Abstract
| Using a Vlasov approach, electron cloud driven instabilities can be modeled to study beam stability on time scales that conventional Particle In Cell simulation methods cannot access. The Vlasov approach uses a linear description of electron cloud forces that accounts for both the betatron tune modulation along the bunch and the dipolar kicks from the electron cloud. Forces from electron clouds formed in quadrupole magnets as well as dipole magnets have been expressed in this formalism. In addition, the Vlasov approach can take into account the effect of chromaticity. To benchmark the Vlasov approach, it was compared with macroparticle simulations using the same linear description of electron cloud forces. The results showed good agreement between the Vlasov approach and macroparticle simulations for strong electron clouds, with both approaches showing a stabilizing effect from positive chromaticity. This stabilizing effect is consistent with observations from the LHC. |