A three-dimensional kinetic theory of continuous-beam stability

This work is a three-dimensional stability study based on the modal analysis for a continuous beam with a 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 those modes sustainable by the cold beam is examined. We found two classes of coupling modes that would not exist if the longitudinal and the transverse perturbations are treated separately. The effects of wall impedance on beam stability is also studied and numerical examples are presented