Paper 
Title 
Page 
THPAN078 
An Elementary Analysis of CoupledBunch Instabilities

3399 

 K. M. Hock, A. Wolski
Liverpool University, Science Faculty, Liverpool



We reconsider the equations of motion of wakefield coupled bunches in the light of recent developments in Delay Differential Equations. In the case of uniform resistive wall in a circular accelerator, we demonstrate an alternative way to obtain the growth rates. For each Fourier mode of bunch displacements, we show that multiple time domain modes can arise from an exact solution of the equation of motion. The growth rate as it is commonly defined corresponds to only one of them. The amplitude of each Fourier mode can therefore evolve with time in a way is not simply exponential. This is a result that has been observed in simulations of wakefield coupled bunches.

