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GEOMETRY STUDY OF AN RF-WINDOW FOR A
GHz TRANSITION RADIATION MONITOR FORLONGITUDINAL BUNCH SHAPE MEASUREMENTS
S. Klaproth∗ 1 , A. Penirschke, Technische Hochschule Mittelhessen, Friedberg, Germany
R. Singh, GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
H. De Gersem, Technische Universität Darmstadt, Darmstadt, Germany
1
also at Technische Universität Darmstadt, Darmstadt, Germany
Abstract
GHz Transition Radiation Monitors (GTRs) can be used
to measure longitudinal beam profiles even for low 𝛽 beams.
In contrast to traditional methods e.g., Fast Faraday Cups
(FFCs) and Feschenko monitors, GTRs are a non-destructive
measurement method and are able to resolve bunch-by-bunch
longitudinal profiles at the same time. It is planned to measure the transition radiation outside the beam line through acustom-design RF window within a frequency range up to
8 GHz using broadband antenna structures. The material andthe shape of the RF-window is crucial in order to minimize
the fraction of the transition radiation that is not propagating in the direction of the antenna. In this contribution, weshow a study of different geometries to suppress reflections
generated at the transition to the RF-window. For higher permittivity the reflections becomes stronger, simultaneously
reducing the measured signal strength at the position of theantenna. Secondly the RF-window’s material must be UHV
compatible and should be durable.

is coherently transformed to the transversal distribution ofthese secondaries using an RF-deflector [2, 5]. The interaction of the beam and the wire is minimal, allowing thebunches to remain suitable for further acceleration.
A new candidate for bunch shape measurements is the
GTR. This type of device is still under investigation, but
has the potential to combine the advantages of both FFCs
and Feschenko monitors, enabling bunch-by-bunch measurements without beam destruction. The GTR comprises threemajor components: a metal target plate with an aperture to
generate transition radiation while the beam passes through,an RF-window for decoupling the transition radiation fromthe inner beam line to the outside simultaneously maintaining the vacuum, and an antenna/coupler structure to observe
the radiation as seen in Fig. 1. This promising concept has

INTRODUCTION
The longitudinal bunch shape is important for conditioning and verifying the beam dynamics of LINACs. In the caseof the GSI UNILAC, the bunch velocities 𝛽 typically range
from 0.05 to 0.15. For these slow bunches, the self-field
widens significantly alongside the beam axis, rendering direct measurement of the longitudinal bunch shape inherently
ambiguous [1]. This applies to devices such as phase probes
and other pick-ups. Therefore, more common tools for longitudinal bunch shape measurements of low-beta beams are
FFCs and Feschenko monitors.
FFCs measure the profile by collecting the bunch charge
in a 50 Ω optimized cup. Typically, the beam’s self-fields
are shielded to suppress signal widening caused by earlyarriving fields on the collector. This enables FFCs to detect
the bunch shape with high precision on a bunch-by-bunchbasis. Additional considerations must be taken on the emission of secondaries during the design phase and later onwhile interpreting the measured signals. Nevertheless, thedestructive measurement makes a further usage of the beam
impossible [2–4].
Feschenko monitors, on the other hand, measure the average bunch shape. The beam passes by a thin wire generating
secondary electrons. The longitudinal structure of the beam
∗ Stephan.Klaproth@iem.thm.deFigure 1: Experimental Setup of the proof-of-concept measurements [6].
been tested successfully at GSI [6]. Consequently, further
investigations were made to optimize the RF window in thecurrent setup. Simulations were carried out using different
possible materials for the RF window, both ideal [7] andrealistic [8], to examine their influence on the expected transition radiation signal. Thereby, a cylindrical RF-window witha wall thickness of 10 mm analog to the proof-of-concept
measurement has been used. In Fig. 2a,b, we illustrate theexpected maximum peak field (𝐸max ) for two different typical 𝛽 values at GSI UNILAC. It becomes evident, that a
low relative permittivity 𝜖r is advantageous for maximizing
the expected signal amplitude. The antenna should be positioned at an angle 𝜃 at least above 40°. As a rule of thumbfor high 𝛽 beams, 𝜃 = 𝛾1 provides a good approximation
for the angle at which the transition radiation peak poweris emitted [10]. In case of GSI UNILAC this corresponds
to approximately 55° to 60°. But actually at these low 𝛽
values the maximum intensity rises continuously towards
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r = 0.6m, β = 0.05

r = 0.6m, β = 0.15

106Alumina995lossy
PTFElossy
Peek700
QuartzFusedlossy
2

10

20

30

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50

60

70

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r = 0.6m, β = 0.15, θ = 2.5◦

Alumina995lossy
PTFElossy
Peek700
QuartzFusedlossy

25
Emax,Abs (V/m)

Emax,Abs (V/m)

15

20

10.0

Signal (V/m)

20

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15

1.0

Alumina995lossy
PTFElossy
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0.1

10

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θ (◦ )

(a)

50

60

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80

θ (◦ )

(b)

0.0

2.5

5.0

7.5
10.0
time (ns)

12.5

15.0

17.5

(c)

Figure 2: The maximum amplitude of the transition radiation peak 𝐸max at 0.6 m distance for (a) 𝛽 = 0.05 and (b) 𝛽 = 0.15
and (c) the reflections after the transition radiation passed for different realistic materials [9]. A circle marker identifies anobservation position inside and a diamond outside the vacuum chamber.
the target as shown in Fig. 2a and 2b. It can be noticed that
only the necessary geometric distance of the antenna to thetarget gives an upper bound to the positioning angle 𝜃.
𝐸⃗ =⃗ 0−1 − 𝑡)𝑞 ⋅ 𝛽 sin 𝜃𝛿 (|𝑅|𝑐(𝑒𝑥̂ cos 𝜃+ 𝑒𝑧̂ sin 𝜃) . (1)22𝜋𝜖0 𝑐0 |𝑅|⃗ 1 − 𝛽 cos2 𝜃

The electrical field of transition radiation for a single
charge in the far-field may be calculated using Eq. (1) [11].
It shows that signal strength increases linearly with higher
𝛽 values. Therefore, the optimal position for the antennashould be chosen with respect to the lowest expected 𝛽 caseto achieve the best overall performance of the GTR. The
performance also depends on the suppression of reflections.
Consequently, the spacing between the bunches defines atime gap within which reflections shall relax to prevent interference with the measured signal of the following bunch. The
UNILAC operates at 36 MHz to 108 MHz, corresponding
to a spacing of 27.78 ns to 9.26 ns between two consecutive bunches. In Fig. 2c we illustrate the signal within thevacuum chamber at |𝑅|⃗ = 0.6 m and 𝜃 = 2.5° at a velocity
𝛽 = 0.15. The simulation time has been adjusted so thatzero aligns with the transition radiation peak to be measured,followed by its reflections. While the reflections fade away
for all materials within 27.78 ns for all materials, the faster
operation mode of 108 MHz may encounter interference between the transition radiation of the following bunch and thereflections of the current one, depending on the RF-windowmaterial used. A well-chosen material can minimize thisinteraction. For instance, the reflection amplitude and relaxation time of quartz-glass perform similarly well compared
to PTFE, while Peek and Alumina suffer significantly fromslowly decaying reflections within the vacuum chamber. For
the quartz-glass RF-window the expected total relaxation
time is about 7.5 ns, which is shorter than the time gap of
the fast operation mode of the UNILAC. So we do not expect severe impacts on the following measured bunch shapedue to reflections of the previous transition radiation. The
impact of the transition radiation on the following bunch
itself is also expected to be negligible, with electric fieldsof about 100 V m−1 compared to the self-fields of the bunch,typically in the range of tens to hundreds of kV m−1 . Bothlow 𝜖r materials would be sufficient in terms of their elec-

trical properties. But the material class PTFE is typicallyused only inside a vacuum chamber or for low vacuum applications, as it may not be vacuum-tight against hydrogenand other light particles [12, 13]. Therefore, we focus in ourgeometry study on the quartz-glass material only. During
this geometry study of the RF-window our aim is to increase
the amplitude of the measured signal outside the vacuum
chamber while reducing the amplitude and relaxation timeof the reflections inside the beam line to further minimize
their impact on the measurements.

SIMULATIONS
Several shapes were evaluated using the CST® PICsolver [9]. The first shape is a cylindrical design, which was
also used in the material analysis, and it includes a larger variant with a 0.5 m inner radius (Fig. 3a). The second shape isa spherical geometry with an inner radius of 0.5 m (Fig. 3b).
The highest transmission through the window is expected
when the transition radiation impinges orthogonally on thewindow surface.

(a)

(b)

(c)

(d)

Figure 3: The shapes studied: (a) cylindrical, (b) spherical,(c) exponential horn, (d) combination of spherical and exponential horn design.
The third shape is an exponential horn (Fig. 3c) witha mouth of 0.5 m. This shape is intended to disperse thetransition radiation as much as possible to create only low
amplitude reflections. The last shape is a combination of

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05 Longitudinal Diagnostics and Synchronization

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r = 1000mm, σ = 100.00ps

r = 1.0m, σ = 100ps
40
30
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combinedcylindercylinder big
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(a)

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r = 1.0m, σ = 400ps, θ = 60◦

15.0

combinedcylindercylinder big
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1.00
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Ef,Abs (kV/m)

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combinedcylindercylinder big
horn
spherical

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time (ns)15

r = 1.0m, σ = 100ps, θ = 60◦
combinedcylindercylinder big
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combinedcylindercylinder big
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r = 1000mm, σ = 400.00ps

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(a)

r = 1000mm, σ = 200.00ps

2.050
θ (◦ )

20

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40

50

60

70

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θ (°)

(c)

Figure 4: Maximum signal strength of the transition radiation 𝐸max at 1 m distance for different geometries and bunch
lengths: (a) 𝜎b = 100 ps, (b) 𝜎b = 200 ps, (c) 𝜎b = 400 ps.
A circle marker identifies an observation position inside anda diamond outside of the vacuum chamber and a square identifies an observer within the chamber walls.
exponential horn and spherical shape (Fig. 3d). The spherical part spans between 50° to 70° with an inner radius of
0.4 m and is enclosed by two exponential horn sections. In
all cases the wall thickness is kept to 10 mm using fusedquartz-glass as RF-window material simulating 1010 single
charged particles in a Gaussian shaped bunch.
In Fig. 4 the maximum intensity of the transition radiationis plotted against the observation angle 𝜃 at a distance of|𝑅|⃗ = 1 m for 𝛽 = 0.15 across all geometries, considering
three different bunch lengths. Clearly the combined shapeperforms subpar compared to all other geometries. The maximum intensity increases with 𝜃 for both shorter bunches(Fig. 4a, 4b), as well as for the 𝜎b = 400 ps case till 𝜃 = 60°.
Beyond this angle the maximum intensity of the transition
radiation stagnates for longer bunches. The exponential
horn geometry shows a slightly lower maximum amplitude

0

0

5

10
time (ns)

15

20

(c)

Figure 5: Signal of the transition radiation inside the RFwindow in (a) at |𝑅|⃗ = 0.4 m and 𝜃 = 0° for a 𝜎b = 400 ps
bunch and outside at |𝑅|⃗ = 1 m and 𝜃 = 60° for (b) 𝜎b =400 ps and (c) 𝜎b = 100 ps bunch.
compared to the cylindrical and spherical shapes, but the difference is negligible. Notably, the maximum intensity scales
linearly with the bunch charge density [11], as expected.
All simulations have been performed with the same total
charge, resulting in a halving of the bunch charge density
between bunch lengths of 𝜎b = 100 ps to 200 ps. Consequently, the maximum intensity also decreases by half, fromapproximately 40 V m−1 to 20 V m−1 , and quartered fromabout 40 V m−1 to 10 V m−1 for 𝜎b = 100 ps to 400 ps. In
Fig. 5a we show the signal of the transition radiation andreflections along the beam axis at a distance of |𝑅|⃗ = 0.4 m
from the target for a 𝜎b =400 ps bunch. For the first 6 ns, thespherical geometry has a higher amplitude than the hornshaped RF-window. Afterward, the reflections become evensmaller in amplitude. In the case of the small cylindricalshape, the signal appears to have a low reflectivity. However, this is due to the overlap between the first reflection
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50

combinedcylindercylinder big
horn
spherical

Emax,Abs (V/m)

Ef,Abs (kV/m)

2.0

1.00
0.9
0.8
0.7

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ISSN: 2 6 7 3 - 5 3 5 0
d 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 1 1with 𝑠0 the maximum amplitude of the primary transition
radiation peak and the increased noise floor offset 𝐶. The
results of the fit are shown in in Fig. 6. The horn-geometry’s
decay time 𝜏 is the smallest on average with 2.7 ns, but theincreased noise floor 𝐶 is one of the worst together withthe combined shape up to 2 V m−1 higher than the other geometries. All other shapes have a decay time 𝜏 of about
3 ± 0.3 ns with a small advantage for the spherical and thelarger cylindrical shape. The smallest increased noise floor
𝐶 of about 1.1 ± 0.1 V m−1 is achieved with the big cylindrical shape, followed closely by the spherical geometry
1.4 ± 0.3 V m−1 .

CONCLUSION
In this paper, we have demonstrated that the permittivityof the RF-window has a significant impact on the reflec-

combinedcylindercylinder big
horn
spherical

4.0

3.5
τ (ns)and the actual transition radiation signal. As a result, thetransition radiation signal broadens, and the maximum amplitude shifts. This first reflection becomes visible in the
big cylindrical shape case around 4 ns. Here, the longer
travel distance of the reflection leads to the delayed signal
and therefore the reflection is separated from the transition
radiation. The widening of the transition radiation signal
also occurs for the horn-shaped geometry, with a small kinkvisible after 1.9 ns. This kink is caused by reflections at
the outer part of the horn mouth, where the gap between
the target and RF-window is small. These early reflections
overlap with the transition radiation, ultimately leading toa widening. The primary peak of the reflected transition
radiation inside the RF-window can be reduced by up to
12 % comparing the highest amplitude of the spherical andthe lowest of horn shape. The transition radiation peak of
the following bunch will interact with the remaining reflections at 9.26 ns, which represents a minimum. So, we do not
expect significant interference effects between the reflectedsignals of consecutive bunches. To further confirm this, additional multi-bunch simulations are required. In Fig. 5b,cthe signal outside the RF-window is shown at 𝜃 = 60° in|𝑅|⃗ = 1 m distance at 𝛽 = 0.15 for two bunch widths of
𝜎b = 400 ps and 100 ps. The aim outside the RF-window
is to maximize the transition radiation signal. With the exception of the combined shape, all geometries exhibit nearly
the same amplitude. This is particularly pronounced in the𝜎b = 100 ps case, where the amplitude is approximately
25 % smaller than the others. In Fig. 5c, the first reflectionof the small cylindrical geometry becomes visible approximately 1 ns after the main peak. This reflection overlaps inthe 𝜎b = 400 ps case leading to the widening of the signal as
discussed already earlier. Additionally, the early reflectionof the horn shape can be seen between 1 ns to 3 ns, resulting
in the kink for longer bunches. The best separation between
the signal and reflections is achieved with the spherical andthe larger cylindrical geometries. In terms of relaxation time𝜏 we perform an exponential fit−𝑡𝑠(𝑡) = 𝑠0 exp 𝜏 +𝐶,
(2)

3.0

2.5

50

60

70

80

θ (◦ )(a)4

combinedcylindercylinder big
horn
spherical

3
C (V/m)Content from this work may be used under the terms of the CC-BY-4.0 licence (© 2023). Any distribution of this work must maintain attribution to the author(s), title of the work, publisher, and DOI

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2

1
50

60

70

80

θ (◦ )(b)

Figure 6: (a) Decay constant 𝜏 and (b) offset 𝐶 of the exponential decay fit averaged over 𝜎b (100, 200, 400 ps) for
each angle 𝜃.
tions of the transition radiation in a GTR. Additionally, we
showed that the shape of the window does not have a major
effect on the measurable intensity of the transition radiation
outside the RF-window. Inside the RF-window, the horngeometry can reduce the amplitude by up to 12 % at the costof a slightly widened signal. The lowest decay time 𝜏 and increased noise floor 𝐶 are achieved with the bigger cylindricaland the spherical designs. The advantage of the alternative
geometries are the ability to separate the transition radiationfrom the reflections, with the horn geometry offering some
improvement and the spherical shape performing best in thisregard. We plan to equip a GTR with a spherical shaped
RF-window to test its influence in a new measurement campaign also adding antennas with higher bandwidth up to
8 GHz bandwidth. Furthermore, simulations of multiple
bunches will be performed to compare with measurementswith respect to the overlapping of reflections and the desiredtransition radiation peaks.

ACKNOWLEDGEMENTS
This work is supported by the German Federal Ministry of Education and Research (BMBF) under contract
no. 05P21RORB2. Joint Project 05P2021 - R&D Accelerator (DIAGNOSE).

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