Incoherent Effect of Space Charge and Electron Cloud

Trapping by resonances or scattering off resonances induced by space charge (SC) or electron cloud (EC) in conjunction with synchrotron motion can explain observations of slow beam loss and emittance growth, which are often accompanied by changes in the longitudinal beam profile. In this paper we review the recent progress in understanding and modeling of the underlying mechanisms, highlight the differences and similarities between space charge and electron cloud, and discuss simulation results in the light of experimental observations, e.g., at GSI, CERN, and BNL. In particular, we address the role of the pinched electrons and describe in detail the complexity of the electron pinch formation. We present simulation results within a dipole or in a field-free region of the beam pipe, which reveal the morphology and main features of this phenomenon, explain the physical origin of the complex electron structures like stripe in either field configuration, and discuss the dependence on some key parameters.