Title: Stability Analysis of Longitudinal Beam Dynamics using Noncanonical Hamiltonian Methods and Energy Principles
Abstract:In the presence of RF focusing and a purely inductive impedance bunch equilibria in the form of Haiessinski distributions--when they exist--are linearly stable. This is the case whether the potential ...In the presence of RF focusing and a purely inductive impedance bunch equilibria in the form of Haiessinski distributions--when they exist--are linearly stable. This is the case whether the potential well distortion associated with the impedance causes bunch lengthening or shortening. We provide a general proof of this fact using Hamiltonian methods and energy principles. In the presence of bunch shortening our analysis indicates that there is a critical current for linear stability. However, this threshold is identical to the critical current defining the condition for the very existence of a Haiessinski equilibrium.Read More