Beam Transfer Functions, Stability Diagrams and Schottky Spectra for Unbunched Beams

Abstract

Beam transfer functions and stability diagrams for unbunched beams can be straightforwardly derived starting from a Hamiltonian which includes collective interactions and using that Hamiltonian in the Vlasov equation. One can start with a very general Hamiltonian which can be applied to longitudinal, transverse, or more complex impedance-like interactions. Furthermore, one can compute Schottky spectra for these same circumstances. Examples are worked out for the standard longitudinal and transverse cases