3D, coupled electromagnetic, thermal, current diffusion in the finger joints of the Alcator C-Mod toroidal field coils

The solution of a transient, 3D current diffusion problem in a massive conductor with thermal coupling has long been an elusive analysis: It requires solving the 3D, time-dependent vector potential, the electric scalar potential, and temperature simultaneously. In the past, analysts have used 2D models with effective out-of-plane properties to approximate the actual 3D configuration. This paper discusses the use of ANSYS to solve this problem in 3D for a particular application: Alcator C-Mod Toroidal Field (TF) coil "sliding finger joints." In addition, because of the wide range in detail involved in the relevant electrical components, the analysis uses submodeling to capture the response of the thin copper fingers and their felt metal pads within the much larger picture of the coil body. The TF coils used in MIT's Alcator C-Mod tokamak are (20) picture frame shaped coils with sliding finger joints at the ends of massive copper plate conductors. Current is transferred at the corners of the coil through finger joints and across copper felt metal pads. As a pulsed machine, the TF coils are ramped up to their flat top currents on a 1-2 s time scale. Early in the transient, the current distribution across the conductor is far from uniform, as most of the current is carried by the conductor skin closest to the plasma. In addition, the diffusion of current into the conductor as the transient progresses is a function of the conductor temperature: high currents on the conductor skin drive up the temperature of the copper, and thus increase its resistivity. This presents a rather difficult design problem, determining the actual current distribution and temperature rise in the finger joint felt metal (FM). The submodel analysis is ultimately used to determine the detailed current and temperature distribution in the finger joint and FM, and thus characterize the operating parameters of this critical element of the magnet. The effects of damaged FM are also evaluated.