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PHYSICAL REVIEW LETTERS

Microbunching Instability in Relativistic Electron Bunches: Direct Observationsof the Microstructures Using Ultrafast YBCO Detectors
E. Roussel, C. Evain, C. Szwaj, and S. Bielawski
Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM), UMR CNRS 8523,
Centre d’Études et de Recherches Lasers et Applications (CERLA), Université Lille 1, F-59655 Villeneuve d’Ascq Cedex, France

J. Raasch, P. Thoma, A. Scheuring, M. Hofherr, K. Ilin, S. Wünsch, and M. Siegel
Institute of Micro- and Nanoelectronic Systems, Karlsruhe Institute of Technology (KIT), 76187 Karlsruhe, Germany

M. Hosaka, N. Yamamoto, and Y. Takashima
Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan

H. ZenInstitute of Advanced Energy, Kyoto University, Uji 611-0011, JapanT. Konomi, M. Adachi, S. Kimura, and M. Katoh
UVSOR Facility, Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585, Japan(Received 27 January 2014; published 25 August 2014)
Relativistic electron bunches circulating in accelerators are subjected to a dynamical instability leading
to microstructures at millimeter to centimeter scale. Although this is a well-known fact, direct experimental
observations of the structures, or the field that they emit, remained up to now an open problem. Here, wereport the direct, shot-by-shot, time-resolved recording of the shapes (including envelope and carrier) of thepulses of coherent synchrotron radiation that are emitted, and that are a “signature” of the electron bunch
microstructure. The experiments are performed on the UVSOR-III storage ring, using electrical fieldsensitive YBa2 Cu3 O7−x thin-film ultrafast detectors. The observed patterns are subjected to permanent
drifts, that can be explained from a reasoning in phase space, using macroparticle simulations.
DOI: 10.1103/PhysRevLett.113.094801

PACS numbers: 41.60.Ap, 05.45.-a, 29.27.Bd

Relativistic electron bunches are known to interact with
their own electromagnetic fields in a nontrivial way, inparticular when they are deviated by a magnetic field, orwhen conducting walls are present in their vicinity. This is
the cause of a striking phenomenon leading to the spontaneous formation of a structure in the longitudinal dimension of the electron bunch: the so-called microbunching
instability [1–3]. This represents one of the most fundamental limitations of stable operation in electron storagerings, as well as a means to produce high intensity coherent
radiation. This effect is observed and studied in a wide
range of storage ring facilities, such as ALS [3], ANKA [4],BESSY [5], DIAMOND [6], ELETTRA [7], MLS [8],Synchrotron SOLEIL [9], and UVSOR [10].
However, comparisons between models and experiments
have been up to now indirect. Indeed, experimental data
have been essentially based on the recordings of the pulsesof millimeter wave coherent emission (coherent synchrotron radiation or CSR), using a bolometer or a diodedetector at a terahertz (THz) beam line. Because of therelatively slow response time of these detection systems,
only the evolution of the pulse energy could be monitored,
and real-time monitoring of the pulse shape evolution was
unfortunately out of reach. Time-resolved recordings using
0031-9007=14=113(9)=094801(5)electro-optic sampling have also shown to be possible [11],though the low repetition rate of these devices does notallow us yet to monitor the dynamical microstructure
evolution over several turns.
In this Letter, we demonstrate the possibility to monitor
the microstructure dynamics in real time (turn-by-turn),
when the electron bunch duration exceeds several tens ofpicoseconds, using a new generation of ultrafast detectors
based on thin films of the high-temperature superconductor
YBa2 Cu3 O7−x (YBCO) [12–14]. Indeed, the temporal
resolution of these detectors is only limited by the bandwidthof readout electronics and oscilloscope speed (16 ps FWHM
here), and thus allows us to record details of the emitted CSR
pulses. Furthermore, full characterization of the CSR pulses(amplitude and carrier) can be carried out, because those
detectors are directly sensitive to the electric field.
In the first part, we present a study of the dynamics above
the microbunching instability, and interpret the pattern
dynamics from the phase space motion. In the second
step, we also present the response of the electron bunchwhen the CSR instability is seeded [15] by a localized laser
perturbation.
The experimental arrangement is displayed in Fig. 1. TheUVSOR-III storage ring is operated in single bunch mode

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Detector signal (mV)oscilloscope(63 GHz BW)

FIG. 1 (color online). Scheme of the experiment. A relativistic
electron bunch is stored in the UVSOR-III storage ring. When theelectron bunch density exceeds a given threshold, a dynamical
instability leads to the spontaneous formation of a pattern in
the longitudinal direction. In this Letter, the coherent emission(with ≈9 mm wavelength) due to the presence of the structure isdirectly monitored, using a new type of thin-film superconducting
detector based on YBCO (see text).

above the threshold for microbunching instability, at acurrent of 60 to 65 mA. In these conditions, coherent
millimeter wave radiation is emitted in the bending magnets,
which is a signature of a modulation of the electron bunch at
millimeter scale. At the output port of the BL6B THz beamline [16,17], we placed the thin-film YBCO detector,
described in detail in Refs. [12–14]. It was operated at
liquid nitrogen temperature without any bias. The detector
was positioned near the focusing point of the beam line, andthe signal was directly recorded by a 63 GHz oscilloscope(Agilent DSOX96204Q) without any amplification.
The coherent synchrotron radiation is composed of a seriesof pulses [Fig. 2(b)], each having a duration of the order of
300 ps, separated by the storage-ring round-trip time (177 ns).
The envelope was found to vary slowly (near threshold), or ina bursting manner far from threshold [Fig. 2(a)]. The firstobservation of typical single pulses [Fig. 2(c)] revealed thatthe electric field evolution, including the optical carrier, could
be directly observed by the YBCO detection system and thatthe carrier frequency was in the 1 cm−1 range.
Then we proceeded to systematic recordings of long timeseries above the microbunching instability threshold. We
summarized their dynamical evolutions as a color map
versus a “fast time” (i.e., resolving the pulse shape), and a“slow time” (associated to the number of round-trips). Alldata displayed a systematic pattern [Fig. 2(d)], with two
visible parts. The first one is a structure at the bunch head[in the lower part of Fig. 2(d), before ≈125 ps], which
systematically drifts towards the tail. The second part (after≈125 ps) is constituted of a combination of two structuresthat move in both directions.
These two directions of motion can be interpreted from areasoning in the phase space of the electrons. Assumingthat the relevant motion occurs in the longitudinal direction[1–3], the state of each electron i at time t is defined by its
instantaneous position zi ðtÞ and an energy variable δi ðtÞ.
The dynamics of the electrons can be described by thefollowing model [18,19]:40 (a)
20
0
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Detector signal (mV)electron bunch withspontaneously formed
longitudinal structure

Detector signal (mV)

Ultra-fastthin-film
YBCO detector

Detector signal (mV)UVSOR-III
storage ring

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Fast time (ps)

PRL 113, 094801 (2014)

200
-40
0

5

10
15
Slow time (µs)

2025FIG. 2 (color online). Typical shape of a single pulse that is
detected by the YBCO ultrafast detector (in red). (a), (b), and(c) represent the same signal at different scales. The color scale
diagram (d) represents the evolution of the (c) signal over manysuccessive turns in the storage ring. Note that the voltage isdirectly proportional to the electric field of the incoming
radiation, and that both the envelope and the carrier are thus
recorded. The dashed line in (d) corresponds to the signal
displayed in (c).

dzi
¼ −ηcδi
dt
 
 2
dδi
ωs
2
δ − F − ηn ξðtÞ;
¼−
z −
τs i
dt
ηc i

ð1Þ
ð2Þ

where t is a continuous time variable corresponding to thenumber of round-trips (i.e., the slow time variable inFig. 2). δi ðtÞ ¼ ½Ei ðtÞ − ER =ER , where Ei and ER are,respectively, the electron energy and a reference energy ofthe storage ring (600 MeV here). ωs =2π is a dynamicalfrequency called the synchrotron frequency (23.1 kHz here,

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Longitudinal position z (cm)
-6

-4

-2

0

2

4

6

8

not to be confused with the revolution frequency in thering). τs is the synchrotron damping time. η is a parametermeasuring the dependence of the round-trip length with theenergy. The term ηn ξðtÞ accounts for the stochastic fluctuations of the synchrotron losses. ξðtÞ is a Gaussian noisewith hξðtÞξðt0 Þi ¼ δðt − t0 Þ. F characterizes the collective
force exerted on electron i by the other electrons.
Parameters, the expression of F, and integration details
are given in the Supplemental Material [20].
The link between the electron phase space distribution
and the data provided by the detector is presented in Fig. 3.
Pattern formation occurs in the electron density distribution, which we will name fðz; δ; tÞ [Fig. 3(a)]. However,
only the projection on the z coordinateZ −∞ρðz; tÞ ¼fðz; δ; tÞdδ;
ð3Þ

10

(a)

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ECSR (arb. units) Density (arb. units)

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which corresponds to the longitudinal shape of the electron
bunch, is relevant to the observations [Fig. 3(b)]. In thisprojection, it is clear that the modulation due to the microstructure is extremely weakly contrasted compared to the“global shape” of the electron bunch. Nevertheless thismodulation is crucial as it leads to the CSR field [Fig. 3(c)]that is observed experimentally. A typical evolution of thiselectric field during a CSR burst is represented Fig. 3(d)[with the same color scale representation as the experimental
diagram in Fig. 2(d)].
The directions of drifts observed experimentally in
Fig. 2(d) can be interpreted from the motion of the electron
bunch distribution in phase space fðz; δ; tÞ. Indeed this
distribution [Fig. 3(a)] is subjected to a global rotation near
the frequency ωs =2π (23.1 kHz for our experiment). Hence,
globally speaking, the structures drifting toward the bunchhead in Figs. 2(d) and 3(d) correspond to structures that arepresent in the lower part of phase space [Fig. 3(a)], andvice versa.

600
0

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20

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-1

50

Number of round-trips
100
150
200
250

300

20

500
10

FIG. 3 (color online). Interpretation of the drifting motions
observed in Fig. 2(d), from the model (2). (a) Distribution of theelectrons in longitudinal phase space (position z energy δ) at agiven time. The CSR instability leads to a microstructure in thisphase space. (b) Longitudinal electron density distribution, i.e.,
obtained by the vertical projection of the distribution (a). (c) CSR
electric field deduced from (b). Note that the structure is moreclearly observable in (c) than in (b), because slow variations are
cut off in the CSR process. The electric field versus time(d) reveals that the structures are permanently drifting, as in
the experiment. This is essentially due to the permanent rotationof the electron distribution (a) at the synchrotron frequency.

Fast time (ps)

-400

0

400
300

0

200
-10

Detector signal (mV)

Relative energy 10-3(E-E0)/E0

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100
0

0

10

20

30
40
Slow time (µs)

50

60

-20

FIG. 4 (color online). Dynamics following a localized laser
perturbation (slicing) at t ¼ 0, when the system is below the
instability threshold. Note that no CSR emission is detected
before t < 0. Interpretations are given in Fig. 5.

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(a)
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Figs. 5(g) and 5(h)], each being associated with nearly verticalparts of the S-shaped slice (phase-space plots in Fig. 5).
In conclusion, we showed that using a YBCO thin-film
superconducting detector sensitive to the electrical field it is
now possible to investigate in detail the CSR pulses at
millimeter-centimeter wavelengths, which result from themicrobunching instability. The actual time scales of theexperiment allowed us to record the carrier and envelope of
pulses, thus, allowing us to analyze the chaotic evolutionsof the bursts in a very detailed way. Extension of thisdetection method can be also performed in cases where thecarrier cannot be resolved, by biasing the detector. In thiscase, only the pulses’ envelopes can be recorded [14], but ata similar speed. More generally, we believe that this new
detector technology will allow us to probe the validity ofexisting and future models, which differ in particular by theway to approximate the evolution equation (as the Vlasov
versus macroparticle approach) and by the numerous
possibilities for the wakefield modeling [27].

t=42 µs (h) t=42.86 µs (i) t=46.32 µs

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0
Fast time (200 ps/div)

FIG. 5 (color online). Numerical simulation of transients after
slicing the electron bunch with a laser, and interpretation in phasespace. (a) Simulation of the detection signals. (b)–(i) Phase-space
distribution (grayscale image) and associated CSR wakefield (redcurve) at different times. For clarity, the reference distribution
before laser perturbation (b) is subtracted from the distributions.
(c),(d),(e), snapshots near t ¼ 0. (f),(g),(h), and (i) are successive
snapshots corresponding to different instants of the “cusp”
feature visible in (a) at t ¼ 40–47 μs.

The phase space dynamics can also be studied below
the microbunching instability threshold, by examining the
response to a perturbation to a short laser pulse. The
experimental response presented in Fig. 4 is obtained using
a 15 ps pulse from a titanium-sapphire laser (800 nm,
10 mJ, with an adjustable grating pulse compressor [26]),
interacting with the electron bunch in an undulator [16], andthe corresponding simulation is displayed in Fig. 5(a). The
data recorded by the YBCO detector display characteristicfeatures, as the cusp (or “Y shape”) present at the right of thecolor scale diagrams. These features can be also understoodfrom the examination of the phase space versus time
[Figs. 5(c)–(i)] and the associated CSR wakefields. From
this chronology, we can see that the cusp appears as asignature of the transformation of the initially straight slice[Fig. 5(c)] into an “S-shaped” slice. It is observed that thepeak response occurs when the inflexion point of the S shapeis nearly vertical. The two branches of the cusp correspond to
the progressive merging of the two pulses [red curves in

We would like to thank Agilent, LeCroy, and Tektronix,
for providing the oscilloscopes needed for the ultrafast dataacquisition. The work was supported by the Joint Studies
Program of the Institute for Molecular Science, the JSPS
fellowship program for research in Japan (S-09171), theProjet International de Coopération Scientifique PICS
project from CNRS, the Grant-in-aid for scientific researches(B20360041) of JSPS, the ANR (Blanc 2010-042301), andused HPC resources from GENCI TGCC/IDRIS (2013x2013057057, 2014x2014057057). The CERLA is supported by the French Ministère chargé de la Recherche,
the Région Nord-Pas de Calais and the FEDER. The KIT is
supported in part by the German Federal Ministry of
Education and Research under Grant No. 05K2010.

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