Analysis of ripple resonance diffusion of alpha particles in burning plasma

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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.