During previous experiments in the satellite machine “Compact Helical System” in NIFS and the design works on a quasi-symmetric stellarator as the “post CHS”, we presented also a new framework of the neoclassical transport theory (theories for drift orbit effect and the Coulomb collision effect in toroidal confinement magnetic fields). Since it was applicable also for other various quasi-symmetric devices, which were planed in the U.S stellarator community, some international and domestic collaboration works based on it also were conducted. Recently, I extended it to various fast-ion-driven effects (momentum input, anisotropic heating, formation of the ambipolar electrostatic potentials, and so on) in NBI-heated and/or burning plasmas, and applied it to NBI-heating experiments. Further extensions to the future burning-core, such as the fast-ion-driven bootstrap current are planed.