ARTICLE DE FOND
ADVANCES IN COHERENT SYNCHROTRON RADIATION AT
THE CANADIAN LIGHT SOURCE
BY
BRANT E. BILLINGHURST AND JOHN C. BERGSTROM
W
hile good sources of radiation are available
for most of the electromagnetic spectrum, an
intense broadband source for the terahertz
region is still lacking. Synchrotrons have
offered a source of radiation for much of the electromagnetic spectrum; however, in normal operation they do not
provide an intense source in the terahertz region. Despite
this, a synchrotron can be used as an excellent source of
terahertz radiation by modifying the operating conditions
of the storage ring to produce coherent synchrotron radiation (CSR). Production of CSR has been demonstrated at
a number of synchrotrons worldwide [1]. At the Canadian
Light Source, research is being performed into the production, the physics, and the application of CSR.
THE BASIC PHYSICS OF COHERENT
SYNCHROTRON RADIATION PRODUCTION
Electrons in a synchrotron travel in discrete groups called
bunches. Normally these bunches are about 10 mm in
length. Under normal operating conditions, the radiation
power produced by one bunch goes as:
P=
2a 2 Ne 2
3c3
(1)
where a is acceleration, N is the number of electrons per
bunch, e is the charge on an electron and c is the speed of
light. By contrast, if the bunch length is smaller than the
wavelength of the radiation, the bunch behaves like a “fat
electron” with charge Ne, and the corresponding radiation
is very nearly coherent in phase. In this case the radiated
power goes as
P=
2a 2 ( Ne )
3c3
2
(2)
In short, the power is no longer linear with the number of
electrons, but quadratic, which in favourable cases can
lead to a factor of 106 increase in power.
Unfortunately it is generally not practical to reduce the
physical bunch length to the degree necessary to truly
achieve this. Instead, in order to achieve the CSR condition, we operate in one of two bunch modes: continuous or
bursting. The continuous mode is achieved by filling each
bunch (up to 210 in total) to roughly 50 microamperes,
and then relying on the radiation impedance to deform the
bunch from its normal Gaussian distribution to a “shark
fin” profile (see Figure 1). The high frequency part of the
“shark fin” distribution acts, in effect, as a short bunch,
which generates the CSR. Although the power increase is
not as high as predicted above, gains of 103-104 can be
achieved. Continuous mode operation has been achieved
at the CLS, because of the naturally smaller bunch length
at lower energies, this was done operating at 1.5 GeV
rather than 2.9 GeV(the normal operating energy of the
CLS).
The mechanism of bursting mode is somewhat more complicated to describe. The bunches are filled to about
B.E. Billinghurst
<brant.billinghurst@
lightsource.ca> and
J.C. Bergstrom,
Canadian Light
Source, University of
Saskatchewan,
Saskatoon, SK
S7N 0X4
SUMMARY
In this paper we describe some of the
research into Coherent Synchrotron
Radiation (CSR) currently under way at the
Canadian Light Source (CLS). We include an
overview of the physics behind the production of CSR, and present two examples of
research being done using CSR. The examples we present are Multi-bunch Interference, which illustrates the research into the
physics of CSR, and Photoacoustic spectroscopy using CSR, which shows an important application of this radiation.
Fig. 1
Graph of “Shark fin” electron density along the longitudinal axis, where the red box roughly delineates the
high frequency component of the electron density.
LA PHYSIQUE AU CANADA / Vol. 67, No. 1 ( jan. à mars 2011 ) C 17
... COHERENT SYNCHROTRON RADIATION (BILLINGHURST/BERGSTROM)
momentum compaction by
fs = const a½
(4)
The momentum compaction is a constant which
depends on the optical setup of the synchrotron. It
defines the relationship between the relative energy
spread of the electrons in the bunch and the longitudinal spread of the electrons (ΔL) over the average
length of one complete orbit of the ring (L0), or
Fig. 2
(A) Arbitrary initial arrangement for 2 electrons traveling through a bending
magnet. The solid red arrow represents the transverse electric field E generated by electron 1. (B) shows the same electrons as at some arbitrary time
later. Notice that the transverse electric field previously generated by electron
1 can now interact with electron 2. Ez is the longitudinal component of
E in the frame of electron 2.
( )
10 mA each, and random noise within the bunch distribution is
sufficient to seed the start of the bursting process. This noise
acts like a very small “micro-bunch” within the larger bunch.
Figure 2 illustrates the mechanism by which these microbunches are enhanced. For the sake of simplicity let’s assume
that the micro-bunch contains 2 electrons moving through a
bending magnet. The trailing electron radiates a transverse
field tangential to the path of the electron. Since the electron’s
path is curved, the transverse field catches up with the leading
electron. Because the leading electron is no longer travelling
parallel to the propagation vector of the field, a component of
the electric field is projected parallel to the motion of this electron, and it gains energy. The net result is that the trailing electron loses energy and the leading electron gains energy, so they
enter slightly smaller and larger orbits respectively. The leading electron will therefore take slightly longer to circle the ring
than the trailing electron, and the electrons will appear to move
closer together longitudinally. Extrapolating now to a multielectron bunch, the resulting micro-bunch radiates more power,
creating a runaway situation which leads to progressively
smaller micro-bunches producing even stronger CSR.
Eventually the process leads to a longitudinal beam instability
which drives the bursting. Following the longitudinal burst,
radiative damping leads to a reformation of the original conditions, and the process starts again. Thus, the bunch behaves like
a repeating shotgun, with the time between firing being in the
sub-millisecond domain. Bursting mode operation has been
achieved at the CLS at both 2.9 and 1.5 GeV. Figure 3 compares the intensity of the radiation observed from CSR to normal synchrotron radiation in the 1 to 30 cm-1 region.
ΔL
= aδ
L0
(5)
Beyond the production of CSR, research is being
performed into both the physics and the application
of CSR. In the following paragraphs we will discuss
one example of each of these avenues of research:
Inter-bunch interference (also known as super-radiance) and Photoacoustic spectroscopy using CSR.
MULTI-BUNCH INTERFERENCE
The power spectrum from an electron synchrotron derives from
the accumulation of light pulses from successive bunches.
For sufficiently short bunches, a unique phase relation exists
between successive fields, and a coherency is established
between bunches. This bunch-to-bunch coherency manifests
itself in an interferogram as a periodic sequence of patterns
similar to the familiar center-burst pattern. The physics behind
this phenomenon has been described in Jackson’s book [2], and
bunch-bunch interference was observed at low resolution by
Shibata et al. [3] using a linac. The CLS was the first to report
the observation of this phenomenon in a Storage Ring and the
first to observe it at high resolution [4].
CSR was produced in the continuous mode by operating the
CLS synchrotron at 1.5 GeV, with the momentum compaction
adjusted to produce a bunch length of a few picoseconds. Total
For practical reasons the synchrotron frequency is usually
measured, rather than the bunch length. The bunch length is
related to the synchrotron frequency by the following equation:
σ=
a
iδ
2π f s
(3)
where σ is the bunch length, a is the momentum compaction,
fs is the synchrotron frequency and δ is the relative energy
spread. Note that the synchrotron frequency is related to the
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Fig. 3
Comparison of the spectrum acquired using normal
Synchrotron radiation (Blue) to CSR (Red).
... COHERENT SYNCHROTRON RADIATION (BILLINGHURST/BERGSTROM)...
I ( λ ) = N e2 i f e ( λ ) i B ( λ )
(6)
where , f(λ) is a bunch length dependent form factor, Ne is the electron population of each bunch and
B(λ) is
⎡ ⎛ N b πd ⎞ ⎤
⎢ sin ⎜ λ ⎟ ⎥
⎠⎥
B (λ) = ⎢ ⎝
π
d
⎛
⎞
⎢ sin
⎥
⎜
⎟
⎢⎣
⎝ λ ⎠ ⎥⎦
2
(7)
with d the bunch separation (~600 mm). The envelope defined by eq. (7) is shown in black in the
insert, with arbitrary normalization.
Fig. 4
Average of 10 interferograms of CSR demonstrating bunch-bunch coherence
as described in the text.
beam current was about 4.9 mA, distributed over 210 bunches.
Spectra were collected on a Bruker IFS 125 HR spectrometer,
using a 75 μm Mylar beam splitter and Infrared Labs Si
Bolometer. A 12.5 mm aperture was used, with gain at 200X, a
scanner velocity of 60 kHz, and a resolution of 0.002 cm-1.
The first features one may notice in the interferogram shown in
Figure 4 are the centerburst-like features spaced at 600 mm
intervals, from 600 to 4200 mm pathlength difference. These
features are due to interference of the coherent light emitted by
one bunch with that of its nearest neighbour, or the bunch once
removed, or twice removed, etc., up to seven times, respectively. Note that this interference demands a well-defined phase
relationship between the light emitted by all bunches.
The Fourier transform of the interferogram, shown in Figure 5,
displays the sharp spectral features that result from these correlations. These features are more readily observed in the
expanded 6.0-6.2 cm-1 region shown in the inset of this figure.
The fine structure in these figures can be explained by considering that the intensity of CSR from Nb successive bunches is
given by
Fig. 5
The ultimate result of this is that the while the average power still goes as Nb(Ne)2, it is now concentrated in a series of high quality-factor peaks,
where the peak power varies as Nb(Ne)2 with Nb being the number of bunches.
PHOTOACOUSTIC SPECTROSCOPY USING
CSR
While the physics behind CSR is important and interesting, the
CLS as a user facility is also concerned about the practical
application of the radiation it produces. There are many applications for CSR: one innovative use of this radiation is as a
source for Photoacoustic spectroscopy (PAS). This application
was first demonstrated at the CLS [5].
Fourier Transform Infrared Photoacoustic Spectroscopy is
a well established technique, which obviates the need for traditional sample preparation methods and allows for the study
of solid and/or opaque samples. Furthermore heterogeneous
and layered samples can be characterized using PAS depth
profiling techniques [6]. PAS can simply be described as
follows: modulated radiation of a wavelength that coincides
with a vibrational mode of the sample impinges on the
sample and is then absorbed. The molecules of the
sample are thus raised to a vibrationally excited
state. When the molecule relaxes back to its
ground state the energy is dissipated as heat, creating a thermal wave in the sample. This heat wave
is then transferred to a carrier gas which in turn
creates a pressure wave. If the modulation occurs
at acoustic frequencies, the pressure (sound)
wave can be detected using a sensitive microphone.
Fourier transform of Figure 4. (Inset) An expansion of a small region of the
main figure with an overlay of equation 7 with d=599.6 mm and Nb=8.
For the experiments described herein an MTEC
PAS cell was used. The gain was set at 2000X and
Helium was used as the carrier gas. Spectra were
recorded using a Bruker IFS 125 HR spectrometer
fitted with a 75 μm Mylar beamsplitter. The aperture was set at 12.5 mm and the scanning frequency was 5 kHz.
LA PHYSIQUE AU CANADA / Vol. 67, No. 1 ( jan. à mars 2011 ) C 19
... COHERENT SYNCHROTRON RADIATION (BILLINGHURST/BERGSTROM)
Fig. 6
PAS spectra of carbon black collected using Hg Lamp
sources (Black), Normal fill synchrotron radiation (Blue) and
CSR (Red). (details in text)
Figure 6 compares PAS spectra of carbon black collected using
an Hg lamp (black), conventional synchrotron radiation with
220 mA in the ring (blue) and CSR with 10.9 mA in the ring
and fs set to 5.5 kHz (red). It is immediately evident that useful spectra are not obtained using either the Hg lamp or normal
synchrotron radiation, while an excellent spectrum is observed
using CSR.
While the result for carbon black demonstrates the advantage
of CSR PAS very well, it lacks the spectral features that are
generally of interest to spectroscopists. Instead α-lactose
monohydrate (milk sugar) was chosen as a test molecule for
this study: this material is known to exhibit a strong absorption
band at ~ 18 cm-1 [7,8]. This substance was obtained from
Sigma Aldrich and used without further preparation.
The red trace in Figure 7 shows a photoacoustic spectrum of alactose monohydrate obtained at 2 cm-1 resolution. CSR was
produced with a current of 10.9 mA divided between two
bunches; the synchrotron frequency was 5.2 kHz. The expect-
Fig. 7
PAS spectrum of α-lactose monohydrate collected using
CSR. (details in text)
ed peak at ~18 cm-1 can clearly be observed in this spectrum,
demonstrating the utility of this technique.
ACKNOWLEDGEMENTS
We thank our collaborators on these projects, including Tim
May (CLS), Dr. Mark deJong (CLS), Dr. Les Dallin (CLS), Dr.
Ward Wurtz (CLS) and Dr. Kirk Michaelian
(CanmetENERGY). Furthermore we would like to thank Dr.
Thomas Ellis (Research Director, CLS) and Dr. Josef Hormes
(Director, CLS) for their vision in allowing this research to proceed and all of the CLS staff without whom none of this
research would have been possible. Research described in this
paper was performed at the Canadian Light Source, which is
supported by the Natural Sciences and Engineering Research
Council of Canada, the National Research Council Canada, the
Canadian Institutes of Health Research, the Province of
Saskatchewan, Western Economic Diversification Canada, and
the University of Saskatchewan.
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