Linearized method for the study of transverse instabilities driven by electron clouds

We present a linearized method to study transverse instabilities due to electron clouds. It is based on an accurate and compact characterization of the cloud dipolar and quadrupolar forces, that can be easily obtained from quick single-pass numerical simulations. The long-term stability properties of the bunch are then predicted by solving the linearized Vlasov equation, taking into account the dipolar forces introduced by the e-cloud along the bunch as well as the betatron tune modulation with the longitudinal coordinate due to the e-cloud quadrupolar forces. The method is benchmarked against macroparticle simulations based on the same characterization of the e-cloud and the results are compared against conventional “brute-force” simulations based on the Particle-In-Cell method. The effect of transverse nonlinearities due to the e-cloud, which are neglected by the linearized method, is also analyzed.