12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

BUNCH COMPRESSOR MONITORS FOR THE CHARACTERIZATION OF
THE ELECTRON BUNCH LENGTH IN A LINAC-DRIVEN FEL
G. L. Orlandi∗Paul Scherrer Institut, Villigen, Switzerland
Abstract
The lasing performance of a Free Electron Laser (FEL)strongly relies on a precise characterization of the electron
bunch length and on the control and stabilization of thebunch compression settings of the machine under normaluser operations. In a FEL driver linac, the so-called Bunch
Compressor Monitors (BCMs) normally ensure the noninvasive monitoring of the electron bunch length. BCMs,
being sensitive to the temporal coherent threshold of theradiation energy emitted by the electron beam crossing thelast dipole of a magnetic chicane or a holed diffraction screen
just downstream, can provide a bunch length dependent
signal resulting from the integration of the detected radiation
pulse energy over the acceptance frequency band of thedetector. Thanks to the non-invasiveness, BCMs are primary
diagnostics in a FEL to stabilize the bunch compression by
feeding back the RF settings of the accelerating structure. In
this contribution, we present a formal method to determine
an absolute measurement of the electron bunch length fromthe analysis of a BCM signal.

INTRODUCTION
The lasing performance of a linac driven x-ray Free Electron Laser (FEL) strongly depends on the beam quality andcapability to preserve it all along the entire acceleration andcompression stages of the electron beam. Electron beams
with a small emittance and a smooth longitudinal profile are
typically generated in a FEL by photocathode guns. In order to counteract the effects of beam emittance dilution due
space charge at the early stage of the acceleration, relatively
long bunch lengths are generated at the cathode. Hencethe necessity to longitudinally compress the electron bunchlength at higher energy stages of the acceleration. Besides
a characterization and optimization of the beam emittance,
the machine set up for FEL users’ operations requires anoptimization of the compression scheme by means of precise
measurements of the electron bunch length that represents
the upper limit for the laser pulse duration. In a linac driven
FEL, absolute and precise measurements of the electron
bunch length are normally carried out by means of rf Transverse Deflecting Structures (TDSs). The rf field resonating
in a TDS structure induces a chirp of the transverse momentum of the electrons in the bunch vs the electron arrival
time. The imaging and the analysis of the spatial trace produced by the electron beam impinging on a downstream
view-screen permits to estimate the electron bunch length
provided that a calibration of the image centroid vs TDS
phase is known [1–5]. Main drawback of a TDS based∗ gianluca.orlandi@psi.chmeasurement of the electron bunch length is the fully beam
invasiveness as well as possible machine protection issues
due to beam losses. After the initial machine set-up, themonitoring of the electron bunch-length during FEL users’
operations is normally ensured by Bunch Compressor Monitors (BCMs) [6–13] also called Bunch Length Monitors. Ina linac-driven FEL, a BCM is normally designed to detect
the synchrotron radiation (SR) emitted by the electron beam
while crossing the fourth dipole of a magnetic chicane or thediffraction radiation produced by the electron beam passing
through a holed diffraction screen placed just downstream ofthe magnetic chicane. The wavelength acceptance of a BCM
detector is designed to match with the temporal coherent
enhancement of the radiation spectral energy emitted by theelectron beam at the given compression stage. BCMs in alinac-driven FEL such as, for instance, SwissFEL [14, 15]
are typically designed not to perform a spectral reconstruction of the detected radiation energy distribution by meansof a spectrometer. Main goal of a BCM is to provide - in areal-time - a bunch-length dependent signal to the machinecompression feedback rather than an off-line reconstructionof the absolute value of the electron bunch length from acumbersome analysis of a spectrogram. In most of the cases,
the BCM output signal is hence the result of the integrationof the detected radiation energy over the full acceptancewavelength band of the detector. The bunch-length dependent output signal of a BCM can be so fruitfully exploited
for a fully non-invasive and shot-sequential monitoring of
the electron beam during a FEL users’ session and for a stabilization of the bunch compression by means of a feedback
loop of the rf parameters (field phase and amplitude) of theaccelerating structures.
In the present work, we will present a formal method ofanalysis of the BCM signals that permits an absolute determination of the electron bunch length. The implementationof the aforementioned formal method will be presented fortwo different scenarios: the simple case of a BCM equippedwith a single detector; the more advanced case of a BCM
equipped with two detectors with a different wavelengthband of acceptance which are simultaneously illuminatedby the same light pulse emitted by the electron beam thanks
to a beam splitter and a suitable optics. In the case of a
BCM with a single detector, the presented method permits
to track the relative variation of the electron bunch lengthwith respect to a reference value - either the mean value overa sequence of data acquisition or the shot-sequential value- as a function of the corresponding statistical fluctuationsof the measured relative variations of the beam charge andBCM signal. In the case of a BCM equipped with two independent detectors having a different acceptance wavelength
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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

12th Int. Beam Instrum. Conf.
ISBN: 9 7 8 - 3 - 9 5 4 5 0 - 2 3 6 - 3

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band, the proposed method permits an absolute determination of the electron bunch length from a suitable analysisof the relative statistical fluctuations of the signals of thetwo BCM detectors and of the charge signal readout. For
a complete overview of the mathematical derivation of themethod and of the numerical simulations of the expected
performances, the reader is addressed to the pre-print [16].
In the present proceedings, the relevant aspects of the formal
derivation of the method will be outlined as well as the beneficial applications to the beam diagnostics of a linac-driven
FEL.

THE EXPERIMENTAL SET-UP
In order to insert into a realistic framework the analysis
method of the BCM output signals for the absolute determination of the electron bunch length, we will refer to the caseof SwissFEL where three BCMs are presently in operation.
SwissFEL is a x-ray linac-driven Free Electron Laser(FEL) facility [14, 15] in operation since 2019 at Paul Scherrer Institut (www.psi.ch). Driven by a S-band injector and a
C-band booster covering the beam energy range 2.1 − 5.8
GeV, SwissFEL is designed to provide tunable and coherent
light pulses in the wavelength region 7−0.7 and 0.7−0.1 nm
in two distinct machine branches: the hard x-ray beam line
ARAMIS and the soft x-ray beam line ATHOS. An S-band
photocathode simultaneously illuminated by two UV lasers
emits - at a repetition rate of 100 Hz - electron bunches witha duration of about 3 ps (rms) according to a 28 ns long
two-bunch macrostructure. Before being split apart in two
distinct machine brunches, the two bunches of the electron
macrostructure experiences a longitudinal compression in
two magnetic chicanes [10, 11, 17–20]. In the first magnetic
chicane (BC1), the compression is operated by means of an
off-crest rf acceleration of the beam in the S-band injector
and a X-band linearization of the beam energy chirp. Afterthe first magnetic chicane, a suitable off-crest setting of therf phases of the Linac-1 of the booster provides the further
energy chirping to the electron beam before entering the second magnetic chicane (BC2). For the two nominal operation
modes of SwissFEL (200 and 10 pC), a longitudinal compression of the electron beam by a factor 150 and 300 up to
20 and 3 fs (rms) can be achieved, respectively. After eachcompression stage, the electron bunch length and the horizontal slice emittance can be characterized by means of two
rf Transverse-Deflecting-Structures (TDS): a S-band and a
C-band structure, respectively. Recently an after-burning
X-band TDS - the so called POLARIX [21] - is in operation
just downstream of the ATHOS undulator beam line. For
the 10 pC operation mode, a further bunch compression up
to the sub-fs level can be operated in the magnetic chicane(ECOL) of the ARAMIS energy collimator. The two main
magnetic chicanes (BC1 and BC2) of SwissFEL as wellas the magnetic chicane of the ARAMIS energy collimator(ECOL) are equipped with BCMs. Both the BC1-BCM and
ECOL-BCM collect the Edge-SR emitted by the electron
beam while crossing the front edge of the fourth dipole ofthe magnetic chicane; for the BC2-BCM a diffraction radiation screen placed just downstream of the second magnetic
chicane constitutes the radiation source. The BC1-BCM,
being designed for monitoring electron bunches in the range
220 − 290 fs (rms), is equipped with two independent Schottky diodes which are sensitive up to more than 2 THz. The
two Schottky diodes are simultaneously illuminated by thesame radiation pulse which two beam splitter in cascade
split off into two optical paths. Two different THz high-passfilters with a low frequency cut-off of 0.3 and 0.6 THz (socalled “thick grid” type) define the low frequency limits of
the radiation spectral energy collected by the two detectorsof the BC1-BCM. The BC2-BCM detector is a MercuryCadmium-Telluride (MCT) covering the wavelength range
2 − 12 µm to monitor 3 − 25 fs (rms) bunch-lengths. In the
ECOL-BC1 a calcium fluoride (CaF2 ) beam splitter permits
to illuminate simultaneously a pyrodetector and an opticalfiber spectrometer covering the wavelength bands 0.9 − 4.0
and 0.9 − 2.5 µm, respectively.

THE METHOD
The formal expression of the temporal coherent component of the spectral distribution of the radiation energy emitted per unit of angular frequency 𝜔 = 2𝜋𝜈 by a bunch of
𝑁 electrons while crossing the dipolar field of the bending
magnet of a chicane or the hole of a diffraction radiation
screen reads:𝑑𝐼 𝑁𝑒 (𝜔)𝑑𝐼 𝑒 (𝜔)𝑑𝐼 𝑒 (𝜔)≃ 𝑁(𝑁 − 1)𝐹(𝜔)≃ 𝑁 2 𝐹(𝜔)
, (1)
𝑑𝜔
𝑑𝜔
𝑑𝜔
𝑒

(𝜔)
where 𝑑𝐼𝑑𝜔is the radiation energy spectrum of the single
particle and 𝐹(𝜔) is the longitudinal form factor (FF) of theelectron beam [22, 23]. In the formula above, we implicitly
assume that the integration over the acceptance solid angleof the detector has been performed as well as that beamtransverse size effects on the FF can be neglected becauseof the highly collimation features of the electron beam as
normally occurring in a linac-driven FEL. The FF is definedas the square module of the Fourier transform of the density
distribution of the 𝑁 electron coordinates along the longitudinal direction. For a Gaussian beam with a length 𝜎, itreads:

𝐹(𝜔) = ∣∫

+∞

−∞

2

𝜔𝜎 2

𝑒𝑗𝜔𝑧/𝑐 𝜌𝑧 (𝑧)𝑑𝑧∣ = 𝑒−( 𝑐 ) .

(2)

The method of analysis of the BCM signal we are going to
introduce is based on a formalism that expresses the shotsequential relative variation of the BCM ouput signal - forinstance, with respect to the mean value over a sequence of
BCM signal acquisitions under a steady state regime of themachine - as a function of the corresponding relative variations of the electron bunch length 𝜎 and of the beam charge
𝑁. Because of the formal dependence on the shot-to-shot
relative variations of bunch-dependent quantities (𝜎 and 𝑁),
the proposed method - as clearer hereinafter - is weakly dependent on bunch-independent features such as the spectral

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12th Int. Beam Instrum. Conf.
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𝐼=∫

𝜔𝑚𝑎𝑥

𝜔𝑚𝑖𝑛

𝑑𝜔 (

𝑑𝐼 𝑁𝑒 (𝜔) 𝑑𝐼 𝑒 (𝜔)
/
).
𝑑𝜔
𝑑𝜔

(3)

Finally, upon applying the natural logarithm to the two sidesof Eq. (3)ln(𝐼) = 2 ln(𝑁) + ln(∫

𝜔𝑚𝑎𝑥

𝜔𝑚𝑖𝑛

𝑑𝜔𝐹(𝜔)),(4)

the shot-sequential relative variation of the BCM signal
Δ𝐼
𝐼 ∗ −𝐼𝐼 =𝐼 due to the corresponding ∗differential relative
𝑁 −𝑁variations of the bunch charge Δ𝑁𝑁 =𝑁 and of the form
Δ𝐹
𝐹 ∗ −𝐹factor 𝐹 = 𝐹 - the latter one due to a relative fluctuation𝜎∗ −𝜎of the bunch length Δ𝜎
𝜎 = 𝜎 - reads
𝜔

𝑚𝑎𝑥
∗
Δ𝐼
Δ𝑁 ∫𝜔𝑚𝑖𝑛 𝑑𝜔[𝐹 (𝜔) − 𝐹(𝜔)]
=2
+
.
𝜔
𝐼
𝑁
∫𝜔 𝑚𝑎𝑥 𝑑𝜔𝐹(𝜔)

(5)

𝑚𝑖𝑛

In previous equation, according to a Taylor series expansion
at the first order in Δ𝜎𝜎 , the FF variation in the integrand of
Eq. (5) can be explicitly expressed as [26]
𝜔𝜎 2

Δ𝜎 2

𝜔𝜎 2

𝐹 ∗ (𝜔) − 𝐹(𝜔) = 𝑒−( 𝑐 ) (1+ 𝜎 ) − 𝑒−( 𝑐 ) ≃2
Δ𝜎 𝜔𝜎 2 −( 𝜔𝜎Δ𝜎 𝜔𝜎 2≃ −2(
) 𝑒 𝑐 ) = −2(
) 𝐹(𝜔).(6)𝜎𝑐𝜎𝑐Upon replacing in the integrand of Eq. (5) the above Taylor
series approximation of the FF difference and explicitly calculating the integral over the frequency band of acceptanceof the detector Δ𝜔 = (𝜔𝑚𝑎𝑥 − 𝜔𝑚𝑖𝑛 ), the shot-sequential
relative variation of the BCM signal can be expressed as afunction of the related beam-synchronous relative variationsof the bunch charge and length by means of the following
equation:
Δ𝐼
Δ𝑁 Δ𝜎
=2
+
𝐺(𝜎, Δ𝜔),
𝐼
𝑁
𝜎

(7)

where
𝜔𝑚𝑎𝑥
2
−( 𝜔𝜎
⎧
⎫
𝑐 ) 𝜔]
[𝑒
{
}
{ 2𝜎
}
𝜔𝑚𝑖𝑛
𝐺(𝜎, Δ𝜔) = ⎨
−
1
𝜔𝑚𝑎𝑥
⎬
√
[𝑒𝑟𝑓
(𝜔𝜎/𝑐)]
𝜋𝑐
{
}
𝜔𝑚𝑖𝑛
{
}
⎩
⎭

(8)

with 𝑒𝑟𝑓 (𝑥) indicating the error function [27]. More information on the above obtained results in [16]. The relative
variations of the physical quantities indicated in Eqs. (7)and (8) can be intended either as the shot-sequential evolution from a given machine shot to the subsequent one or,under conditions of steady state machine operations, as therelative statistical fluctuations of such quantities with respect
to the corresponding mean values over a beam-synchronous
sequence of acquired data. According to the formula inEqs. (7) and (8), the shot-sequential relative variation of theelectron bunch length Δ𝜎𝜎 can be tracked as a function of
the corresponding relative variations of the measured BCM
Δ𝑁
output signal Δ𝐼
𝐼 and of the bunch charge 𝑁 provided thata calibration of the BCM signal can be performed with anabsolute measurement of the bunch length 𝜎, for instance,by means of a Transverse Deflecting Strucure (TDS) [1–5].
In the particular case of a BCM equipped with two independent detectors simultaneously collecting in two different
frequency bands Δ𝜔𝑖 = (𝜔𝑖𝑚𝑎𝑥 − 𝜔𝑖𝑚𝑖𝑛 ) - with 𝑖 = 1, 2 the coherent radiation light pulse split off by a beam splitter into two distinct optical paths, the formula in Eqs. (7)and (8) applied to each of the two detector signals ( Δ𝐼
𝐼 )𝑖 with 𝑖 = 1, 2 - allows for an absolute determination of theelectron bunch length 𝜎 by means of the following equation:
[(

Δ𝐼
Δ𝑁
) −2
]=
𝐼 2
𝑁

𝐺(𝜎, (Δ𝜔)2 )×[𝐺(𝜎, (Δ𝜔)2 ) − 𝐺(𝜎, (Δ𝜔)1 )]Δ𝐼
Δ𝐼× [( ) − ( ) ] .
(9)
𝐼 2
𝐼 1

For more details on the formal derivation of the Eq. (9) andhow this formula can be practically handled to determine
the absolute value of the electron bunch length 𝜎 from theanalysis of the beam-synchronously acquired sequences ofa two-detector BCM signals 𝐼𝑖 - with 𝑖 = 1, 2 - and of thebeam charge readouts 𝑁, the reader is addressed to [16]. In
this bibliographic reference, the complete derivation of theformal results is supported by numerical simulations for abenchmark of the predictions of the obtained formulae.

CONCLUSIONS AND OUTLOOKA fully non-invasive monitoring of the bunch length ina linac-driven Free Electron Laser (FEL) is normally performed by a Bunch Compressor Monitor. The BCM input
signal is the radiation emitted by the electron beam whenexperiencing a longitudinal compression, i.e., while crossing
the last bending dipole of a magnetic chicane or the holed
screen of a diffraction radiator placed just downstream of it.
The BCM sensitivity to the electron bunch length is as higher
as better is the matching of the acceptance wavelength bandof the detector with the threshold of the temporal coherent
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distribution of the single particle spectrum that, for a given
wavelength band of the BCM, does not change from a rf shot
to another. Consequently, for the further formal developments, we will refer to the normalized expression of Eq. (1)𝑒 (𝜔)with respect to the single particle spectrum 𝑑𝐼𝑑𝜔. Such anormalization procedure of Eq. (1) appears even more reasonable and feasible considering that, in many experimental
contexts, the single particle radiation energy spectrum isweakly dependent or even independent of the angular frequency in the given wavelength band of acceptance of the
BCM detector. For instance, this is the case of the single
particle spectrum of the Edge-SR in the long wavelength
regime [24, 25] which can be reasonably applied to two of
the three BCMs of SwissFEL.
Upon normalizing Eq. (1) with respect to the single parti𝑒 (𝜔)cle spectrum 𝑑𝐼𝑑𝜔and performing the integration of thetwo sides of the resulting ”normalized” expression of Eq. (1)with respect to the frequency band of acceptance of the BCM
detector Δ𝜔 = (𝜔𝑚𝑎𝑥 − 𝜔𝑚𝑖𝑛 ), the ”normalized” output
signal of the BCM reads

237

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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 2 6enhancement of the radiation spectral energy emitted by theelectron beam. Most of the BCMs in operation in a FEL areequipped not with a spectrometer for the off-line reconstruction of the temporal coherent enhancement of the radiationenergy spectrum but with a broad band detector providing areal-time output signal that is the result of the full integrationof the collected radiation energy over the wavelength bandof acceptance of the detector itself. Therefore, the output
signal of a BCM does not provide an absolute estimate of theelectron bunch length but a charge and bunch-length dependent signal. Nevertheless, thanks to the non-invasiveness,
the BCM output signal can be fruitful exploited to stabilize
the bunch compression in a linac by feeding back phases andamplitudes of the rf accelerating structures. With reference
to the formal results and numerical simulations reported
in [16], in this conference proceedings we presented a mathematical method that permits to decouple in the BCM output
signal the independent contribution of the bunch length andcharge. In the case of a BCM equipped with a single detector,
under conditions of a steady state machine operations andprovided that the BCM signal has been previously calibrated
by means of an absolute measurement of the bunch length,
the proposed method permits to track the shot-sequential
relative variation of the electron bunch length as a functionof the corresponding beam-synchronously acquired relative
variations of the BCM output signal and of the charge signal. Moreover, in the case of a BCM equipped with two
independent detectors with different wavelength bands ofacceptance, which are simultaneously illuminated by thesame radiation pulse split off into two distinct optical paths
by a beam splitter, the proposed method permits an absolutedetermination of the electron bunch length by means of asuitable analysis of the two-detector BCM signals and of thecharge signal. Perspectives and potentialities of the proposed
mathematical method of analysis of the BCM signal appear
clear. Thanks to the proposed method, the compression feedback loop of the linac can be fed with a post-processed BCM
signal that is not a simply bunch-dependent signal but isitself an absolute measurement of the electron bunch length.
Moreover, in CW superconducting linac-driven FEL, where
the non-invasiveness is a mandatory feature for most of theelectron beam diagnostics, the implementation of the proposed method allows for a fully non-invasive, shot-sequential
and absolute determination of the electron bunch-length.

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