$X$-band rf structure with integrated alignment monitors

We present the electrical design for an $X$-band traveling wave accelerator structure with integrated alignment monitors to measure the transverse wake, which will be used as part of the PSI-XFEL project and in the CLIC structure testing program. At PSI, it will compensate nonlinearities in the longitudinal phase space at the injector prototype of the PSI-XFEL. At CLIC it will be tested for breakdown limits and rates in the high gradient regime. The prolonged operation of such a structure in the PSI-XFEL injector, albeit not for the CLIC parameter regime, will constitute a good quality test of the manufacturing procedures employed. The operation in the PSI-XFEL injector will be at a relatively modest beam energy of 250 MeV, at which transverse wakes can easily destroy the beam emittance. For this reason, the layout chosen employs a large iris, $5\pi /6$ phase advance geometry, which minimizes transverse wakefield effects while still retaining a good efficiency. As a second important feature, the design includes two wakefield monitors coupling to the transverse higher order modes, which allow steering the beam to the structure axis, potentially facilitating a higher precision than mechanical alignment strategies. Of special interest is the time domain envelope of these monitor signals. Local offsets due to bends or tilts have individual signatures in the frequency spectrum, which in turn are correlated with different delays in the signal envelope. By taking advantage of this combined with the single bunch mode at the PSI-XFEL, the use of a relatively simple detector-type rf front end should be possible, which will not only show beam offsets but also higher order misalignments such as tilts in the structure. The resolution of these monitors is determined by the tolerance of the random cell-to-cell misalignment leading to a spurious signal in the monitors.

Figure 1

Variation of the cell diameter and iris aperture along the structure omitting the monitor cells described later. The first cell has 9.986 mm iris diameter, the last one 8.239 mm.

Figure 2

Variation of group velocity and $r/Q$ along the structure.

Figure 3

The mode launcher geometry converting the waveguide mode into the circular ${\mathrm{TM}}_{01}$ mode at a match better than $-45\mathrm{dB}$.

Figure 4

Reflection coefficient for the input and output matching cells.

Figure 5

Dispersion diagram of lowest two dipole bands in cell 36.

Figure 6

Limits of lowest dipole band and synchronous frequency versus cell number. Also shown is the location of the wakefield couplers with their respective bandwidths.

Figure 7

Transverse wake impedance for the structure as calculated via the dual resonator model [13].

Figure 8

Wake monitor cell using side coupled output waveguides with electric short on one side.

Figure 9

Simulated output signals from upstream and downstream monitors versus frequency.

Figure 10

Signal envelope from upstream and downstream monitors vs time.

Figure 11

Signal envelope upstream and downstream monitors vs time assuming structure axis tilted to beam axis.

Figure 12

Signal envelope upstream and downstream monitors vs time assuming bent structure.

Figure 13

Signal envelope upstream and downstream monitors vs time assuming random, uncorrelated misalignment of individual cells in the structure. The signal value is normalized to the standard deviation of the misalignments (1 mm here).

Figure 14

Double resonator chain used to model the collective wake in the lowest two dipole bands. It is fully characterized by the resonant frequencies and cell-to-cell couplings $\omega$ and $\kappa$ for the TE and TM parts as well as the TM capacitor giving the coupling to the beam.

Figure 15

Transverse wake function of $X$-band structure.