmetric coordinate that plays the role of time in the canonical equations. In this tutorial paper, we review the basics of the Hamiltonian description for magnetic field lines, emphasizing the role of a variational principle and gauge invariance. We present representative applications of the formalism using cylindrical and magnetic flux coordinates in tokamak plasmas.