Electron cloud cyclotron resonances in the presence of a short-bunch-length relativistic beam

Computer simulations using the 2D code POSINST were used to study the formation of the electron cloud in the wiggler section of the positron damping ring of the International Linear Collider. In order to simulate an x-y slice of the wiggler (i.e., a slice perpendicular to the beam velocity), each simulation assumed a constant vertical magnetic field. At values of the magnetic field where the cyclotron frequency was an integral multiple of the bunch frequency, and where the field strength was less than approximately 0.6 T, equilibrium average electron densities were up to 3 times the density found at other neighboring field values. Effects of this resonance between the bunch and cyclotron frequency are expected to be non-negligible when the beam bunch length is much less than the product of the electron cyclotron period and the beam velocity, for a beam moving at v≈c. Details of the dynamics of the resonance are described.