Wake Field Simulation of a Collimator

Collimators are used to lower the background noise in linear collider systems. Unfortunately they introduce at the same time short range wake fields. This can lead to transverse kicks and finally to off axis beams. Thus, to avoid instabilities the wake field effect must be taken into account during the design phase of a collimator.

The collimator shown in Figure 1 has transverse dimensions of 38 mm and a taper of 300 mrad. Due to symmetry conditions the simulation can be reduced to one quarter of the structure as shown in Figure 2. The longitudinal boundaries are covered by waveguide ports. The waveguide ports serve for absorbing hollow waveguide modes which can be excited at the discontinuity. The beam itself is absorbed by special boundary conditions implemented in CST PS.

Bunch length, total charge and beam velocity are denoted in Figure 3. The blue line in the picture indicates the beam axis. A direct integration method was used to obtain the wake fields and later on the loss factor. The corresponding axis of integration is illustrated by the red line in Figure 3.

In Figure 4 the absolute value of the electric field is shown. In the beginning it consists only of the self field of the moving electric charges. When passing the discontinuity this self field excites wake fields, which can deflect subsequent particles.

The loss factor is determined by the longitudinal wake potential according to [1]. A parameter study (see Figure 5) very clearly shows the increase of the losses introduced by the collimator with increasing taper angle. The trend in the results was also reported in the study performed in [2].

As shown in this article, CST PS can be used to predict the wake field effects in accelerator systems. The time dependent field distribution can be easily obtained. Wake potential, impedance, bunch spectrum and loss factor are automatically evaluated by the program and given in the result tree. With a combination of this data and the postprocessing templates, the user has several options to obtain information customized to the specific needs.

References:

[1]  T. Weiland, R. Wanzenberg, "Wakefields and Impedances," Proceedings of the CAT-CERN Accelerator School (CCAS), pp. 140-180, 1993.

[2] C.-K. Ng, T. O. Raubenheimer, P. Tenenbaum, "Numerical Calculations of Short-Range Wakefields of Collimators," Proceedings of the Particle Accelerator Conference, Chicago, USA, pp. 1853-1855, 2001