Calculation of magnetic coordinates by differential form approach

Abstract

We calculate the nonorthogonal magnetic coodinates of a standard magnetic field model for large-aspect-ratio tokamak by differential form approach. In calculation, we paid attention to the behaviours of magnetic coordinates. Hamiltonian-like behaviours of magnetic coordinates along the magnetic field lines encourages to use differential forms. Differential form approach gave us a intuitive picture that the magnetic fields owe the same as the equations of motion of massless charged particles. We defined field action and showed that magnetic field is given by least action principle. We proved also that there exists only one magnetic coordinate system describe magnetic fields as defined form. We derived the guiding center Lagrangian simply and obtained canonical variables of the guiding center Hamiltonian.