GUIDING CENTER EQUATIONS OF MOTION IN TOROIDAL GEOMETRY

Abstract

We have derived the guiding center equations of motion in magnetic coordinates from the phase-space Euler-Lagrange formulation. Paying attention to the Hamiltonian-like behavior of magnetic coordinates along the magnetic field line, we make use of differential forms and calculate magnetic coordinates for the standard magnetic-field model of a large aspect-ratio tokamak. From the resultant relations between magnetic and toroidal coordinates, we obtain the guiding center equations of motion in toroidal coordinates which can be utilized to describe the motion of an ion in a toroidal magnetic equilibrium in the presence of the electrostatic fluctuations of the drift wave turbulence. However, in the present work, we restrict ourselves to investigate the single particle trajectories of ions in toroidal geometry. The derived equations will be used in transport studies through the test particle problem.