Abstract
The beam interaction with transverse magnetic (TM11-like) modes in standing-wave linear accelerators leads to the phenomenon of beam blowup whenever the average beam current exceeds a critical value. Previous theories that estimate a lower bound for that threshold current neglect the interaction of the neighboring modes in the periodic structure. A more realistic estimate has been developed that carefully includes the effect of the coupling on the damping mechanism and takes into consideration all factors influencing the system response. Developed results supply the designers with the various parameters that could be varied, should higher values than the previously mentioned threshold current be needed. The reported analysis takes care of a complete tank length of coupled cells with emphasis on the side-coupled structures for their distinct advantages in machines of high current capacity. The physics of the oscillation mechanism is cast in one final formulation with known transient solution. The external force function is made available for discussing the steady-state solution when the pulse frequency is a submultiple of the resonance frequency, which causes the off-centered beam to be deflected and usually puts one of the constraints on beam focusing.
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