Trajectory Simulation of fast ions in Tokamak

Abstract

A numerical scheme based on Symplectic Integration Algorithm (SIA) has been used to calculate fast ion trajectories in tokamak magnetic con guration. First the superiority of the symplectic algorithm over the non symplectic algorithm, like Range-Kutta Algorithm (RKA), has been demonstrated by solving a simple problem namely the Henon-Heiles Hamiltonian. In this regard the stability of the schemes as well as the energy conservation in long period calculations have been highlighted. The phase space trajectories of stars were investigated for di¤erent initial conditions and di¤erent energies and it is concluded, for long time simulations, the energy of a given star is well conserved in case of SIA while in case of RKA energy is not conserved therefore for long time simulations SIA is of great importance and is impossible to ignore it. Then SIA has been used to nd the exact trajectories of, trapped and passing, fast ions in tokamak (fusion reactor) toroidal devices. In particular, we have investigate the e¤ect of an intrinsic magnetic eld perturbation, i.e. toroidal eld ripples which are there due the discrete number to toroidal coils around the torus. The simulations are carried out for circular ux surfaces. Again we have found that the numerical scheme used shows excellent conservations of particle energy as well as angular momentum (in axi-symmetric elds). The e¤ect of TF-ripples on these trajectories has been investigated and it is shown that the resonance between toroidal precession of bananas and the toroidal eld ripples can result in spreading of the trajectories meaning thereby that an enhanced radial di¤usion of fast ions.