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12th Int. Beam Instrum. Conf.
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IBIC2023, Saskatoon, Canada
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ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - T U P 0 2 2CHARACTERISATION OF CHERENKOV DIFFRACTION RADIATIONUSING ELECTRO-OPTICAL METHODS
A. Schlögelhofer1,∗ , T. Lefèvre, S. Mazzoni, E. Senes, CERN, Geneva, Switzerland
L. Duvillaret, KAPTEOS, Saint-Helene-du-Lac, France1
also at TU Wien, Vienna, Austria
Abstract
The properties of Cherenkov diffraction radiation (ChDR)
have been studied extensively during the recent years to beexploited for non-invasive beam diagnostic devices for shortbunches. The dependence of charge and the influence ofthe bunch form factor on the coherent part of the radiatedspectrum have been demonstrated and studied in the past.
However, the actual field strength of coherent ChDR as wellas its study in time domain need further investigation. In
this contribution we are using electro-optical techniques
to investigate and quantify these parameters. The electrooptical read-out brings the advantage of high bandwidth
acquisition and insensitivity to electromagnetic interference,
whereas at the same time a large fraction of the acquisition
setup can be installed and operated outside of the radiation
controlled areas. We will present experimental results fromthe CLEAR facility at CERN as well as simulations of thepeak field of the temporal profile of beam-generated ChDR
pulses.

INTRODUCTION
Cherenkov diffraction radiation (ChDR) describes the radiation produced at the surface of a dielectric by the electricfield of a relativistic charged particle passing by in the vicinity of the dielectric. This mechanism is illustrated in Fig. 1,
where the ChDR is emitted at the well-defined Cherenkov
angle 𝑐𝑜𝑠(𝜃𝐶ℎ ) = 1/(𝑛1 𝛽) with 𝑛1 denoting the refractive
index of the dielectric medium and 𝛽 = 𝑣/𝑐 the normalized
velocity of the charged particle. The produced ChDR can beanalysed to measure critical properties of a beam of charged
particles, e.g. its length or position [1]. While previous
work focused on studying the qualitative behaviour of ChDR
and measuring the frequency spectrum to reconstruct beam
properties [2–4], this contribution shows the measurementof the electric field strength generated by coherent ChDR interms of absolute numbers by sampling its temporal profile.

METHODOLOGY
An electro-optical probe (eo-probe) [5] was used to obtain a real-time high bandwidth measurement insensitive toelectromagnetic interference.

Working Principle of the Eo-Probe
The eo-probe is fully dielectric and, amongst other optical elements, contains a sensing crystal made out of BSO(Bi12 SiO20 ). It utilizes the Pockels effect, which describes∗ andreas.schloegelhofer@cern.ch𝑛1
𝑐𝑡
𝑛1𝐶ℎ𝐷𝑅
𝜃𝐶ℎℎ𝑏𝑒𝑎𝑚 𝑓𝑖𝑒𝑙𝑑𝑒−𝑣𝑡

𝑛0Figure 1: Schematic of the ChDR principle in a dielectric
medium (𝑛1 ≈ 3). The Cherenkov condition 𝑛1 ⋅ 𝑣/𝑐 > 1
must be satisfied to produce ChDR.
the linear change of the refractive index of a medium exposed to an external electric field. This induced refractive
index change introduces a birefringence in the BSO crystal.
A continuous-wave sensing laser of known polarization issent through the crystal. During exposure to an external
electric field, the BSO crystal alters the polarization state of
the sensing laser. The modulated laser light passes throughpolarizers, and its changed polarization state is then analyzed
with fast photodiodes. Using this principle, the eo-probe
measures the electric field vector up to field strengths ofMV/m.
The eo-probe (with a bandwidth ≤ 10 GHz) was placedin the accelerator hall. All the other parts of the detection
system were placed outside the radiation-controlled area.
The sensing laser was transported to the probe via 20-metrelong optical fibres. The signal was measured with a highbandwidth oscilloscope (10 GHz, 256 GSa/s, 10-bit) andthen corrected for the change of insertion loss during themeasurement as well as converted according to the antenna
factor of the probe to obtain an absolute electric field measurement. As the electric field strength scales linearly withthe bunch charge, the bunch charge was also independentlyrecorded. All the data presented in this contribution arenormalized to a bunch charge of 300 pC.

CALIBRATION
To calibrate the system’s response, a first measurement
campaign was performed on the direct beam field of anelectron bunch propagating in air.
The bandwidth of the data acquisition system is limited
to 10 GHz. Therefore, as electron bunches at the CLEAR

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facility [6] typically are only a few ps long, the bandwidth
is insufficient to measure the entire power spectrum of theelectron bunches. The direct beam field of an electron bunch
was measured to calibrate the data acquisition system forshort bunches. The calibration setup is illustrated in Fig. 2.
This measurement was compared to the analytical formula
describing the peak electric field strength obtained from thedirect beam field of a particle bunch [7]:𝐸𝑎𝑛𝑎𝑙𝑦𝑡𝑖𝑐 =𝑒𝑁13/2√2 2𝜋 𝑐𝜖0 𝜎 𝑟Figure 3 shows the measured peak electric field strengthas a function of the distance from the beam. The measuredvalue of 203.1 ± 6.3 V is smaller by a factor 7.1 ± 0.2 than theanalytical value of 1435.2 V. This discrepancy is expected
due to the bandwidth limitation of the acquisition systemitself as well as the timing jitter between the trigger signal
and the electron beam. Both these effects lead to a lower signal amplitude being measured and the resulting discrepancy
is discussed in detail below.

(1)

where 𝑒 denotes the elementary charge, 𝑐 is the speed oflight in vacuum, and 𝜖0 is the vacuum permittivity (it isassumed 𝜖0 = 𝜖𝑎𝑖𝑟 in this frequency range). The transverse
distance from the beam is denoted 𝑟 (cf. Fig. 2). The
number of particles in the bunch 𝑁 and the bunch length 𝜎must be adapted to the experimental conditions. For a chargeof 300 pC and a bunch length of 5 ps (1 𝜎), Eq. (1) yields
𝐸𝑎𝑛𝑎𝑙𝑦𝑡𝑖𝑐 = 1435.2 / 𝑟 [V/m] for the peak electric field.

The bandwidth of the acquisition system was limited toan upper frequency of 10 GHz for all the presented measurements. As the electron bunches are only a few ps long, asignificant part of the high-frequency spectrum is not measured accordingly. This behaviour is shown in Fig. 4 andaccounts for a factor ≈ 4.0 for a bunch length of 5 ps (1 𝜎)and an upper-frequency limitation of 10 GHz.

Power spectrum, a.u.

𝑡𝑜 𝑎𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛

Bandwidth Limitation𝑒𝑜 − 𝑝𝑟𝑜𝑏𝑒

1.0≤ 20 GHz≤ 10 GHz

0.50.0100

𝑏𝑒𝑎𝑚 𝑓𝑖𝑒𝑙𝑑

101102r
1.0−Intensity, a.u.

𝑒103Frequency, GHz
σ = 5.0 ps

0.50.0Figure 2: Schematic of the measurement of the direct beam
field using an eo-probe. For the calibration measurement,
the distance r between the beam and eo-probe was varied
over a distance of ≈ 100 mm.

−150−100−500Time, ps50100150Figure 4: Power spectrum and time profile of bandwidth limited acquisition (dashed lines) compared to full bandwidth(solid line).

20

Timing Jitter

Euncalibrated = (203.1 ± 6.3) / r
Electric field, kV/m

Eanalytic= 1435.2 / r

151050020406080Distance, mm

100120Figure 3: Uncalibrated peak electric field strength of thebeam field as a function of the distance (dashed line) to becompared to the analytical expectation (solid line).

Single shot traces were analyzed to get a rough estimateof the reduction of the peak signal due to the timing jitter
present. For the data point closest to the beam (r = 11.7 mm),
600 single-shot traces were acquired. The average of themaximum of each single trace divided by the maximum of
the averaged traces yields a factor 2.1, which is also illustrated in Fig. 5.
Together with the bandwidth limitation, this rough estimation yields a total scaling factor of 8.4, which needs to becompared to the obtained factor of 7.1 from the calibration
measurement. Using this simple approach, we would overestimate the results by ≈ 18%. However, it shows that theobtained factor of 7.1 from the calibration is justified.
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Intensity, a.u.

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ISSN: 2 6 7 3 - 5 3 5 0d o i : 1 0 . 1 8 4 2 9 / J A C o W - I B I C 2 0 2 3 - T U P 0 2 275lute values after calibration are shown in blue. Error bars
indicate the standard deviation of each measurement. The
experimental data was fitted for a 1/ℎ decay. The orangemarkers stem from a CST simulation [9] considering theexperimental setup in a 3D layout. The peak electric field
was sampled at 10 mm from the exit surface of the radiator.
Table 1 gives an overview of the simulation parameters.

alignedaverage

average

50
250
1.5

2.0
2.5
Time, ns

3.0 1.5

2.0
2.5Time, ns

3.0

Table 1: CST Simulation Parameters

Figure 5: Traces from the closest data point r = 11.7 mm.
Left: Average of all traces. Right: Average of traces aligned
in time to the maximum of each trace.

SolverBandwidth
Cells / wavelength
Bunch charge
Bunch length
Lorentz factor
Impact parameter
Relative permittivity (Al2 O3 )MEASUREMENT OF THE
COHERENT CHDR FIELD
Using the same eo-probe and acquisition setup as forthe calibration measurement, the electric field strength ofChDR emitted from a dielectric radiator was measured. A
schematic of the installation is shown in Fig. 6. The experiment was installed in air, therefore 𝑛0 ≈ 1. The radiator was
made out of Alumina (97.6% Al2 O3 ) with a relative permittivity of 𝜖𝑟 ≈ 9.0 (1.0 − 8.5 GHz, 25∘ C) [8]. The radiator
had a cylindrical geometry with a diameter of 36 mm and acentral axis length of 47.6 mm. It was inserted into a metal
body at its Cherenkov angle 𝜃𝐶ℎ = 70.55∘ and machined tobe flush with the chamber aperture (∅ 80 mm). The centre of
the chamber aperture was aligned at the corresponding beam
position using a reference laser. During the measurements,
the whole setup was moved transversely with a motorized
linear stage to vary the impact parameter ℎ from 10 - 50 mm.
The eo-probe was positioned 10 mm away from the radiatorsurface on the central axis of the radiator.

𝑒𝑜 − 𝑝𝑟𝑜𝑏𝑒𝑚𝑒𝑡𝑎𝑙𝑟𝑎𝑑𝑖𝑎𝑡𝑜𝑟𝑛0𝜃𝐶ℎℎEChDR = (354 ± 25) / h50

Simulation (CST)403020100010203040Impact parameter, mm5060

Figure 7: Calibrated peak electric field strength of coherent
ChDR as a function of the impact parameter. Absolute values
after calibration are shown in blue, error bars indicate thestandard deviation of each measurement.

𝑡𝑜 𝑎𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛

𝐶ℎ𝐷𝑅

𝜎𝛾
ℎ𝜖𝑟

Wakefield
100 GHz
10300 pC
5 ps
392.4
10-50 mm
9.060

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𝑏𝑒𝑎𝑚 𝑓𝑖𝑒𝑙𝑑𝑒−𝑚𝑒𝑡𝑎𝑙Figure 6: Schematic of the ChDR measurement setup. The
impact parameter ℎ was varied during the measurement bymoving the setup with respect to the electron beam.
The measurement results are shown in Fig. 7. The peakelectric field 10 mm from the exit surface of the radiator isshown as a function of the impact parameter ℎ. The abso-DISCUSSION AND CONCLUSION
The measurement of the absolute electric field strengthof ChDR showed that for a short electron bunch (5 ps (1 𝜎),300 pC, 200 MeV) the peak electric field is in the order of
10 kV/m for an alumina radiator. It decreases proportionallyto the inverse distance between the particle beam and theradiator surface. It also was shown that the numerical simulations performed with CST agree with the experimental
findings regarding absolute numbers of the peak electricfield. This qualifies numerical simulations to predict coherent ChDR for different beam parameters and radiator geometries. The knowledge of the absolute value of the electricfield generated by coherent ChDR enables the targeted development of dielectric diagnostic devices like bunch length
monitors and beam position monitors.

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ACKNOWLEDGEMENTS
This work was supported by the European Union’s Horizon 2020 Research and Innovation Programme under grantno. 951754 (FCCIS).

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