Three-dimensional stability theory of a continuous beam with axisymmetric Kapchinskij-Vladimirskij distribution

This work is a three-dimensional stability study based on the modal analysis for a continuous beam with an axisymmetric Kapchinskij-Vladimirskij (KV) distribution. The analysis is carried out self-consistently within the context of linearized Vlasov-Maxwell equations and electrostatic approximation. The emphasis is on investigating the coupling between longitudinal and transverse perturbations in the high-intensity region. The interaction between the transverse modes supported by the KV distribution and the “usual transverse modes” is examined. We found two classes of “coupling modes” that would not exist if longitudinal and transverse perturbations are treated separately. We also found that some transverse modes can interact among themselves through longitudinal perturbation to cause instability. The effects of wall impedance on beam stability is also studied and numerical examples are presented.