Slip-stick mechanism in training the superconducting magnets in the Large Hadron Collider
Superconducting magnets can exhibit training quenches during successive powering to reaching nominal performance. The slip-stick motion of the conductors is considered to be one of the mechanisms of training. In this paper we present a simple quantitative model where the training is described as a discrete dynamical system matching the equilibrium between the energy margin of the superconducting cable and the frictional energy released during the conductor motion. The model can be solved explicitly in the linearized case, showing that the short sample limit is reached via a power law. Training phenomena have a large random component. The large set of data of the LHC magnet tests is postprocessed according to previously defined methods to extract an average training curve for dipoles and quadrupoles. These curves show the asymptotic power law predicted by the model. The curves are then fit through the model, which has two free parameters. The model shows a good agreement over a large range, but fails to describe the very initial part of the training.