Abstract
The cumulative beam breakup problem excited by the resistive-wall wake is formulated. An approximate analytic method of finding the asymptotic behavior for the transverse bunch displacement is developed and solved. Comparison between the asymptotic analytical expression and the direct numerical solution is presented. Good agreement is found. The criterion of using the asymptotic analytical expression is discussed.
Highlights
The cumulative beam breakup (BBU) problem in a periodic linear accelerator excited by the resonance wake is well understood [1,2,3,4]
The electric field induced by this asymmetric image charge will attract the beam even closer to the metal wall, though the magnetic field induced by the asymmetric image current will push the beam back to the axis
We study the BBU problem due to this long-range resistive-wall wakefield
Summary
The cumulative beam breakup (BBU) problem in a periodic linear accelerator (linac) excited by the resonance wake is well understood [1,2,3,4]. [9], and the FFS of the TESLA [10] For these cases, we study how the resistive-wall wake will dilute the beam. The conclusion we draw from the comparison is that the asymptotic resistive-wall cumulative BBU is a locally averaged current problem.
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