Unavoidable trapped mode in the interaction region of colliding beams

We discuss the nature of the electromagnetic fields excited by the beams in the beam pipe of an interaction region. In trying to find an optimum geometry for this region with a minimum of electromagnetic wave excitation, we have discovered one mode, which remains even in a very smooth geometry. This mode has a longitudinal electrical component and can be easily excited by the beam. By analyzing the structure of this mode we have found a way to absorb this mode. The work was done in connection with a proposal for a future electron-positron collider.

Figure 1

Electric force field line distribution at the time when a relatively short bunch has just passed a pipe connection. The red line shows the bunch line charge density distribution and the bunch trajectory.

Figure 2

Electromagnetic field line distribution at the time when a short bunch has passed the ougoing pipe connection. The green lines show force lines with an opposite direction in comparison with other force lines shown in blue. The red line shows the bunch line charge density distribution and the bunch trajectory.

Figure 3

Electric field line distribution (left plot) and surface current distribution (right plot) of the trapped mode. Each surface current plane has a longitudinal slope of the corresponding sign. The red lines show the direction of the colliding beams.

Figure 4

FCC ee IR. The red lines show the boundary of the IR beam chamber.

Figure 5

Geometry of the IR model 1. The cross section near the pipe connection shows how the incoming pipes were squeezed to the half circle shape.

Figure 6

Wakefield potential (red line) of a 2.5 mm bunch and a bunch shape (blue line) in the IR model 1.

Figure 7

Spectrum of the excited fields (real part) in the IR model 1.

Figure 8

Electric field line distribution for the trapped mode in model 1.

Figure 9

Geometry of the IR model 2. The cross section near the pipe connection shows two small sharp transitions to the elliptical shape. The spectrum of the exited fields in this model is shown in right lower plot.

Figure 10

Inside and outside view of the transition in the IR model 3.

Figure 11

Wake potential (red line) of a 2.5 mm bunch in model 3. The blue line shows bunch linear charge density distribution.

Figure 12

Real (red line) and imagery (blue line) parts of the wakefield potential spectrum in the IR model 3.

Figure 13

Electric field line distribution for the trapped mode in model 3.

Figure 14

The geometry (blue lines) of the IR near one of the pipe connections with a fragment of the top wall (red colored plate) with the longitudinal coupling slots. Grey lines show the electric force line of the mode. Electric force lines that can be seen through the slots are perpendicular to the slot. That means that the mode field can escape out through these slots. The slot dimensions and number of them will be optimized for better absorption of the trapped mode.

Figure 15

IR smooth geometry with HOM absorbers.

Figure 16

A cumulative spectral density of the energy losses (red line) and a real part of the spectrum of the excited field (blue line). The horizontal blue line shows the level corresponds to the loss factor of the trapped mode. Above this level we have mainly propagating modes.