SINGLE BUNCH BEAM BREAKUP- A GENERAL SOLUTION*

Caporaso, Barletta and Neil (CBN) found a solution to the problem of the single-bunch beam breakup in a linac[1]. However, their method applies only to the case of a beam traveling in a strongly betatron-focused linac under the in-fluence of the resistive wall impedance. We suggest in this paper a method for dealing with the same problem. Our methods is more general; it applies to the same problem under any impedance, and it applies to a linac with or with-out external betatron focusing. 1 CBN RESULTS We denote the location along the linac by the variable z. The beam is taken to be traveling in the positive z direc-tion, and the entrance to the linac is located at z = 0. We assume throughout this paper that the charged particles are uniformly distributed longitudinally within the unperturbed bunched beam. For z> 0, the equation of motion for a beam particle i