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Longitudinal instabilities of bunched beams caused by short-range wake fields

University of British Columbia

This thesis investigates the effects of short-range wake fields on the collective longitudinal motion of charged particle bunches in circular accelerators, especially the onset of instability. At high intensity, a short-range wake field can distort the bunch potential well and thereby change the stationary distribution. It is shown that if this is not taken into account, instability thresholds will be incorrectly predicted. An integral equation derived from the linearized Vlasov equation is used to find the instability thresholds in the case of space-charge impedance alone for various distribution functions. The thresholds for instability caused by the coupling between the m = ±1 azimuthal modes have been obtained analytically for several common distributions. The criterion determining these thresholds appears to be the same as that for thresholds beyond which no stationary distribution can be found. A numerical method is also used to solve the linearized Vlasov equation for the self-consistent case, including distortion of the stationary distribution, and to find the thresholds. Physical explanations are provided for the eigenmodes and instability thresholds predicted by this method. This results in a much simpler stability criterion, which depends only on the stationary distribution and does not require solution of the linearized Vlasov equation. The behaviour of electron bunches beyond the instability threshold has also been studied using multiparticle tracking. Some interesting phenomena have been seen when the bunch length is smaller than that of the wake field. Under some conditions the bunch length oscillates in sawtooth fashion, i.e. slow relaxation is followed by fast blow-up. It has also been found that the bunch may split into two equal sub-bunches which oscillate around each other in binary star fashion. These effects may explain some recent observations in electron storage rings at SLAC and CERN.

Thesis/Dissertation

application/pdf

2009-04-16

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http://hdl.handle.net/2429/7226

Physics

University of British Columbia

UBCV

DSpace