Analysis of multibunch free electron laser operation

At the SASE-FEL user facilities FLASH and European XFEL, superconducting TESLA type cavities are used for acceleration of the driving electron bunches. The high achievable duty cycle allows for operating with long bunch trains, hence considerably increasing the efficiency of the machine. However, multibunch free electron lasers (FEL) operation requires longitudinal and transverse stability within the bunch train. The purpose of this work is to investigate the intra-bunch-train transverse dynamics at FLASH and European XFEL. Key relationships of superconducting rf cavity operation and the resulting impact on the intrabunch-train trajectory variation are described. The observed trajectory variation during multibunch user runs at FLASH is analyzed and related to both, intrabunch-train variations of the rf and the following impact on the multibunch FEL performance.

Figure 1

Horizontal offset $\mathrm{\Delta }x$ recorded at two BPMs, upstream (left column) and downstream (center column) of the injector module and the SASE radiation energy $\mathrm{\Phi }$ (right column) at FLASH [9]. The upper and mid row show the data of each bunch (black) and the mean value of each bunch train (red) within different time frames of machine operation. The bottom row exemplarily shows the data of one bunch train (black) and the corresponding 1 min mean of each bunch (red).

Figure 2

Schematic drawing of pulsed rf operation with typical numbers at FLASH.

Figure 3

Simulated accelerating gradients in ACC6 for a $650\mu \mathrm{s}$ flattop with the current FLASH $Q_L$-setup for different beam currents $I_b$. The vector sum is constant during the flattop. Feedback is switched on and there is no detuning considered. The different colored lines correspond to eight individual cavities.

Figure 4

Simulated accelerating gradient slopes in ACC6 for a $650\mu \mathrm{s}$ flattop for different mean cavity detuning $\mathrm{\Delta }f$. The vector sum is constant during the flattop and there is no beam loading. The different colored lines correspond to eight individual cavities.

Figure 5

Measured effect of Lorentz force detuning at FLASH. The left plot shows the detuning for individual cavities in the injector module without compensation. The rf flattop is from $600\mu \mathrm{s}$ to $1400\mu \mathrm{s}$, the range between the dashed lines indicates the typical beam timing. The mean accelerating gradient is $16\mathrm{MV}/\mathrm{m}$. The right plot illustrates the effect of Lorentz force detuning compensation with piezo-tuners during the flattop at the third accelerating module at FLASH.

Figure 6

Measured intrabunch-train variation of the amplitude $\mathrm{\Delta }{V}_0$ of the accelerating field. The left plot shows the amplitude variation as a function of bunch index for eight cavities located in the injector module. The right plot shows a histogram of the maximum intrabunch-train amplitude variation of all 56 cavities at FLASH. The rms value is $245\mathrm{kV}/\mathrm{m}$.

Figure 7

Amplitude of slow intra-bunch-train trajectory variation, $\mathrm{\Delta }{\widehat{u}}_{\max }$ (lower left), and the corresponding coefficient of determination $R^2$ (upper left) for the horizontal (blue) and vertical (red) plane at each BPM. The right graph shows the mean offset variation ${\overline{\mathrm{\Delta }\widehat{u}}}_{\mathrm{und}}=\sqrt{\mathrm{\Delta }{\widehat{x}}_{\mathrm{und}}^2+\mathrm{\Delta }{\widehat{y}}_{\mathrm{und}}^2}$ at the entrance of the undulator section as a function of final beam energy $E$ for different user runs.

Figure 8

Analysis of the intra-bunch-train variation of the SASE radiation energy, $\mathrm{\Delta }\mathrm{\Phi }$, recorded at FLASH during different user runs with 400 bunches. The right plot shows $\mathrm{\Delta }\mathrm{\Phi }$ as a function of the horizontal intrabunch-train offset variation $\mathrm{\Delta }{x}_{\mathrm{und}}$, measured at the entrance of the undulator section. In the mid graph $\mathrm{\Delta }\mathrm{\Phi }$ is plotted as a function of the vertical offset variation $\mathrm{\Delta }{y}_{\mathrm{und}}$. In the left graph, $\mathrm{\Delta }\mathrm{\Phi }$ is plotted as a function of beam energy $E$. The colored dots represent data available in the DAQ-system, the black crosses correspond to logbook entries.

Figure 9

Relative intrabunch-train variation of the SASE energy $\mathrm{\Delta }\mathrm{\Phi }$ as a function of the horizontal (left) and vertical (right) intrabunch-train offset, $\mathrm{\Delta }{x}_{\mathrm{und}}$ and $\mathrm{\Delta }{y}_{\mathrm{und}}$, respectively, at the entrance of the undulator at FLASH. The black dots represent data from several user runs with similar beam parameters at a mean beam energy of about 680 MeV (top) and 965 MeV (bottom). The red triangles are results of GENESIS simulations. For each user run the bunch with maximum SASE energy is used for reference by means of $\mathrm{\Delta }\mathrm{\Phi }$, $\mathrm{\Delta }{x}_{\mathrm{und}}$, and $\mathrm{\Delta }{y}_{\mathrm{und}}$.