1. Overview Field description for the LHC (FiDeL) – introduction and overview of the model Magnetic measurements Beam dynamics as observed through beam based measurements Precision and Control of the LHC – precision in controlling the tune – precision in controlling the chromaticity Conclusions 04/12/2014 1 Nicolas Aquilina (University of Malta)

2. Fringe fields – multipoles It is possible to show that the following is a solution of the 3D magneto-static equations (for the full derivation please see paper: http://arxiv.org/abs/1404.1762) where b is a constant and h is given by Note that B u and B v are proportional to each other so that it is not possible to describe a quadrupole with this solution. However, it is possible, due to the linearity of the equations, to add several of these solutions together as follows: for any functions f(h+iz) and g(h-iz) with 2 Bruno Muratori, Darsbury

3. 3 Vjeran Vrankovic (PSI)

4. SYMPLECTIC integrator of z-dependent Hamiltonian Reference: Y. Wu, E. Forest and D. S. Robin, Phys. Rev. E 68, 046502, 2003 The solution of the equation of motion for this Hamiltonian using Lie algebra formalism is (Transfer Map or Lie Map): The transfer map M(σ) can be replaced by a product of symplectic maps which approximates it (symplectic integrator). | PAGE 4 Equivalent paraxial Hamiltonian in the extended phase space: scaled vector potential 4 th canonical pairs independent variable | PAGE 4 BeMa | December 2014 Barbara Dalena, CEA

5. Realistic transfer map computation: scheme of the method | PAGE 5 BeMa | December 2014 Barbara Dalena (CEA)

6. 2D magneto-static simulations: magnetic error distributions 6 Goal: understand source of resonances 2D calculation including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA) 1000 models per magnet type and current level have to be calculated (<1 d with advanced and additional licenses, before 10 d) Performed for momentum of 2.14 GeV/c, 2.78 GeV/c, 14 GeV/c, 26 GeV/c Coils can be displaced, no rotation: Main coils (2 x 4 DOFs),  = 3 mm F8 (2 x 4 DOFs),  = 1 mm PFW (2 x 2 DOFs),  = 0.7 mm Iron is displaced in y-direction,  = 0.02/3 mm 2.14 GeV/c Reference radius r = 10 mm Simone Gilardoni, CERN