Analysis of ripple resonance diffusion of alpha particles in burning plasma

α粒子的约束在托卡马克系统中很重要。在计算α粒子轨道时，采用了忽略Larmor半径的导引中心方程，而对于磁场变化特征长度与Larmor半径相比不可忽略的球形托卡马克，导引中心方程则不适用。虽然这些差异，这是有限的拉莫尔半径的影响，出现在香蕉尖的位置，差异是定量的，而不是定性的。其次，我们分析了波纹共振扩散，这是由香蕉粒子的运动和磁场波纹的共振，从数值和理论。扩散系数在涟漪共振能附近增强，而在波纹共振能附近增强不明显，因此在共振能附近存在局部极小值，具有M型能量依赖性。涟漪共振是由香蕉颗粒的环形进动的径向变化引起的，并且在相空间中产生岛。

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.