We review the theory of the longitudinal stability of a single bunch. We point out that many stability analyses are inconsistent because of the neglect of nonlinear effects. We reformulate the stability problem to be able to include nonlinear phenomena and derive the usual coupled-mode instabilities. We then examine the effect of nonlinearities and find that they can induce a bunched beam to look like an unbunched beam with the peak current; in other words, the Boussard criterion must be used.
DOE contract number: W-7405-ENG-36 OSTI Identifier 5901492 Research organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States).