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Beam pipe - - - - - -- Chao (1993) Collective Instabilities in Wakefield Coupled Bunches Objective - OCS6 Damping Ring - Transverse Growth Rates Kai Hock Liverpool Accelerator Group Meeting, Cockcroft 14 February 2007
Uniform Resistive Wall Transverse Force No wakefield this side Chao (1993) Wake potential
v Equation of motion y s = c No wakefield Wakefield from bunch ahead n n+1 n+2
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Trial solution Modes Eigenvector / Mode Circulant Matrix (Gray 2006)
Characteristic Equation e.g. 2 bunches, Mode 0 Multiple solutions: If assume dominated by betatron oscillation … a = 1 b 1 = 0.1 b 2 … = 0 tau = 1 | Left hand side – right hand side |
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Simulation Method - Integrate over one time interval between slices - Repeat for next interval SHMKick
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