Modelling and transmission-line calculations of the final superconducting dipole and quadrupole chains of CERN's LHC collider: methods and results

Summary form only given, as follows. A long chain of superconducting magnets represents a complex load impedance for the powering and turns into a complex generator during the energy extraction. Detailed information about the circuit is needed for the calculation of a number of parameters and features, which are of vital importance for the choice of powering and extraction equipment and for the prediction of the circuit performance under normal and fault conditions. Constitution of the complex magnet chain impedance is based on a synthesized, electrical model of the basic magnetic elements. This is derived from amplitude and phase measurements of coil and ground impedances from d.c. to 50 kHz and the identification of poles and zeros of the impedance and transfer functions. An electrically compatible RLC model of each magnet type was then synthesized by means of a combination of conventional algorithms. Such models have been elaborated for the final, 15-m long LHC dipole (both apertures in series) as well as for each aperture of the final LHC main quadrupole (Short Straight Section). The relevant sector chains each contains 154 dipoles and 51 (or 47) quadrupoles. The Saber simulator was used for the calculation of the currents and voltages in the chains under various conditions and this during powering and extraction. The analysis of each chain comprised: determination of resonance frequencies, ripple calculations, ramping studies, determination of transient phenomena, leakage current calculations, earthing considerations and determination of the effect of damping. The main results from these simulations are presented in the paper. Finally, the future plans for an extension of the study will be given.