Fusion Engineering and Design 9 (1989) 117-121 North-Holland, Amsterdam 117 ANALYSIS OF THERMO-ELECIROMAGNETIC STRESSES IN HIGH FIELD RESISTIVE COILS P. MOLFINO, G. MOLINARI, M. REPETTO Universita’ di Genova, Dipartimento di Ingegneria Elettrica Via Opera Pia, 114 16145 Genova GE, Italy A. BIANCHI, C. PALOMBY, E. PICCO, F. ROSATELLi and A. ROSSANI Ansaldo S.p.A. Corso Perrone, 25, 16151 Genova GE, Italy TOKAMAK The problem of the accurate computation of thermo-electromagnetic stresses in a toroidal field coil for Tokamak machines will be an important task in the design of future high field Tokamak machines. The high value of flux density, and the pulsed current operation of these machines, imply critical working conditions and require a correct modelling of the thermal and electrical diffusion phenomena. In this paper are presented the thermo-electromagnetic model developed for this aim and the results obtained by implementing this mode1 in the code COMPELL. These results are then used to derive input data for the structural analysis code, ANSYS, thus providing the means for a rather detailed analysis of the structure. 1. Introduction The construction of high field Tokamak machines, aimed at attaining ignition conditions with a small size and a high density plasma, poses the problem of the accurate computation of electromagnetic, thermal and structural stresses in the toroidal field (TF) coils. In fact, the high value of the magnetic flux density, exceed- ing 10 T, and the pulsed operation working condition, are extremely critical from the point of view of the mechanical reliability of the structure. For these reasons the design of the TF coil involves the computation of magnetic and thermal fields with a high level of accuracy. The problem to be solved is a coupled thermo-elec- tromagnetic (TEM) one, which defines the input data needed for a subsequent stress analysis of the coil. The thermo-electromagnetic field problem is a typical cou- pled problem where the thermal and electromagnetic fields interact with each other, modifying material prop- erties such as electric and thermal conductivity and specific heat. Because of this interaction between the two field equations, the solution of the field problem needs a computer program able to solve the two cou- pled field equations simultaneously. In fact, since the range of variation of the parame- ters within the expected temperature range is rather large and the time constants of the two diffusion phe- nomena comparable, a simultaneous solution of the two equations is required, in order to obtain high accuracy. The results of the thermo-electromagnetic calculations, computed at several time-instants of the transient, must then be used to derive the input data for the structural analysis of the TF coils. To this aim, an interface routine is needed, devoted to translate the results from the thermo-electromagnetic code into nodal forces for the evaluation of stresses and displacements. 2. Thermo-electromagnetic model Starting from the expression of Ohm’s law in terms of fields and also including the Hall effect, it is possible to express the electric field E as a function of the magnetic field H as: vxE=vx(pJ-hp,,JxH)= -p,,(aH/at), (1) where p is the electric resistivity, h is the Hall constant, and p,, the permeability of free space. Eq. (1) is the basic electromagnetic equation chosen to solve the field problem. The equation for temperature T is expressed in terms of power losses due to eddy currents in the conductors as: v+cvT)-~,(~~~)= -PIJI~. (2) where k is the thermal conductivity and cp the specific 0920-3796/89/$03.50 0 Elsevier Science Publishers B.V.