A general theory of beam breakup instabilities

Summary form only given, as follows. The beam breakup instabilities (BBUs) in linear accelerators were reexamined with the use of a simple continuum model. The standard mode coupling approach in microwave engineering was adopted to treat the cumulative, regenerative, and convective BBU in a unified manner. In addition to being able to recover all major classical solutions as limiting cases, this simplified treatment, in several instances, provides a rather different perspective on the role of the focusing magnetic fields, spreads in betatron frequencies, spreads in the breakup mode frequencies, etc., than has been given ill the past. Dimensionless parameters were constructed which provide an immediate assessment of the relative importance of these effects, as well as the anticipated BBU growth when these various factors are incorporated. A highly accurate numerical scheme has been devised which directly integrates the governing equations. Excellent agreement between the numerical results and the analytic theory was observed. The numerical studies include other effects, such as stagger tuning and nonlinear focusing, which defy analytical treatment. BBU growth in a recirculating geometry was investigated with the use of a continuum model. Properties of BBU growth were contrasted between the linear and recirculating geometries