Superconducting Magnets for the LHC: Conception, Optimization and Inverse Problem Solving

The Large Hadron Collider (LHC), approved by the CERN Council in December 1994, is a 7+7 TeV proton accelerator-collider, to be installed in the existing 27 km long LEP tunnel. The main technological challenges of the machine are the superconducting magnets, in total over 8'000 units immersed in superfluid helium, and the very large cryogenic system, which maintains the entire string of cryomagnets at its working temperature below 2 K. The paper gives an overview on the design process of the superconducting magnets where mathematical optimization techniques are applied. For the concept phase genetic optimization algorithms are used, followed by deterministic methods for the coil and iron cross-section optimization. Inverse problem solving is finally applied to trace manufacturing errors.