Linear response model of the vertical electromagnetic force on a vessel applicable to ITER and future tokamaks
Vertical displacement events (VDEs) and a subsequent plasma disruption cause severe electromagnetic force on the vacuum vessel of axisymmetric magnetic confinement fusion devices like tokamaks and spherical tokamaks. This force is a dominant factor for the supporting system of the vacuum vessel and in-vessel components and a lot of efforts have been devoted to predict the possible force in future machines such as ITER. The eddy and halo currents induced in the vessel accompanying VDE and current quench complicate the analysis of the electromagnetic force and usually, computer simulations are required to employ for the analysis. So far, a database of vertical force for ITER has been created based on DINA simulation. However, no theory has been developed for systematic explanation of the simulation data. The problem of calculating vertical electromagnetic force on the vessel is reformulated to a linear response problem. First, it is shown that a burdensome task of calculating in-vessel halo and eddy currents is reduced to the calculation of the source term of the vertical force, or a force exerted on the plasma by poloidal field (PF) coils. The calculation is carried out without relying on the knowledge of currents in the vessel. The vertical force then emerges as a result of linear response, or electromagnetic shielding by the vessel. The model provides an analytical way of calculating vertical force. As an example of application, dependence of vertical force on current quench rate is derived analytically. The obtained formula well reproduces the simulation result of DINA.