Theory and Simulation study of the Particle motion and Kink mode in a Tokamak

Abstract

Particle transport can directly affect the confinement performance. When the perturbation is present, wave-particle resonance gives severe loss of particles, thus it is important to understand particle motion in the Tokamak in the presence of the wave. To understand such mechanism we have studied, first the single particle motion without perturbation for different species, next we have analytically found different types of Kink mode for various magnetic equilibrium, and then, we have found how particle moves when the Kink mode is present and how they transport when resonating with the Kink mode.To understand the typical ideal MHD mode, we have solved second order Euler-Lagrange equation for minimizing energy for diverse structure of the displacementfor external and internal Kink modes. When the magnetic shear is small or reversed, two branches of modes were observed, where one has characteristics of the internal Kink mode and the other has the external Kink mode. And when the magnetic shear is approximately zero, the Kink mode displacement turns out to be rapidly oscillating spatially with extremely large amplitude with the growth rate on the order of ε^4.Several resonances of wave-particle interaction are investigated and it has been found that the wave-particle bounce and precession induce very strong particle transport. When the wave frequency is un-related to these values, diffusion coefficient suddenly becomes large when the wave amplitude is 10 times of the original value. But when the wave frequency is exactly same as the particle bounce frequency, drastic transport starts to occur at twice of initial amplitude. Also when the wave resonantly interact with particle precession, the particle diffusion starts to increase rapidly at 6 times of the initial amplitude.Tracing the particle trajectory in detail, we have found that as the particle resonates with internal Kink mode, the particle will gain energy and move stochastically in a Tokamak. After a certain time when the wave amplitude becomes large enough, these particles will hit the wall consequently.