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Beam-breakup (BBU) suppression due to BBU mode detuning is analyzed. The BBU growth equation with linear detuning is solved by the WKB approximation and saddle-point calculations, and an asymptotic formula for BBU growth amplitude is evaluated, which shows substantial saturation in BBU growth for appropriate detuning. Theoretical results are confirmed by comparison with numerical BBU simulations.
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Ken Takayama (1992) studied this question.
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