Analysis of superconducting Rutherford cables through a lumped parameter circuit

The upgrade of the LHC, High Luminosity Large Hadron Collider requires more powerful bending magnets. Four of the 1232 dipoles based on Nb-Ti technology will be replaced with magnets made of Nb3Sn in order to create space for collimators. This technology will allow the induction magnetic field of the magnets to pass from 8 to 11 Tesla. In this way, shorter magnets are needed for the same integrated field. Nb3Sn has never been used in magnet technology and its use represents a technological challenge. One of the main characteristic of Nb3Sn is its fragility. This feature could damage one or more of the forty strands of the Rutherford Cable during cool down and assembling phase, creating a breakage. The current flow will be interrupted in correspondence to the breakage and in order to preserve the transport current, it has to flow from the broken strand to others (current distributions). The aim of this thesis focuses on the analysis of a Rutherford superconducting cable with a breakage through lumped parameter circuits. In the first phase, a steady state model has been developed to allow us to calculate the values of the adjacent and crossing strands as a function of the spatial coordinate during current plateau. In order to reduce the complexity of the problem, the developed circuit is made of only three strands. Each of these strands represent a typology in which the forty strands of the cable have been divided : broken, adjacent and crossing strands. The model has been validated by a comparison with numerical software THEA (Thermal, Hydraulic and Electric Analysis of a generic superconducting cable). Subsequently of the validation, some parametric studies have been carried out in order to understand which physical parameters of the cable play a key role in the current distribution. In the second phase, the time dependence of the model has been implemented by adding dynamic components. The circuit under exam has been solved through state space representation.