Analysis and Optimisation of Orbit Correction Configurations Using Generalised Response Matrices and its Application to the LHC Injection Transfer Lines TI 2 and TI 8

The LHC injection transfer lines TI 2 and TI 8 will transport intense high-energy beams over considerable distances. In their regular part a FODO lattice is used with 4 bending magnets per half- cell and a half-cell length of 30.3 m, similar to that of the SPS. The relatively tight apertures in these lines require precise trajectory control. Following an earlier study a baseline correction scheme was chosen where two out of every four consecutive quadrupoles are complemented with correctors and beam position monitors ("2-in-4"). With the ordering of the equipment approaching, a further in-depth investigation has been made using a newly developed analytic method. This method evaluates, based on the design specifications, the global performance of an orbit correction system in terms of observability, correctability, correction range and response singularity. In addition, orbit and error envelopes are obtained over the full beam line in an efficient and rigorous manner, providing insights not easily accessible with conventional tools. The cost/performance ratio of a given configuration can be optimised, both analytically through the elimination of structural defects and numerically through fine-tuning. Finally, features for failure mode analysis allow the user to diagnose observed performance anomalies, and features for critical-element analysis enable the user to identify weak spots in the configuration. The method is described in detail to facilitate the interpretation of the results obtained for TI 2 and TI 8, and to allow their application to other orbit correction systems. The new, optimised 2-in-4 scheme permits some hardware economies at comparable performance. Further exploration has identified an alternative scheme with a 1-in-3 corrector and 2-in-3 position-monitor pattern. At an overall cost comparable to the 2-in-4 scheme this latter configuration maintains the possibility of intuitive one-to-one correction, important in the commissioning phase, at a performance slightly above the nominal aperture budget, but allows to reduce, using computer support, the corrected maximum trajectory excursions significantly below those of the 2-in-4 scheme.