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R. Panaś, A. I. Wawrzyniak, NSRC SOLARIS, Kraków, Poland,
K. Łasocha, CERN, Meyrin, Switzerland,
A. Curcio, INFN LNF, Frascati, Italy.

I
This work presents a natural extension of prior theoretical investigations regarding the utilization of coherent diffraction radiation for assessing longitudinal characteristics of electron beams atSolaris. The study focuses on the measurement results obtained at the linac injector of the Solaris synchrotron and their analysis through a theoretical model. The ﬁndings are compared withprevious estimates of the electron beam longitudinal proﬁle. This contributes to the future diagnostics at the ﬁrst Polish free electron laser (PolFEL) project, where it will be used for the optimization ofparticle accelerator performance.

COHERENT DIFFRACTION RADIATIONBUNCH LENGTH MEASUREMENTElectromagnetic radiation is emitted when a beam of charged particles accelerates or changes
medium of propagation. If the emitted wavelength is comparable or greater than the bunch length,
the radiation is said "coherent" because the contributions from the single particles within the beaminterfere constructively and the bunch emits as a whole. In that case the emitted radiation power is
proportional to the square of the bunch form-factor and increases with decreasing bunch length.
For bunch lengths on the picosecond scale variations in the peak current can be easily monitoredby GHz-THz detectors like Schottky diodes. Diffraction radiation is the radiation that a bunch ofparticles emits when crossing two regions of limited size with different index of refraction. This canbe accomplished if the beam passes through a hollow disk of dense material. If the disk surface ismetallic the radiation is emitted from localized layers of that surface, in such a way that the beam
properties are imprinted into the emitted radiation at the transition plane and can be exploited for
diagnostics. The spectral angular distribution of energy emitted backward in the form ofdiffraction radiation from a perfectly conducting round disk, with an internal and external radiusequal to respectively and , can be described with the following formula:

The diagnostic technique considered for PolFEL is based on the power balance of CDR radiationcollected by Schottky diodes in different ranges of sub-THz radiation. As seen from Eq.
theemitted energy depends on the bunch length through the form factor. If the transverse sizeof the bunch is negligible, one has:whereis the normalized dimensionless beam current passing through the disk. Simply
speaking, the form factor is squared modulus of the Fourier transform of the beam current. In
certain cases, 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 by Eq. (1) The
described technique is not limited to only one type of radiation, and has been previously
demonstrated with measurements based on CDR and Coherent Cherenkov Diffraction
Radiation. In the SOLARIS linac the beam is bunched, with the 3~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 . As result the corresponding form factor also differsfrom the smooth form factor of a single Gaussian bunch as presented in Figure 2. A larger
aperture allows more radiation to enter the detector and thus for diodes with different apertures,
it will change the power balance on the basis 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 of the diode aperture. Bunch length to power ratio after this correction ispresented below in Figure 3.

wheredenotes the bunch charge, is vacuum permittivity, is the velocity of light,
is theratio of particle velocity and the velocity of light and is the Lorentz factor. The quantity
iscalled bunch form factor and strictly depends on the shape of the electron bunch. An example ofspectral-angular distribution of emitted CDR energy is shown in Figure 1.

Figure 3: Bunch length to power ratio, corrected
Figure 2: Form factors calculated
for SOLARIS injector bunch train and a single for diode aperture.
Gaussian bunch.

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

EXPERIMENTAL SETUP AND MEASUREMENTS
The characterized electron beam was at the end of the linac in beam dump section. After passing through 0.15 mm thick ﬂange, the electrons move in the air and can be used for beam diagnostics 20
cm behind ﬂange, before they end up in the lead beam dump.The arrangement for measuring the length of the electron beam proﬁle visible at includes an aluminum radiator with a radius of 2.54 cm
and a 5 mm radius hole at its center. Additionally, a golden-coated Ø3" 90° Off-axis parabolic mirror and three diodes from different bands are employed as detectors, used alternately.
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. the solution to this problem will be
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.An important factor to consider is not only the sensitivity but also the input aperture of the diodes. FWHM of the longitudinal electron bunch proﬁle at SOLARIS linac was estimated at 12ps. As can be seen in the Figure 5, the signal from the diode in the highest band is at the noise level, for this reason, the ratio of the signals from the diode in the middle and the lowest band was used forthe calculations. This obviously lowers the accuracy of our measurement and is the most likely cause of the difference from the expected value. From the ﬁrst measurements using CDR radiation, theestimated FWHM of the longitudinal electron beam proﬁle was about 20 ps.

RADIATOR

26.5 - 40 GHz

DIODE

3.0

2.5

2.5

2.5

2.0

2.0

2.0

26.5 GHz to 40 GHz
Sensitivity 1500 mV/mW,
WR-28 Waveguide, Ka-Band

MIRROR

1.0

1.0

0.5

0.5

0.5

0.0
0200

400600t [ns]

800

1000

50 GHz to 75 GHz,
Sensitivity 1000 mV/mW,
WR-15, V-Band

1.5

1.0

0.0Figure 4: Experimental setup.

1.5]
Vm[langis]Vm[langis1.533 GHz to 50 GHz,
Sensitivity 1200 mV/mW,WR-22, Q-Band

50 - 75 GHz

3.0]
Vm[langisEND FLANGE

33 - 50 GHz

3.00.0200

400600800t [ns]

1000

200400600

800

1000

t [ns]

Figure 5: Signals measured by diodes with diﬀerent bands.

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 data and calculating the bunch length have been developed and updated. Schottky diodes were acquired and placed in the setup, enabling the ﬁrst measurements
and calculations.The results obtained after the analysis do not align with the expectations. The possible cause is a weak signal, which, in the case of a diode in the highest frequency range, made it
impossible to extract the signal from the noise level.It is anticipated that by improving the signal strength from the diode in the highest band, the estimated bunch length will decrease and become closer
to the one from the previous estimate. In order to increase the signal strength, the system will be re-adjusted using motorized platforms, 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 be installed on diodes.The tested system has shown potential, indicating that it can be used as alow-cost alternative to more complex systems like transverse deﬂecting cavities (TDC) and streak cameras for monitoring the longitudinal beam proﬁle. After appropriate calibration using the methods
mentioned above, such a system based on the CDR could monitor the degree of bunch compression after magnetic chicane.

IBIC 2023 - Saskatoon, Canada

roman.panas@uj.edu.pl