Electron-Cloud Pinch Dynamics in Presence of Lattice Magnet Fields

The pinch of the electron cloud due to a passing proton bunch was extensively studied in a field free region and in a dipolar magnetic field. For the latter study, a strong field approximation helped to formulate the equations of motion and to understand the complex electron pinch dynamics, which exhibited some similarities with the field-free situation. Here we extend the analysis to the case of electron pinch in quadrupoles and in sextupoles. We discuss the limits of validity for the strong field approximation and we evaluate the relative magnitude of the peak tune shift along the bunch expected for the different fields.