Fast Ion Trajectory Calculations in Tokamak Magnetic Configuration Using Symplectic Integration Algorithm

Abstract

A numerical scheme based on Symplectic Integration Algorithm (SIA) has been used to develop an orbit following code to calculate fast ion trajectories in tokamak magnetic configuration. For the purpose of demonstrating the expediency of symplectic schemes, the algorithm has been applied to the H´enon-Heiles system and compared with non- symplectic Runge–Kutta Algorithm (RKA) for numerically integrating the Hamiltonian equations. In contrast to RKA, the long-time stability of SIA has been highlighted. Furthermore, the SIA has been used to find the exact trajectories of, trapped and passing, fast ions in tokamak. In particular, the effect of an intrinsic magnetic field perturbation has been investigated, i.e. toroidal field ripples. This perturbation is toroidal field ripple (TFR) which are there due the discrete number to toroidal coils around the torus. The numerical scheme used shows excellent conservation of particle energy as well as of angular momentum (in axi-symmetric case). The effect of TFR on these trajectories has been simulated and it is shown that the resonance between toroidal precession of bananas and the field ripples results in spread of the trajectories for banana particles, whereas the passing fast ions are unaffected.