AC Losses and current distribution models

•  A correct evaluation of AC losses and current distribution is a key point for the design of superconducting magnets. In particular it is extremely important for SMES Magnets, Fusion Magnets, and Accelerator Magnets.

• The AC losses must be calculated in order to correctly design the cryogenic system and to avoid or at least control the transitions to the normal state (quenches)

• The current distribution must be calculated for three main reasons:

1) It is very important for a correct evaluation of the AC losses

2) A strong current non uniformity can significantly degrade the thermal stability of a superconducting cable leading to premature quenches

3) A strong current non uniformity can affect the field quality of the field generated by the superconducting cables. This phenomenon must be known and corrected for a good operation of accelerator magnets

• A very large effort has been dedicated to the development of numerical models to calculate ac losses and current distribution in the Superconducting systems.

• This kind of modeling gives the possibility to explore in a very fast and cheap way a wide range of possible cable configurations, with different geometric and electric parameters. This would be extremely expensive to attain with an experimental apparatus.

• The following main models for the calculation of AC losses and Current distribution have been realized:

FOR HIGH-Tc AND LOW-Tc SUPERCONDUCTING TAPES, STRANDS AND BULKS

¨      A 3DT model that utilizes an equivalent network of the cable derived by discretizing by means of finite volumes and considering an integral formulation of the MQS Maxwell equations. The unknowns of the model are the currents through the faces of the finite volumes: the current density into the finite volumes is calculated by means of a least square approach. The experimental validation of the model in collaboration with CESI (Milano) is going on.

FOR LOW-Tc MULTISTRAND CABLES

¨     A 1DT model that utilizes an equivalent distributed electric model of the cable. The unknowns of the models are the currents in the strands (or macro-strands) of the cable which are functions of the position along the cable length and of the time. The model has been developed in the frame of a collaboration with the LHC Division of CERN (European Center for Nuclear Research), Geneva, Switzerland and with EFDA (European Fusion Development Agency).