In addition to the usual circularly symmetric TM010 mode used to accelerate particles in an rf linac, there is a large number of modes with cos 4) or sin (0 dependence, for example the TMlxx modes. These latter modes possess a uniform magnetic (dipole) field near the axis of symmetry and therefore can deflect the beam away from the axis. Any portion of an accelerated beam that is off-axis will drive these modes, so that subsequent portions of the beam will be deflected. This deflected beam will then resonantly drive the same modes in downstream cavities, so that still later portions of the beam will be more severely deflected, and so on. In this paper I report the results of numerical simulations of this so-called cumulative beam-breakup instability. The simulation assumes that only the TMlio mode acts to deflect the beam, and further assumes that this mode does not couple from one accelerating cavity to the next.*
|