# A Combined Electromagnetic and Mechanical Approach for EU-DEMO Toroidal Field Coils
## 3 The Electro-Magneto-Mechanical Framework  
As mentioned, each plasma pulse is described by the current evolution of each coil over time. The reference scenario scheduled for DEMO [10] is currently discretized into three time points: (i) premagnetisation (PREMAG); (ii) start of Flattop (SOF) and (iii) end of Flattop (EOF). Figures 2 and 3 show the current vs. time in the CS modules and PF coils, respectively, taken from [10]. Each instant describes a magnet system in equilibrium, where the Lorentz force field is globally balanced in all directions. Considering a cylindrical reference system centered on the machine axis on the equatorial plane, each poloidal coil is subjected to a radial force, which is self-balanced along 360-degrees, and to a positive or negative vertical force, depending on whether the magnets tend to attract or repel each other. The total vertical action given by the poloidal magnets is zero. Figure 1: Isometric view (**a**) and top view (**b**) of the 3D model of the DEMO magnet systems, where inter-coils structures and supports are also visible. TF stands for toroidal field coil system; PFi stands for poloidal field coil number i; CS stands for Central Solenoid; GS stands for gravity support; OIS stands for outer inter-coil structure; IIS stands for inner inter-coil structure. Figure 2: Evolution of the currents in the CS modules during the plasma scenario. The modules are numbered as CS3U, CS2U, CS1, CS2L and CS3L from top to bottom of the machine. TF ENRG, PREMAG, SOF and EOF are the time points corresponding to the energization of the TF coils, premagnetization, start of flattop and end of flattop, respectively. From the structural viewpoint, in a tokamak all coils are inter-linked by suitable mechanical systems and fixed to the ground by specific support structures. Two types of systems connect the TF coils one-another: the outer inter-coil structures (OISs) and the inner inter-coil structures (IISs). OISs are located above and below the equatorial ports of the vacuum vessel and form two rings that close the TF assembly and contrast the coils out of plane loads. IISs are located at the top and the bottom of the TF inner straight leg to prevent the de-wedge effect due to eventual outward (i.e., toward the plasma) radial displacements. In normal operation, the overall vertical forces are given by the dead loads only so that the TF connections to the ground are defined \"gravity supports\" (GSs) [11]. They are designed to withstand the vertical loads and to exhibit a rather low radial stiffness to follow the shrinking of the machine from room temperature (293 K) to the superconductive coil operating temperature (4.2 K). Even if the toroidal field is supported by a stationary current in the D-magnets, the mutual interaction with the poloidal system leads the TF system to withstand cyclical loads too. In particular, 20,000 cycles are scheduled for DEMO [2]. To assess the TF coils and their structures under the fatigue phenomena, for each plasma pulse it necessary to analyse the load conditions causing a stress field in the magnets. To this aim, a total of six representative time points have been considered:  
1. Initial situation with dead weight and pretension of the bolted joint connections. 2. Cooldown from the room temperature (293 K) to the operating temperature of the superconducting magnets (4.2 K). 3. Energization of the TF coils (TF ENRG) to the operative current (66 kA) [5]. 4. Premagnetization (PREMAG). 5. Start of Flattop (SOF). 6. End of Flattop (EOF). The framework of the presented approach consists of two sequentially coupled parts: the electromagnetic section (EMS) and the structural section (SS). In all cases, the governing equations are solved computationally, by means of the finite element method. EMS is further split two sequentially coupled steps.