First measurement of energy dispersion in an electron beam due to quantum fluctuations in undulator radiation

Evaluation of longitudinal phase space based on corrugated structures

A corrugated structure—a small radius corrugated pipe or two corrugated metal plates with an adjustable gap—is recommended in the reef.9 to remove the linear energy correlation (chirp) in a relativistic electron beam and first confirm this experimentally.10. When an electron beam is displaced relative to the center of the corrugated structure and passes close to the corrugated wall, it experiences a time-dependent transverse kick in the direction of the wall, so that the beam becomes perpendicular to the wall. . This characteristic of the corrugated structure is exploited in the FEL scheme, i.e. the fresh slice technique11and for diagnostic purposes to measure beam lengths12,13 and more recently for electron beam longitudinal phase space (LPS) measurements14.

In the European XFEL, development of an LPS evaluation project using corrugated structures was initiated in October 2020 and implemented in January 2022.15. The new probe consists of a 5 m long corrugated metal plate mounted after the SASE2 undulator and a GAGG:CE screen mounted in the downstream arc to take LPS images of the electron beam. The transverse kick strength of a corrugated plate depends on the current distribution of the beam and the distance between the beam and the corrugated plate. Corrugated structures in PSI14 and SLAC16 Both use movable jaws with appropriate mechanics to adjust beam spacing. However, in our evaluation the distance between the beam and the corrugated plate is controlled by a trajectory bump. This significantly simplifies the design of the entire system. A simplified configuration of the diagnostic beamline is shown in Fig. 1, where the beam energy Ehorizontal dispersion in screen position \(D_x\)and the deviation parameter \(K_{max}\) According to the experiment described in this paper. To demonstrate the measurement of the longitudinal phase space of an electron beam with a corrugated structure, we modeled the entire diagnostic beamline, see “Construction”.


An ideal particle distribution with a Gaussian current profile was tracked using Ocelot.17 through the entire diagnostic beamline (Fig. 1). The effect of a single corrugated plate on the electron beam was simulated based on an analytical approach.18,19. We observed the slice beam parameters at two beamline positions, first in front of the corrugated structure and then in the screen (left column, Fig. 4). Corrugated structures can be seen to induce beam A. \(\ Son\)-B mail, in our case the most pronounced vertical plane, the plane of the transverse kick, an energy chirp, and a slice energy spread.

Figure 4

Modeling longitudinal phase space measurements with corrugated structures. The initial beam parameters of an ideal Gaussian beam were chosen to be close to the beam parameters estimated during quantum diffusion effect measurements. The left column shows the beam distribution before the corrugated structure and in the position of the screen, the right column shows the image of the streaked beam and its analysis.

The right column of Figure 4 shows an image of a linear beam on the screen and the result of processing this image, see “Image Analysis”. If we select a fragment with minimum energy dispersion, the measurement accuracy will be higher. As we can see, from the image analysis the spreading slice energy is at a minimum at the beam head.

Image analysis

The streaked beam image was analyzed by fitting each column of pixels with a Gaussian function, where the center of said fit corresponds to the mean slice energy and the standard deviation of the slice energy spread. The processing algorithm is the same as in the processing of real images taken during measurement as well as images acquired in simulation.

Energy calibration and resolution

To calibrate the energy axis of the diagnostic system, the horizontal spread at the screen position was measured by scanning the voltage of the last accelerator RF station and measuring the center of mass of the beam on the screen. It was a measurement \(D_x=0.454\) m

We independently verified the energy calibration of our diagnostic system using the images we acquired. The average energy of an electron beam is reduced by synchrotron radiation, and the analytical formula for the energy loss in an undulator with length is L The form is:

$$\begin{aligned} U= frac{4 \pi ^2}{3 } \frac{ r_e E^2 K^2 L}{ mc^2\lambda _w^2}. \end{aligned}$$


The average energy loss can be measured by knowing the spread over the screen position and the shift in the center of mass of the beam image on the screen for different undulator configurations. The result is shown in Figure 5. One can also consider this measurement in a different way. That is, the energy loss generated in the undulator can be used for dispersion calibration. By doing this we get the following dispersion values: 0.451 m for measurements along the length of the undulator and 0.450 m for measurements along the length of the undulator. of the. They are in good agreement with measurements using energy conversion in the accelerator.

Figure 5
Figure 5

Average beam energy loss due to synchrotron radiation. The left plot shows the beam energy loss measurements for a range of undulator magnetic lengths L. The right plot shows the beam energy loss measurements for a range of undulators. of the The parameters theoretical lines obtained with Eq. (4).

One possible effect that can affect dispersion calibration in this way is energy loss due to coherent radiation in the undulator.20. However, as shown in21, this effect is strongly suppressed by the transverse size of the electron beam. Our estimates show that the energy loss due to coherent radiation is negligible for any reasonable electron beam model.

Energy resolution was also measured. The maximum resolution of 1.43 MeV corresponds to the head of the beam, and decreases towards the tail of the beam.

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