Transverse-Longitudinal Coupling in Intense Beams

The coupling between transverse and longitudinal perturbations is studied self-consistently by considering a beam of K-V distribution. The analysis is carried out within the context of linearized Vlasov-Maxwell equations and electrostatic approximation. The perturbation is assumed to be azimuthally symmetric but axially non-uniform (kz ¿ 0). It is shown that the coupling affects both the longitudinal and transverse modes significantly in the high density and low frequency region. Two new classes of longitudinal modes are found which would not exist if the transverse motions of particles are neglected. The effect of resistive wall impedance on beam stability is also studied. It is found that the longitudinal impedance can cause the transverse modes also to be weakly unstable.