Electro-thermal FEM simulations of the 13-kA LHC joints

The interconnections between the superconducting main dipole and main quadrupole magnets are made of soldered joints of two superconducting Nb-Ti cables embedded in a copper busbar stabilizer. The primary cause of the September 2008 incident in the LHC was a defect in an interconnection between two dipole magnets. Analyses of the incident show that possibly more defects might be present in the 13kA circuits, which can lead to unprotected resistive transitions. To avoid the reoccurrence of such an event, thorough experimental and numerical investigations have taken place to determine the safe operating conditions of the LHC. However to show measured curves is beyond the scope of this article. Furthermore, improvements in the design have been proposed in the form of additional parallel copper pieces, or shunts, which bridge the possible voids in the soldering and offer a bypass for the current in case of a quench. The purpose of this work is to support the design choices and to indicate the sensitivity to some of the free parameters in the design. Electro-thermal Finite Element Method (FEM) simulations are performed, making use of COMSOL Multiphysics. The use of FEM allows for a profound three-dimensional analysis and some interesting features of the shunted busbar can only be revealed this way. Especially current redistribution in the shunted area of the interconnect gives important insights in the problem. The results obtained using the model are very sensitive to the exact geometrical properties as well as to the material properties, which drive the Joule heating inside the interconnection. Differences as compared to a one-dimensional model, QP3, are presented. QP3 is also used for simulations of non-shunted busbar joints as well as shunted busbars. Furthermore, margins are given for the soldering process and the quality control of the shunted interconnections, since the contact area between the stabilizer pieces and the shunt is an important quality aspect during the manufacturing of a safe interconnection.