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EXPERIMENTAL VERIFICATION OF THE COHERENT DIFRACTION
RADIATION MEASUREMENT METHOD FOR LONGITUDINALELECTRON BEAM CHARACTERISTICS
R. Panaś∗ , A. I. Wawrzyniak, NSRC SOLARIS, Kraków, Poland
K. Łasocha, CERN, Geneva, Switzerland
A. Curcio, INFN LNF, Frascati, Italy
Abstract
This paper presents a natural extension of prior theoreticalinvestigations regarding the utilization of coherent diffraction radiation for assessing longitudinal characteristics ofelectron beams. The study focuses on the measurement
results obtained at the SOLARIS synchrotron and their analysis through a theoretical model. The findings are comparedwith previous estimates of the electron beam’s longitudinal
profile.

COHERENT DIFFRACTION RADIATIONElectromagnetic radiation is emitted when a beam ofcharged particles accelerates or changes medium of propagation (abruptly or continuously in terms of the local electromagnetic susceptibility) [1, 2]. If wavelength of the theemitted radiation is comparable or greater than the bunch
length, the radiation is said to be "coherent" because thecontributions from the distinct particles within the beaminterfere constructively, and the bunch radiates as a whole.
In the low frequency limit the emitted radiation power isproportional to the square of the bunch intensity, while forintermediate frequency ranges the power decreases with increasing bunch length. For bunch lengths of the picosecond
scale, variations in the radiation intensity can be easily monitored by GHz-THz detectors like Schottky diodes [3, 4]. For
shorter bunches, far-infrared diagnostics are needed, suchas spectrometers [5].
Coherent radiation can be coupled out of the beamlines
through suitable transparent windows, eventually transported
in air into power detectors. For the diagnostic purposes of
the PolFEL project [6], application of the Coherent Diffraction Radiation (CDR) was investigated at SOLARIS [7].
Diffraction radiation is a type of radiation that a bunch ofparticles emits while passing close to the boundary of two
media with different indices of refraction, which allows fornon-destructive bunch length measurements [8].
In the experimental setup at SOLARIS, the beam passes
through a hollow alluminium disk. The radiation is emitted
from localized layers of that surface, imprinting the beam
properties into the emitted radiation at the transition planeand enabling diagnostics. The fact that the disk is hollow
allows the beam not to be scattered, preserving the emittanceeven if the particles do not propagate inside it.
The spectral angular distribution of energy emitted backward in the form of diffraction radiation from a perfectly∗ roman.panas@uj.edu.pl

conducting round disk, with an internal and external radiusequal to respectively 𝑎 and 𝑏, can be described with thefollowing formula [9, 10]:𝑄2𝑑2 𝐼= |𝐹 (𝜔)| 2 ××𝑑𝜔𝑑Ω(4𝜋 3 𝜖0 𝑐5 𝛽4 𝛾 2 ) ∫ 𝑏2𝜔𝜌𝜔𝜌  𝑗 𝜔22𝜌22𝑐𝑑𝜌𝜌𝐾1×𝐽1𝑒,𝛽𝛾𝑐𝑐 sin 𝜃𝑎(1)where 𝑄 denotes the bunch charge, 𝜖0 is the vacuum permittivity, 𝑐 is the velocity of light, 𝛽 is the ratio of particle
velocity to the velocity of light, and 𝛾 is the Lorentz factor. The quantity 𝐹 (𝜔) is called the bunch form factor andstrictly depends on the shape of the electron bunch. The
theoretical prediction of the spectral-angular distribution ofCDR emitted with the experimental setup at SOLARIS isshown in Fig. 1.

Figure 1: CDR spectral-angular distribution for the SOLARIS injector bunch repetition pattern and beam energyof 550 MeV.

BUNCH LENGTH MEASUREMENT
The diagnostic technique considered for PolFEL is basedon the power balance of CDR radiation collected by Schottky

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diodes in different ranges of sub- THz radiation. Following
Eq. (1), the emitted energy depends on the bunch length
through the form factor 𝐹 (𝜔). If the transverse size of thebunch is negligible, one has [11]:∫ ∞𝐹 (𝜔) =𝐼 (𝑡)𝑒 𝑗 𝜔𝑡 𝑑𝑡,(2)−∞where 𝐼 (𝑡) is the normalized dimensionless beam current
passing through the disk. Simply speaking, the form factor is the Fourier transform of the beam current. In certaincases, for example when the beam consists of a single Gaussian bunch, an exact analytical formula for the form factor
can be given, parametrized by the RMS bunch length. Thisparameter can be then experimentally retrieved by calculating the ratio of CDR power at two distinct frequencies
and comparing it to the theoretical predictions given byEq. (1). The described technique is not limited to only one
type of radiation, and has been previously demonstrated withmeasurements based on CDR [3] and Coherent Cherenkov
Diffraction Radiation [4].
In the SOLARIS linac the beam is bunched, with the3 GHz bunch repetition rate. The shape of a single bunch
differs from the Gaussian and the bunch intensity is modulated proportionally to the 100 MHz sinewave [12, 13]. As
result the corresponding form factor also differs from thesmooth form factor of a single Gaussian bunch as presentedin Fig. 2.

be used to refine an earlier measurement, but cannot serve
as a standalone indicator, due to a local extremum it takesfor bunch lengths of approximately 16 ps FWHM.

EXPERIMENTAL SETUP AND
MEASUREMENTS
The measurement were taken in the end part of the SOLARIS linac, close to the beam dump section. After passing
through 0.15 mm thick flange, the electrons move in the air
and after 20 cm they reach the experimental setup.
The arrangement for measuring the length of the electron
beam profile is visible in Fig. 3. It includes an aluminumradiator with a radius of 2.54 cm and a 5 mm radius hole atits center. Additionally, a golden-coated Ø3" 90° Off-axis
parabolic mirror focuses the radiation towards the aperturesof three diodes sensitive to different frequency bands are
employed as detectors, used alternately.

Figure 3: Experimental setup.

Figure 2: Form factors calculated for SOLARIS injector
bunch train and a single Gaussian bunch. In both cases theFWHM bunch length is equal to 12 ps.
Although deriving the information on the bunch lengthfrom a narrow frequency band is not possible at SOLARIS,
due to the oscillatory character of the form factor, the bunch
length might be derived from the cumulative power withinthe broader frequency bands.
In the previous theoretical study [14] it was determinedthat the ratio of the powers within 26.5-40 GHz and 3350 GHz bands allows to discriminate between bunch lengths
in the range from 5 to almost 25 ps full width at half maximum (FWHM). Complementary, the power emitted within
50-75 GHz band, while comparing to 33-50 GHz band, canSchottky diodes produced by Mi-Wave [15] were used forthe experiment, with the frequency band corresponding tothe ones discussed in the previous section. An importantfactor to consider was not only the sensitivity of the diodes,
but also their input aperture. A larger aperture allows moreradiation to enter the detector and thus for diodes with different apertures, it will change the power balance on thebasis of which the longitudinal profile is estimated. The
apertures of the diodes differed, therefore it was necessary
to normalize the signals with respect to the surface area ofthe diode aperture.
The diodes were placed in the holder, in the same place.
The big difficulty was the fact that it was impossible to adjust
the diode position during the beam operation. In the future,
this problem will be solved by the installation of remotely
controlled platforms on which the diodes will be placed,thanks to which it will also be possible to change the diodes
during the measurement without having to pull them out as
it is now.
As can be seen in the graph Fig. 4, the signal from thediode in the highest frequency band is at the noise level.

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This obviously lowers the accuracy of our measurement andis the most likely cause of the difference from the expectedvalue. For this reason, the ratio of the signals from the diodein the middle and the lowest band was considered the mostreliable.

Figure 4: Signals measured by diodes with different bands.
Calculating the ratio of the measured powers, we can compare them with theoretical curves which describe the change
in ratio as a function of the bunch length, as presented inFig. 5. Results from both measurements estimate the FWHM
of the longitudinal electron beam profile to be around 20 25 ps. In the work [12], the FWHM of the longitudinal

electron bunch profile at SOLARIS linac was estimated at
12 ps.

CONCLUSION
In this contribution, progress has been made at SOLARIS
towards an experimental test of the CDR-based characterization of the electron beam’s longitudinal profile for PolFEL
project. Additionally, tools for processing the measured dataand calculating the bunch length have been developed andupdated. Schottky diodes were acquired and placed in thesetup, enabling the first measurements and calculations.
The results obtained from the experiment do not alignwith the theoretical expectations. The possible cause is aweak signal, which, in the case of a diode in the highest
frequency range, made it almost impossible to extract thesignal from the noise level.
It is anticipated that by improving the signal strength fromthe diode in the highest and medium band, the estimatedbunch length will decrease and become closer to the one
from the previous estimate. In order to increase the signalstrength, the system will be re-adjusted using motorizedplatforms, which could be done online with the present beam.
Currently, adjusting the setup with the beam is not feasible.
If that proves insufficient, additional horn antennas will beinstalled on diodes.
The tested system has shown potential, indicating thatit can be used as a low-cost alternative to more complex
systems like transverse deflecting cavities (TDC) and streak
cameras for monitoring the longitudinal beam profile. Afterappropriate calibration using the methods mentioned above,
such a system based on the CDR could monitor the degreeof bunch compression after magnetic chicane.

Figure 5: Solid lines: theoretically predicted ratio of CDR
power within different bands as a function of the bunchlength. Dashed lines: experimentally measured CDR ratios.
Black crosses indicate the crossing points and therefore theestimated bunch lengths. Grey cross indicate a crossing
point rejected based on the low-medium band ratio.

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12th Int. Beam Instrum. Conf.
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