Scaling Laws for the Field Quality at Injection in the LHC Dipoles

The selection and use of reference magnets as a mean to improve predictability and reproducibility of the operation of the LHC depends on whether few magnets can be found that represent the average behavior of a sector, or, in the limit, of the whole accelerator. The purpose of this note is to show that it is possible to select magnets that represent well, on average, a family in the population of the magnets produced so far. We refer to this property by saying that the behavior of a single magnet can be scaled to be equal to the average of a family of magnets. The procedure used to achieve this equivalence is referred to as the scaling law.