Methods and results of modeling and transmission-line calculations of the superconducting dipole chains of CERN´s LHC collider

Electrical modeling and simulation of the LHC magnet strings are being used to determine the key parameters that are needed for the design of the powering and energy extraction equipment. Poles and zeros of the Laplace expression approximating the Bode plot of the measured coil impedance are used to synthesize an R/L/C model of the magnet. Subsequently, this model is used to simulate the behavior of the LHC main dipole magnet string. Lumped transmission line behavior, impedance, resonance, propagation of the power supply ripple, ramping errors, energy extraction transients and their damping are presented in this paper.