In all the magnetic confined plasma machines, the magnets which have to produce the magnetic field for the confinement, stability and heating of plasma are realized by means of superconducting cables, otherwise the required energy to produce such a large magnetic fields on such a large volumes will be too high for the technology to be feasible. Usually Cable in Conduit Conductor (CICC) are utilized , with strand realized by means of  NbTi or Nb₃Sn, stabilized with copper. In order to obtain a good performance of the magnets,  which operate in pulsed regime, it is necessary to reduce as much as possible a.c. losses in the cable and to avoid to reach quench conditions, when transition from superconducting state  to normal state of the cable happens. If such an event occurs machine must be stopped as soon as possible in order to avoid permanent damage of itself. It is thus very important to be able to simulate the magnets behaviour in the pulsed regime in the design phase.

A lot of phenomena must be considered when modelling superconducting magnets for FTC. The electro-magnetic phenomena which are responsible of transport current distribution among the strands of the cable and of a.c. losses in the cable sectors  must be taken into account. Also the electromagnetic phenomena which are concerned with current distribution in the terminations and joints between cable sectors of the coil have an important role and must be included in the model. Finally the thermo-hydraulic phenomena which are responsible of temperature distribution of solid bodies and temperature, velocity and pressure distribution of Helium in the superconducting cable needs to be taken into account. The electromagnetic phenomena end the thermohydraulic phenomena are strongly coupled each other due to the temperature dependence of the electric field vs. current density curve of the superconducting and stabilizer materials.

Since year 2000 the Applied Superconductivity Laboratory is involved in a reasearch program which is supported and coordinated by the European Fusion Development Agreement (EFDA) (www.efda.org),   with the main goal of the development of code THELMA for the calculation of current distribution, a.c. losses, helium temperature, velocity and pressure distributions in the superconducting coils which are of interest for the nuclear fusion applications. Code THELMA allows the complete description of  a superconducting coil by simultaneous solution of the equation of the electromagnetic models of the cable-sectors, of the cable terminations and joints, and of the thermohydraulic model of helium and of the thermal model of all solid bodies.

The electromagnetic model of the cable-sector is based on a distributed parameters circuit approach and has been developed by the Department of Electrical Engineering of the University of Bologna. The electromagnetic model of the cable-terminations and joints between cable-sectors is based on a lumped parameters circuit approach, as much as current distribution in the superconducting cable is concerned, and on a finite element approach as much as current density distribution in the solid normal material of joints/terminations is concerned; the model has been developed by the Department of Electrical, Mechanical and Management Engineering of the University of Udine (www.uniud.it). The thermo-hydraulic model of helium flow and the thermal model of all the solid bodies have been developed by the Department of Energetics of Politecnico of Torino (www.polito.it).

The research activity is coordinated by the EFDA Close Support Unit in Garching and from the Superconductivity Division of the Research Center of ENEA in Frascati (www.frascati.enea.it). A contribution is given from the Applied Superconductivity Center of the University of Twente, as much as the experimental validation of the code is concerned. The THELMA code is now in the validation phase.

References:

1.      P.L. Ribani, “CDCABLE. A code to calcolate current distribution in superconducting multi-filamentary cables”, TASK N. TW0-T400-1/01 Deliverable N.8, Report of University of Bologna, May, 2002

2.      M. Breschi, P.L. Ribani, “Measurements of self and mutual induction coefficients of the strands of a multi-strand multi-stage cable and comparison with numerical results”, TASK N. TW1-TMC-CODES, Design and interpretation codes, Report of University of Bologna, October 2002.