Transverse wakefield of waveguide damped structures and beam dynamics

In the design of new high energy particle colliders with higher luminosity one is naturally led to consider multi-bunch operation. However, the passage of a leading bunch through an accelerator cavity generates a wakefield that may have a deleterious effect on the motion of the subsequent bunches. Therefore, the suppression of the wakefield is an essential requirement for beam stability. One solution to this problem, which has been studied extensively, is to drain the wakefield energy out of the cavity by means of waveguides coupled with the cavity and fed into matched terminations (2). Waveguide dimensions are chosen to yield a cutoff frequency well above the frequency of the accelerating mode so that the latter is undamped. This paper presents a thorough investigation of the wakefield for this configuration.; The effectiveness of waveguide damping has typically been assessed by evaluating the resultant {dollar}Qsb{lcub}ext{rcub}{dollar} of higher order cavity modes to determine their exponential damping rate. We have developed an efficient method to calculate {dollar}Qsb{lcub}ext{rcub}{dollar} of the damped modes from popular computer simulation codes such as MAFIA. This method has been successively applied to the B-factory RF cavity.; We have also found another type of wakefield, associated with waveguide cut-off, which decays as {dollar}tsp{lcub}-{lcub}3over2{rcub}{rcub}{dollar} rather than in the well-known exponentially damped manner. Accordingly, we called it the persistent wakefield. A similar phenomenon with essentially the same physical origin but occurring in the decay of unstable quantum states, has received extensive study (3).; Then we have developed various methods of calculating this persistent wakefield, including mode matching and computer simulation. Based on a circuit model we estimate the limit that waveguide damping can reach to reduce the wakefield.; Finally, based on an analytic treatment of the Beam Break-Up (BBU) instability, we show that bunch to bunch accumulation effects are limited for any wakefield that falls off at least as fast as {dollar}tsp{lcub}-1{rcub}.{dollar} As a consequence, there is no significant qualitative difference in the effect on BBU of a {dollar}tsp{lcub}-{lcub}3over2{rcub}{rcub}{dollar} decaying wakefield and an exponentially damped one, and even the quantitative difference is small when the characteristic decay lengths are the same. The persistent wakefield, in particular, turns out to have a small effect based on the current Next Linear Collider parameters.