Volt-second balance with the toroidal magnetic flux based on Poynting's theorem in tokamaks

The equation of the volt-second balance is derived based on Poynting's theorem with the toroidal magnetic flux involved. The poloidal voltage appears in association with the poloidal current and the change in the toroidal magnetic field. The influence of the toroidal flux is investigated numerically for two cases: the plasma current ramp-up and ramp-down case and the auxiliary heating case. The simulations reveal that full Poynting's theorem with both the poloidal and toroidal fluxes involved certainly holds and so does each component of the theorem. (paper)