Impedance and component heating

The impedance is a complex function of frequency, which represents, for the plane under consideration (longitudinal, horizontal or vertical), the force integrated over the length of an element, from a “source” to a “test” wave, normalized by their charges. In general, the impedance in a given plane is a nonlinear function of the test and source transverse coordinates, but it is most of the time sufficient to consider only the first few linear terms. Impedances can influence the motion of trailing particles, in the longitudinal and in one or both transverse directions, leading to energy loss, beam instabilities, or producing undesirable secondary effects such as excessive heating of sensitive components at or near the chamber wall, called beam-induced RF heating. The LHC performance limitations linked to impedances encountered during the 2010-2012 run are reviewed and the currently expected situation during the HL-LHC era is discussed.