Correlation between magnetic field quality and mechanical components of the Large Hadron Collider main dipoles

In this work a detailed analysis of the influence of the mechanical components and the assembly procedures of the LHC main dipole on the field shape at room and cryogenic temperatures has been done. The analysis of the productions of cables, copper wedges and austenitic steel collars showed that the dimensions are inside the tolerance limits with some exceptions for the early productions of the wedges and for few dimensions of the collars. Moreover, the productions of the six suppliers of cables and of the two of collars are very homogeneous. Some differences (~15%) have been found only in the magnetization of the two suppliers of the inner layer cable of about 15%. Coupling magneto-static models and the geometrical measurements of the mechanical components the influence of the dimensions on the field quality of the dipoles has been investigated; in particular, the main results are: Superconducting cables: * The simulations show that the cable dimension variations could account for most of the specified random components of a2 and a4 and it is negligible for the other multipoles. * For high order allowed harmonics (b5 and b7) measured at 1.9 K there is a difference between magnets that can be traced back to the difference in magnetization between inner cable manufacturers. Copper wedges: * A relevant systematic effect on the b3 (1.5 units) of the first produced wedges is visible in the collared coil magnetic measurements at room temperature. This explains part of the upward trend observed in b3 in the first 25 collared coils. * It has been shown that the advices given at the beginning of the wedge production brought to a more careful control on the manufacturing and as a result the total influence of the copper wedge dimensions on the collared coil magnetic field is not relevant Austenitic steel collars: * The collar shape is the driving mechanism of field harmonics only for the even normal and odd skew in particular for b2 and a3 in Firm3, where collars of the supplier S2 are used. Two independent observations support this fact: firstly, we have strong correlations between apertures of the same magnet as expected from the assembly procedure. Secondly, the 134 expected values based on the measured dimension of the collars agree with magnetic measurements both for the average and for the standard deviation. A more general study on the random components of the field harmonics has been worked out in order to evaluate the uncertainty in the coil position in the transverse cross-section generated by mechanical tolerances. This is one of the main sources of random components of the field harmonics, limiting the possibility of obtaining a perfect field quality. We reviewed the data of the production of dipoles relative to four accelerators to analyze the agreement of the Monte-Carlo estimates with the measured values. The above quoted Monte-Carlo method, widely used in the past, gives similar estimates for normal and skew harmonics of the same order. However, already in the Tevatron production it has been observed that random components of normal and skew harmonics of the same order can differ of a factor 4 to 6. We proposed to associate different amplitudes to generate normal and skew harmonics, in order to better fit the experimental data. The final result of the analysis is an improved phenomenological model based on the acquired experience of the four large scale dipole productions to describe and forecast the random errors in a superconducting dipole. With these studies we found that there is an improvement of the degree of precision in positioning the cable block: for the first dipole production, Tevatron, the order of magnitude of geometric random components is compatible with a random movement of the blocks of ~ 65 μm whilst for the more recent productions (LHC and RHIC) e the lowest values is recorded (52 - 54 μm). In order to better estimate the field errors the four classes of harmonics are separately considered and four displacements are calculated. For RHIC and LHC dipole productions random movements of the blocks of ~50 μm r.m.s. are needed for the odd normal multipoles, ∼30 μm for the even skew, and 5 to 20 μm for the even normal and for the odd skew. Such parameters allow estimating the random geometric errors with an average error of ∼20%. In the last chapter a method based on magnetic measurements at room temperature to locate electrical shorts in the coil of the main LHC dipole has been presented. The approach is reliable since the field anomalies generated by the short are, in general, very large compared to the natural spread in field quality induced by tolerances and assembly procedures. We have shown that using an electromagnetic code, one can forecast the effect of shorts between adjacent cables on field quality, and that the comparison to experimental data gives a location of the short. The method is very sensitive, also allowing to detecting if the short is perfect or only partial. Along the LHC main dipole production, 18 coils presenting electrical shorts have been analyzed and rescued using this procedure.