# A Combined Electromagnetic and Mechanical Approach for EU-DEMO Toroidal Field Coils
## 4 Electromagnetic Calculation Methodology-EMS Section  
To proceed with the structural analysis, it is necessary to complete the magnetic assessment at the main time points of the plasma scenario (PREMAG, SOF and EOF). The final purpose consists of obtaining the Lorentz forces on the toroidal and poloidal coils by means of the electromagnetic model and automatically transferring the loads to the structural environment. The 3D electromagnetic model is made of the three main DEMO magnet systems and also includes an equivalent coil for an ideal plasma wire, as shown in Figure 4a,b. The dimensions and positions used to create the magnet domains are taken from [7,8]. The geometry is built entirely in the APDL environment of Ansys software, with a parametric script to rapidly deal with changes in the structures and to split the domain into different component sub-domains to be able to produce a mapped mesh. The model is implemented in FORTRAN parametrical language (for a direct usage in Ansys APDL) to have the possibility of defining the coils as an equivalent smeared domain (for the CS and PF coils) as well as a detailed winding system specifying each turn (for the TF coil), as shown in Figure 4b,c. To this aim, the script starts with a bi-dimensional mesh of the magnet cross-section and then extrudes it along the coil axis. The key idea is to exploit the magnetic discretization for the structural model together with its nodal load information. For the PF coils and the CS, periodic boundary interfaces are easily identified, as these coils have an axisymmetric geometry. Further, the sixteen TF coils show a 22.5-degree periodicity around the machine axis. Additionally, since one TF coil is completely included inside the repetitive sector considered, a cutting plane is needed to identify the boundary interfaces for this magnet. The TF was therefore trimmed on the equatorial plane, thus obtaining two open circuits with separated but coincident nodes on the cutting plane. By applying mirrored boundary conditions, it is possible to create a continuous current distribution. Figure 4: The 3D electromagnetic model: (**a**) global view where the air domain is visible; (**b**) detail of the CS, TF, PF coils and plasma; (**c**) a detail of the TF coil, which is modelled as a fully detailed winding pack. As described, the analysis is organized in two steps:  
* The first step is the electrostatic analysis. The current at the ith time point of the scenario is applied as a nodal value by selecting one of the two periodic boundary faces of each magnet. The correspondent periodic face of each magnet is placed at zero potential. To this aim, eight-node 3D linear solid elements are used, with 1 dof per node (voltage), which can calculate the current density distribution inside the magnet sections. For the magnets modelled as smeared domains (CS and PF), to obtain a constant current density distribution on the coil cross-sections, the resistivity of each element is defined as a material property linearly variable as a function of the radial position. It is important to underline that, if this material property were not properly defined by this linear function, the current density would record an increase from the inner to the outer radius of the coil, thus producing a wrong electromagnetic force field. For the TF coil, modelled detailing its winding pack, each single cable can be assigned a constant resistivity, and no linear function is needed. The cable heterogeneity can be neglected. An example of the current density distribution obtained is shown in Figure 5.
* The second step is the magnetostatic analysis. The input data for the calculation are given by the current density distributions previously obtained. The previous discretization is exploited, made of eight-node 3D linear solid elements. The magnetic vector potential formulation is implemented; therefore, the three components of the potential are the nodal degrees of freedom.