Higher-order mode-based cavity misalignment measurements at the free-electron laser FLASH

At the Free-Electron Laser in Hamburg (FLASH) and the European X-Ray Free-Electron Laser, superconducting TeV-energy superconducting linear accelerator (TESLA)-type cavities are used for the acceleration of electron bunches, generating intense free-electron laser (FEL) beams. A long rf pulse structure allows one to accelerate long bunch trains, which considerably increases the efficiency of the machine. However, intrabunch-train variations of rf parameters and misalignments of rf structures induce significant trajectory variations that may decrease the FEL performance. The accelerating cavities are housed inside cryomodules, which restricts the ability for direct alignment measurements. In order to determine the transverse cavity position, we use a method based on beam-excited dipole modes in the cavities. We have developed an efficient measurement and signal processing routine and present its application to multiple accelerating modules at FLASH. The measured rms cavity offset agrees with the specification of the TESLA modules. For the first time, the tilt of a TESLA cavity inside a cryomodule is measured. The preliminary result agrees well with the ratio between the offset and angle dependence of the dipole mode which we calculated with eigenmode simulations.

Figure 1

Different scenarios for a bunch (red) traversing a cavity. In the top row, the paraxial trajectory has an offset $x$ with respect to the cavity axis, and the middle row shows a trajectory tilt angle $\alpha$. The bottom scenario illustrates a tilted bunch with angle $\mathrm{\Theta }$ traversing the cavity on axis.

Figure 2

Longitudinal cross section of a TESLA cavity.

Figure 3

Geometry and orientation of the higher-order mode (upstream and downstream) and fundamental power coupler (downstream).

Figure 4

Normalized amplitude $V$ of the beam-excited ${\mathrm{TE}}_{111}\text{−}6$ dipole mode for different beam trajectories. The dots are results of eigenmode calculations, and the dashed lines indicate a linear fit. In the left graph, paraxial trajectories with different offsets $x$ are evaluated; the right graph shows the amplitude as calculated for different trajectory tilt angles $x^{\prime }$ through the longitudinal center of the cavity.

Figure 5

Schematic drawing of the experimental setup used for the HOM-based cavity misalignment measurement. Eight cavities are located inside one accelerating module, followed by a BPM. The rf is switched off, assuring a drift space between the upstream and downstream BPMs. The beam position and angle at each cavity are calculated from the BPM readings. For each dimension, two steerers are needed in order to get any combination of beam offset and angle at a cavity. Each cavity is equipped with an upstream and a downstream HOM coupler. At each coupler, the signals are filtered, down-converted, and digitized.

Figure 6

Beam position and angle as calculated for the first cavity of ACC2 at FLASH during a HOM-based cavity misalignment measurement. The $x\text{−}y$ plane (left) and the $x\text{−}{x}^{\prime }$ plane (right) for 3300 trajectories are plotted. For each plane, two steerers are driven randomly within a defined range, giving, e.g., in the $x\text{−}{x}^{\prime }$-plane a tilted rectangular shape. Its inhomogeneous filling is due to beam losses.

Figure 7

Normalized beam-excited spectrum as recorded from a HOM coupler at ACC4 at FLASH. The left plot covers a wide frequency range including several monopole and dipole bands. The highlighted peak in the left plot and its magnification in the right one shows the ${\mathrm{TE}}_{111}\text{−}6$ dipole mode used for the diagnostic. Note its double-peak character, indicating a frequency deviation between the two parts of the orthogonally polarized doublet.

Figure 8

Beam-excited ${\mathrm{TE}}_{111}\text{−}6$ dipole mode in the time domain from the HOM electronics of the downstream coupler of cavity eight in ACC1. The sampling rate is 108 MHz. The measured raw signal (left) and the processed signal (right) are plotted. The oscillation of the raw signal in the first 100 samples is the calibration signal of the readout electronics. For this particular beam trajectory, the digitizer is in saturation till sample 180. Since it is in saturation till sample 343 for other beam trajectories, the processed signal is cut till that point for all trajectories to ensure a quantitative comparison.

Figure 9

Normalized amplitude of the first dipole mode at the upstream coupler (left) and of the second mode at the downstream coupler (right) at cavity two in ACC2 as a function of beam offset $x$ and $y$. The dots are color coded by the relative signal strength, giving a bright yellow point at 1 and a dark blue point at 0. The red lines indicate the fitted polarization axes for both modes.

Figure 10

Normalized amplitude $V$ of the second dipole mode at the upstream coupler at cavity two in ACC2 as a function of the transformed horizontal beam trajectory offset $\tilde{x}$ (upper left), vertical offset $\tilde{y}$ (lower left), horizontal tilt ${\tilde{x}}^{\prime }$ (upper right), and vertical tilt ${\tilde{y}}^{\prime }$ (lower right). Note that each data point appears in every graph.

Figure 11

Normalized amplitude $V$ of the first dipole mode at the downstream coupler at cavity two in ACC2 as a function of the transformed horizontal beam trajectory offset $\tilde{x}$ (upper left), vertical offset $\tilde{y}$ (lower left), horizontal tilt ${\tilde{x}}^{\prime }$ (upper right), and vertical tilt ${\tilde{y}}^{\prime }$ (lower right). Note that each data point appears in every graph.

Figure 12

Normalized amplitude $V$ of the dipole mode at the downstream coupler of cavity eight in ACC2 as a function of beam offset $x$ and $y$. The dots in the left plot show qualitatively the offset dependency and are color coded by the relative signal strength, giving a bright yellow point at 1 and a dark blue point at 0. The normalized amplitude of the highlighted points is plotted in the right graph as a function of the transformed vertical offset $\tilde{y}$, including a linear fit with a slope of 8.7%/mm.

Figure 13

Dipole mode residuals $\mathrm{\Delta }V$ of the linear fit presented in Fig. 12 as a function of the transformed vertical trajectory offset $\tilde{y}$ (left) and transformed vertical trajectory angle ${\tilde{y}}^{\prime }$ (right). No distinct systematic is identifiable in either graph.

Figure 14

Normalized power of the dipole mode as measured at each coupler at the injector module at FLASH as a function of beam offset $x$ and $y$. The upper left plot shows the upstream coupler of the first cavity, $C:1/u$, for example, and the lower right plot the downstream coupler of the eighth cavity, $C:8/d$. The dots are color coded by the relative signal strength, giving a bright yellow point at 1 and a dark blue point at 0. The red dots indicate the fitted cavity centers. Note the unequal axes limits for cavities 1–4 and 5–8.

Figure 15

Schematic drawing of the HOM-based cavity misalignment measurement setup as described in Fig. 5. The drawing illustrates exemplarily four module alignment scenarios (left) for the horizontal plane. The right-hand side shows the corresponding measurement result. The cavity offsets $x_{\mathrm{cav}}$ and tilts $x_{\mathrm{cav}}^{\prime }$ are measured with respect to the axis which is defined by the upstream and downstream BPM (red line). The latter BPM is located inside the cryomodule. The upper two and the lower two cases, respectively, are indistinguishable.

Figure 16

HOM-based cavity misalignment measurements for the horizontal (left) and vertical (right) planes. The results of two independent measurement shifts are plotted in red and blue, respectively. The upper plot shows the calculated cavity center $u_{\mathrm{cav}}$ (dots) and the deduced module axis (lines) with respect to the BPM reference axis. The middle row illustrates the residual cavity offset $\mathrm{\Delta }{u}_{\mathrm{cav}}$ with respect to the calculated module axis.

Figure 17

Histogram of the fitted residual cavity offset $\mathrm{\Delta }{u}_{\mathrm{cav}}$ with respect to the calculated module axis of the first five accelerating modules at FLASH. Both transverse planes are included. The fitted standard deviation is ${\sigma }_{\mathrm{cav}}=342\mu \mathrm{m}$.