Calculation of inductances and induced currents in cryogenic by-pass line for SIS100 particle accelerator at FAIR

Quality of electric current delivered to the magnets of a particle accelerator is essential for safety and reliability of its operation. Even small discrepancies strongly affect the properties of particle beams. One of the sources of the disturbances is the appearance of induced currents caused by the electromagnetic interactions between the elements of the machine. In this paper the calculations of induced currents in by-pass lines of a SIS100 particle accelerator are presented. In order to find the values of the currents the self-inductances and mutual inductances of the by-pass lines are found. Due to the complex geometry of the line, especially of Ω-shaped dilatations, the numerical approach was employed. The calculations show that the size of induced currents increases with the distance between the cables in an individual bus-bar. The maximum discrepancy of the magnetic field in a dipole magnet is found to be 7.7 μT. The decrease of distance between the cables allows one to obtain a discrepancy of 1.2 μT.