Analysis of ripple resonance diffusion of alpha particles in burning plasma

粒子的约束在托卡马克系统中是很重要的。在计算α粒子轨道时，采用了忽略Larmor半径的导向中心方程，但该方程不适用于球形托卡马克，因为球形托卡马克中磁场变化的特征长度与Larmor半径相比不可忽略。虽然这些差异是有限拉莫尔半径效应，表现为香蕉尖端的位置，但差异是定量的，而不是定性的。其次，对香蕉粒子运动与磁场波纹共振引起的波纹共振扩散进行了数值和理论分析。扩散系数在脉动共振能量附近增强，而在脉动共振能量附近增强不大。因此，它们在共振能量附近有一个局部最小值，因此它们具有m形的能量依赖性。波纹共振是由香蕉粒子的环形进动的径向变化引起的，并在相空间中产生岛屿。

The confinement of alpha particles is important in tokamak systems. Guiding center equations which ignores Larmor radius are used in order to evaluate alpha-particles orbits, while the equations are not valid for spherical tokamaks in which the characteristic length of variation of magnetic field is not negligible compared with Larmor radius. Although these differences, which are finite Larmor radius effects, appear as locations of banana tips, the differences are quantitative, not qualitative. Next we analyzed the ripple-resonance diffusion, which are caused by the resonance of banana-particle motions and magnetic field ripples, numerically and theoretically. The diffusion coefficients are enhanced around the ripple resonance energy while they are not so much enhanced in the neighborhood of it. Consequently, they have a local minimum near the resonance energy, and hence they have an M-shaped energy dependence. Ripple resonance is caused by a radial change of the toroidal precession of banana particles, and creates islands in a phase space.