scispace - formally typeset
Search or ask a question
ReportDOI

A Sub-Picosecond Photon Pulse Facility for SLAC

28 Aug 2001-
TL;DR: In this article, it is shown that the injection-damping ring system used to inject into the PEP-II B-Factory can be used for this purpose, without any modification to the linear accelerator except for a sequence of 4 bending magnets to compress the electron bunch.
Abstract: It is possible to generate very bright sub-picosecond pulses of spontaneous x-ray radiation utilizing the electron beam from the SLAC linear accelerator and an undulator. The present injection-damping ring system used to inject into the PEP-II B-Factory can be used for this purpose, without any modification to the linear accelerator except for a sequence of 4 bending magnets to compress the electron bunch. With a charge of 3.4 nC per bunch accelerated to 28 GeV and a 10 m long undulator it is quite feasible to generate pulses of x-rays of 8.3 kV energy (in a spectrum extending to over 1 MeV), 80 fsec long (full-width-half-maximum), with a peak brightness of the order of 10{sup 25} photons/(sec x mm{sup 2} x mrad{sup 2} x 0.1% bandwidth), and 10{sup 8} photons per pulse in a 0.1% bandwidth. This facility could be built and operated ahead of the LCLS schedule and would provide both a powerful tool for research in its own right, as well as a way to conduct critical accelerator and x-ray optics R and D for the LCLS.

Summary (3 min read)

Introduction

  • It is possible to generate very bright sub-picosecond pulses of spontaneous x-ray radiation utilizing the electron beam from the SLAC linear accelerator and an undulator.
  • This proposal envisions electron bunch compression in three stages, starting with the existing damping ring bunch compressor (Ring-To-Linac section, RTL).
  • A new 10-m long undulator located here produces intense spontaneous x-ray radiation, which is transported to an experimental hutch, placed outside the FFTB area.
  • This paper is organized as follows: - Section 1: Layout of the facility and main performance parameters.
  • Cost and construction schedule, also known as - Section 7.

1. General layout and projected performance

  • A single electron bunch with 2.2×1010 electrons is extracted from the North Damping Ring, as is currently done for injection into the PEP-II storage ring.
  • A second stage of compression requires the addition of a new magnetic chicane to the linac at the 9 GeV location, which compresses the bunch down to 160 fsec rms (50 µm).
  • The radiation is transported to an experimental area placed outside the FFTB.
  • Table 1 lists the main characteristics of the spontaneous radiation and of the electron beam at the undulator.

2. Scientific opportunities and LCLS R&D

  • The most exciting feature of the SPPS will be its combination of synchrotron radiation brightness with sub-picosecond pulse length.
  • Probe techniques in use today include optical laser spectroscopy5, electron diffraction6, x-ray diffraction7, and x-ray absorption spectroscopy8.
  • For complicated structures, this becomes impossible, and a direct structural measurement through diffraction or core-level spectroscopy is needed.
  • In Table 2 the SPPS performance is compared with some existing and proposed sub-psec x-ray facilities: the Ultrafast X-Ray Facility at the Advanced Light Source, the proposed re-circulating linac light source 5 Femtochemistry and Femtobiology: Ultrafast Reaction Dynamics at Atomic Scale Resolution, V. Sandstroem, ed., World Scientific, Singapore 1997.
  • These are all facilities capable of delivering bunches of the order of 100-200 fsec long.

LCLS FEL11

  • The peak brightness of SPPS will exceed that of any existing hard x-ray source by several orders of magnitude, and its pulse length of <100 fsec will allow it to explore the same time correlations as the fastest existing or proposed sources.
  • The SPPS should prove to be a valuable tool for developing ultrafast x-ray techniques.
  • And <100 fsec long pulses, important R&D, critical to the LCLS and x-ray FELs in general, could be conducted with a tool that would have no equal in the world in terms of short pulses, peak brightness, and photon flux.
  • One method planned for the LCLS uses a transverse RF deflector to ‘streak’ the bunch onto a profile monitor.
  • When operated at full bunch compression, the average temporal structure of the SPPS photon pulses will be similar, both in profile and duration, to the 80 fsec (fwhm) long electron bunches.

3. Electron acceleration and compression

  • The electron beam parameters are largely governed by the boundary conditions of supplying beam to the SPPS parasitically to PEP II operation.
  • The positron and electron bunches for PEP II are extracted from the linac at the 3 GeV and 9 GeV locations respectively into beamlines that by-pass the rest of the linac.
  • The linearly correlated energy spread of 1.6% (rms) in the bunch is introduced by accelerating, in the linac sections between the damping ring and the chicane, at an RF phase of −20° from accelerating crest, as shown in Figure 5d.
  • It was found, through computer simulation studies, that the problem of wakefields could be alleviated by shaping the initial charge distribution in the bunch in such way as to over compress19 the bunch in the first RTL compressor.
  • 19 F.-J. Decker, R. Holtzapple, T. Raubenheimer, “Over-Compression, a Method to Shape the Longitudinal Bunch Distribution for a Reduced Energy Spread” in LINAC94, August 1994.

Parameter Symbol Value Unit

  • These parameters have been verified by 6-D particle tracking using the code Elegant21.
  • The processes of emittance growth due to incoherent (ISR) and coherent synchrotron radiation (CSR) in the various bends have been computed and found to increase the emittance by 15-20%.
  • In the FFTB, the large energy spread requires a new sextupole magnet to be located at the point of largest momentum dispersion.
  • The new 10-cm long sextupole magnet is already available from the SLC final focus where it was never used.
  • With the new sextupole, the remaining chromatic effects increase the emittances by only 2-3 %.

4. The undulator

  • The choice of photon energy range depends on the electron energy and on the undulator characteristics.
  • An internally copper plated stainless steel beampipe, with either circular or oblong cross section, will be inserted in the gap when the segments are assembled.
  • The structure of the undulator is shown in the figures below:.
  • The two figures of merit for the photon beam distribution are εp, the photon emittance, and σp,hutch, the photon beam size in the experimental hutch a distance D = 92 meters from the undulator.

5. The radiation characteristics

  • This Section tabulates the main properties of the radiation.
  • The simulations described in Section 3 indicate that, at full compression, the energy spread in the electron beam will be ~1.5 % .
  • In these units the quantity γ∗θ [rad] represents the angular radius of the far-field distribution for arbitrary values of γ.
  • **100% multilayer efficiency assumed Power loading of SPPS optical elements.

6. Take-off optics and experimental area layout

  • This choice is suggested by the limited space in the FFTB and by the desire to operationally decouple the experimental area from the electron beam to allow access to the experiment when the linac is being set up or during accelerator studies.
  • In the first case the incidence angle would be too large to transmit X-rays and in the second case the mirror array would need to be impracticably long.
  • In the present conceptual layout the extracted beam would exit the chamber at an angle of 8.5°.
  • Given the cited beam line parameters, multilayer optics will be employed for energies between ~800 eV to ~13 keV, and crystals for energies of ~ 6 keV and higher.
  • The section of the beam line between the outside of the FFTB tunnel and the hutch will rest on standard support frames and will be shielded with modular concrete segments to satisfy radiation safety requirements.

7. Schedule and cost

  • The facility would be located in the Final Focus Test Beam (FFTB), in the area eventually occupied by the LCLS undulator.
  • The advantage of starting the research in the FFTB is twofold: it is the most cost and time effective way to achieve sub-picosecond pulses and it allows to carry out accelerator studies that are important for the LCLS R&D, while providing a powerful source of spontaneous radiation for experiments.
  • This cost (in thousand of dollars) is divided amongst the various components as follows: Compressor and other magnets, electron beam instrumentation 658 Undulator 1,551 X-ray optics 397 Vacuum equipment 564 Controls, cabling, MPS/PPS, power supplies 548 Experimental hall, hutch, laser clean room 664 Laser for pump-probe experiments 691 Accelerator and undulator physics design, project management 1,032 Contigency (30%) 1,832.

Indirect costs 1,710

  • The staff needed during the construction phase (17 months) is as follows.
  • The numbers represent the Full Time Equivalent over the 17 months construction period.
  • Engineering, design and inspection 1.6 Labor and technical support 7.2 Accelerator physics and undulator magnetic design 3.0 X-ray optics physics and beamline design 1.0 Project Management 1.6.
  • The cost of running the facility has yet to be estimated, but it will take advantage of the fact that the linear accelerator (where most of the power consumption is) will be available because the rf is normally left on in between PEP-II fills.
  • This work is supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences (contract number DE-AC03-76SF00515), also known as *Acknowledgements.

Did you find this useful? Give us your feedback

Figures (21)

Content maybe subject to copyright    Report

SLAC-PUB-8950
A Sub-Picosecond Photon Pulse Facility for SLAC
Work supported by Department of Energy contract DE–AC03–76SF00515.
M. Cornacchia et al.
Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309
August 2001
LCLS-TN-01-7

1
A Sub-Picosecond Photon Pulse Facility for SLAC*
M. Cornacchia
a
, J. Arthur
a
, L. Bentson
b
, R. Carr
a
, P. Emma
b
, J. Galayda
a, b
, P. Krejcik
b
,
I. Lindau
a
, J. Safranek
a
, J. Schmerge
a
, J. Stohr
a
, R. Tatchyn
a
, A. Wootton
c
Introduction
It is possible to generate very bright sub-picosecond pulses of spontaneous x-ray radiation utilizing the
electron beam from the SLAC linear accelerator and an undulator. The present injection-damping ring
system used to inject into the PEP-II B-Factory can be used for this purpose, without any modification to
the linear accelerator except for a sequence of 4 bending magnets to compress the electron bunch. With a
charge of 3.4 nC per bunch accelerated to 28 GeV and a 10 m long undulator it is quite feasible to
generate pulses of x-rays of 8.3 kV energy (in a spectrum extending to over 1 MeV), 80 fsec long (full-
width-half-maximum), with a peak brightness of the order of 10
25
photons/(sec×mm
2
×mrad
2
×0.1%
bandwidth), and 10
8
photons per pulse in a 0.1% bandwidth.
This facility could be built and operated ahead of the LCLS schedule and would provide both a powerful
tool for research in its own right, as well as a way to conduct critical accelerator and x-ray optics R&D for
the LCLS.
This proposal envisions electron bunch compression in three stages, starting with the existing damping
ring bunch compressor (Ring-To-Linac section, RTL). A second stage of compression is added in the
form of a simple magnetic chicane installed at the 9-GeV location in the linac. A third compression stage
is the existing Final Focus Test Beam (FFTB) beamline where a bunch length of 80 fsec (full-width-half-
maximum, fwhm) at 28 GeV is produced. A new 10-m long undulator located here produces intense
spontaneous x-ray radiation, which is transported to an experimental hutch, placed outside the FFTB area.
The FFTB hall, in terms of its size and infrastructure (mechanical and temperature stability), is very
suitable for setting up such a source.
This paper is organized as follows:
- Section 1: Layout of the facility and main performance parameters.
- Section 2: Scientific opportunities and LCLS-directed R&D.
- Section 3: Physics and engineering aspects of electron bunch compression.
- Section 4: The undulator and its electron optics.
- Section 5: The characteristics of the spontaneous radiation emitted by the undulator.
- Section 6: Take-off x-ray optics and experimental area.
- Section 7: Cost and construction schedule.
The concept of using the SLAC linac to generate radiation from an undulator has evolved from
several earlier proposals
1,2,3,4
a
Stanford Synchrotron Radiation Laboratory, a division of Stanford Linear Accelerator Center
b
Technical Division, Stanford Linear Accelerator Center
c
Lawrence Livermore National Laboratory
1
P.H. Fuoss, NIM A264, 497 (1988).
2
J. Seeman, R. Holtzapple, “An ‘NLC-Style’ Short Bunch Length Compressor in the SLAC Linac”, SLAC-PUB-6201 (1993).
3
P. Emma, J. Frisch, “A Proposal for Femtosecond X-ray Generation in the SLC Collider Arcs”, SLAC-PUB-8308 (1999).
4
P. Krejcik, “Parameters for a 30 GeV Undulator Test Facility in the FFTB/LCLS”, SLAC-PUB-8806 (2001).
SLAC-PUB-8950
LCLS-TN-01-7
August 2001

2
1. General layout and projected performance
The general layout of the facility is shown in Figure 1.
new
new
chicane
chicane
in linac at 9 GeV
in linac at 9 GeV
Damping
Damping
Rings
Rings
e
e
-
-
1.2 mm
1.2 mm
50
50
µ
µ
m
m
12
12
µ
µ
m
m
6 mm
6 mm
SLAC Linac
SLAC Linac
1.2 GeV
1.2 GeV
28 GeV
28 GeV
FFTB
FFTB
RTL
RTL
e
e
+
+
Figure 1. Layout of the SPPS in the SLAC accelerator complex. The root-mean-square bunch length (rms) is
shown at various stages.
A single electron bunch with 2.2×10
10
electrons is extracted from the North Damping Ring, as is
currently done for injection into the PEP-II storage ring. With reference to Figure 1, the electron
bunch compression will be done in three stages, starting with the existing Ring-To-Linac (RTL)
compressor at the exit of the damping rings, where the bunch length is compressed from 20 psec (6
mm) to 4 psec (1.2 mm) - rms values. A second stage of compression requires the addition of a new
magnetic chicane to the linac at the 9 GeV location, which compresses the bunch down to 160 fsec
rms (50
µ
m). The third stage of compression occurs in the bends of the present FFTB beamline,
which produce a 35 fsec rms bunch length (12
µ
m) at 28 GeV (80 fsec fwhm). A 10 m long
undulator in the FFTB generates spontaneous radiation at the undulator fundamental photon energy
of 8.3 keV and extending to over 1 MeV. The radiation is transported to an experimental area placed
outside the FFTB. Table 1 lists the main characteristics of the spontaneous radiation and of the
electron beam at the undulator.
Table 1. Main SPPS radiation (8.3 keV) and electron beam (28 GeV) parameters
Peak photon brightness
9.1×10
24
photons/(sec×mm
2
×mra
d
2
×0.1% bw)
Pulse length
80
fsec, fwhm
Average photon
brightness
2.2×10
13
photons/(sec×mm
2
×mra
d
2
×0.1% bw)
Average flux
3.1×10
9
ph/(sec×0.1% bw),
integrated over all angles

3
Photons/pulse
1.0×10
8
In a 0.1% bw, integrated
over all angles
Bunch repetition rate
30
Hz
Charge per bunch
3.4
nC
Energy
28
GeV
Horizontal e
-
emittance
(rms)
9.1x10
-10
m-rad
Vertical e
-
emittance
(rms)
1.8x10
-10
m-rad
2. Scientific opportunities and LCLS R&D
The most exciting feature of the SPPS will be its combination of synchrotron radiation brightness
with sub-picosecond pulse length. This combination will allow the powerful techniques of x-ray
diffraction and x-ray absorption spectroscopy to be used to study fast dynamics at the atomic level.
Sub-psec dynamics are typically studied in pump-probe fashion, using a femtosecond optical laser as
pump. Probe techniques in use today include optical laser spectroscopy
5
, electron diffraction
6
, x-ray
diffraction
7
, and x-ray absorption spectroscopy
8
.
Of these techniques, laser spectroscopy has been by far the most useful, because of the ready
availability of tunable, intense, fsec lasers. However, due to its long wavelength, a laser cannot
directly give structural information on an atomic scale. Atomic structure must be deduced indirectly
from spectroscopy of the outer electron levels. For complicated structures, this becomes impossible,
and a direct structural measurement through diffraction or core-level spectroscopy is needed.
Electron and x-ray diffraction can both determine structures, but these methods are difficult to use in
the sub-psec range. Sources for electron diffraction are intense, but the time resolution is limited by
the difficulty in making sub-psec low-energy electron pulses. Specialized x-ray sources such as laser-
induced plasmas can be very fast, but their low brightness is a severe limitation on their utility.
In Table 2 the SPPS performance is compared with some existing and proposed sub-psec x-ray facilities:
the Ultrafast X-Ray Facility at the Advanced Light Source, the proposed re-circulating linac light source
5
Femtochemistry and Femtobiology: Ultrafast Reaction Dynamics at Atomic Scale Resolution, V. Sandstroem, ed., World
Scientific, Singapore 1997.
6
H. Ihee, et al., Science 291, 458 (2001).
7
R. W. Schoenlein, et al., Science 287, 2237 (2000).
8
C. P. J. Barty, et al., in Time-Resolved Diffraction, J. Helliwell and P.M. Rentzepis, eds., Oxford Univ. Press, New York
1998, p. 44.

4
(ERL) at LBNL, and the projected LCLS Free-Electron Laser. These are all facilities capable of
delivering bunches of the order of 100-200 fsec long. In this table the SPPS undulator is optimized
for 1.5 Å radiation. As it will be discussed in Section 6, undulators covering different wavelength
ranges are also possible. The final choice of undulator remains to be made, and will be based largely
on the requirements of the experiments.
Table 2. Radiation characteristics of the SPPS and other ultra-fast x-ray facilities.
Facilities Peak
brightness*
Pulse length
(fwhm, fsec)
Average
brightness *
Average
flux
(ph/s, 0.1%-bw)
Photons/pulse
0.1%-bw
Rep.
rate
(Hz)
SLAC SPPS
9.1×10
24
80 2.2×10
13
3.1×10
9
1.0×10
8
30
ALS Ultrafast
Fac.(undulator)
9
6
×10
19
100 6×10
10
3×10
6
300 1×10
4
LBNL ERL
10
1.0×10
23
100 1×10
14
2×10
10
2.0×10
6
1×10
4
LCLS FEL
11
1.5×10
33
230 4.2×10
22
2×10
14
1.7×10
12
120
* photons/sec/mm
2
/mrad
2
/0.1%-bandwidth
The peak brightness of SPPS will exceed that of any existing hard x-ray source by several orders of
magnitude, and its pulse length of <100 fsec will allow it to explore the same time correlations as the
fastest existing or proposed sources. The brightness of SPPS will greatly expand the practical range of
sub-psec x-ray diffraction experiments. Where current experiments are limited to high-reflectivity
perfect crystals, the SPPS would allow the use of weaker reflections and powder diffraction. This
would allow studies of a wide variety of phase transitions and chemical reactions in solids. While
SPPS could not support diffraction from very weakly-scattering samples such as gases and biological
crystals, core-level x-ray spectroscopy (NEXAFS and EXAFS) could be used to provide some atomic
structural information. For most experiments it will be necessary to accumulate data over many
pulses, using reversible reactions or reactions in which the reactants can be replenished. The 30Hz
repetition rate of SPPS is particularly favorable for this kind of stroboscopic experiment, since it
matches well with the repetition rates of fsec pump lasers.
Table 2 lists the expected properties of the LCLS x-ray FEL source, which should be constructed at
SLAC in a few years. This source and the other linac-based x-ray facilities that follow will soon
revolutionize the field of fast time-resolved x-ray science
12
. However, there is much to be learned
about performing sub-psec x-ray experiments properly. The SPPS should prove to be a valuable tool
for developing ultrafast x-ray techniques. Areas that require R&D include:
Synchronization. The synchronization of an optical pump laser with an x-ray source at the sub-
psec level will be challenging. Even measuring the time correlation of two such disparate
pulses with precision below 100 fsec will require exploiting and developing novel nonlinear
x-ray effects.
9
Schoenlein and others, “Generation of femtosecond x-ray pulses via laser-electron beam interaction”, Appl. Phys. B 71,
1-10 (2000), Table 1
10
A. Zholents, “On the possibility of a femtosecond x-ray pulse source vased on a recirculator linac”, CBP Tech Note-210,
Nov. 14, 2000.
11
LCLS Design Study Report, SLAC-R-521 (1998).
12
LCLS: The First Experiments, G. Shenoy and J. Stohr, eds., SSRL 2000.

Citations
More filters
23 Feb 2007
TL;DR: In this paper, the physics and characteristic properties of single-pass FELs, as well as current technical developments aiming for fully coherent x-ray radiation pulses with pulse durations in the 100 fs to 100 as range are reviewed.
Abstract: In a free-electron laser (FEL) the lasing medium is a high-energy beam of electrons flying with relativistic speed through a periodic magnetic field. The interaction between the synchrotron radiation that is produced and the electrons in the beam induces a periodic bunching of the electrons, greatly increasing the intensity of radiation produced at a particular wavelength. Depending only on a phase match between the electron energy and the magnetic period, the wavelength of the FEL radiation can be continuously tuned within a wide spectral range. The FEL concept can be adapted to produce radiation wavelengths from millimeters to Angstroms, and can in principle produce hard x-ray beams with unprecedented peak brightness, exceeding that of the brightest synchrotron source by ten orders of magnitude or more. This paper focuses on short-wavelength FELs. It reviews the physics and characteristic properties of single-pass FELs, as well as current technical developments aiming for fully coherent x-ray radiation pulses with pulse durations in the 100 fs to 100 as range. First experimental results at wavelengths around 100 nm and examples of scientific applications planned on the new, emerging x-ray FEL facilities are presented.

242 citations


Cites methods from "A Sub-Picosecond Photon Pulse Facil..."

  • ...This has recently been confirmed experimentally at the sub-picosecond pulse source at SLAC, where 30 kA peak currents are achieved from 80 fs, 3 nC electron bunches accelerated to 28 GeV [21]....

    [...]

Journal ArticleDOI
TL;DR: The principle of the oversampling method, which takes advantage of "continuous" diffraction patterns from noncrystalline specimens, is reviewed and the ongoing experiments of imaging nonperiodic objects, such as cells and cellular structures, using coherent and bright X rays produced by third-generation synchrotron sources are discussed.
Abstract: Recent work is extending the methodology of X-ray crystallography to the structure determination of noncrystalline specimens. The phase problem is solved using the oversampling method, which takes advantage of "continuous" diffraction patterns from noncrystalline specimens. Here we review the principle of this newly developed technique and discuss the ongoing experiments of imaging nonperiodic objects, such as cells and cellular structures, using coherent and bright X rays produced by third-generation synchrotron sources. In the longer run, the technique may be applicable to image single biomolecules using anticipated X-ray free electron lasers. Here, computer simulations have so far demonstrated two important steps: (a) by using an extremely intense femtosecond X-ray pulse, a diffraction pattern can be recorded from a macromolecule before radiation damage manifests itself; and (b) the phase information can be retrieved in an ab initio fashion from a set of calculated noisy diffraction patterns of single protein molecules.

70 citations

Journal ArticleDOI
TL;DR: The x-ray free electron laser based on the principle of self-amplified spontaneous emission is the basis of the fourth generation X-ray source user facilities of this century.
Abstract: The intensity of x-ray sources has increased at a rapid rate since the late 1960s by ten orders of magnitude and more through the use of synchrotron radiation produced by bending magnets, wigglers and undulators. Three generations of radiation sources have been identified depending on amplitude and quality of the radiation provided. While user facilities of the third generation were being constructed, a new concept of radiation generating devices was being developed that offers an even larger increase in peak and average brightness than had been achieved till then. The new concept of the x-ray free electron laser based on the principle of self-amplified spontaneous emission will be the basis of fourth generation x-ray source user facilities of this century. The paper will start with a brief history of the development of x-ray sources, it will then discuss some of the differences between storage ring and free electron laser based approaches, and will close with an update of the present development of x-ray free electron laser user facilities.

30 citations

Journal ArticleDOI
TL;DR: In this paper, the electric field in the temporal and spectral domain of coherent diffraction-limited transition radiation is studied, and a general expression for the spatiotemporal electric field is derived, and closed-form solutions for several special cases are given.
Abstract: The electric field in the temporal and spectral domain of coherent diffraction-limited transition radiation is studied. An electron bunch, with arbitrary longitudinal momentum distribution, propagating at normal incidence to a sharp metal-vacuum boundary with finite transverse dimension is considered. A general expression for the spatiotemporal electric field of the transition radiation is derived, and closed-form solutions for several special cases are given. The influence of parameters such as radial boundary size, electron momentum distribution, and angle of observation on the waveform (e.g., radiation pulse length and amplitude) are discussed. For a Gaussian electron bunch, the coherent radiation waveform is shown to have a single-cycle profile. Application to a novel THz source based on a laser-driven accelerator is discussed.

27 citations


Cites background from "A Sub-Picosecond Photon Pulse Facil..."

  • ...However, for ultra-relativistic electron beams (E > 1 GeV), the space charge limitation on charge density is reduced and short bunches containing charge on the order of several nC can be achieved (Cornacchia et al., 2001)....

    [...]

Journal ArticleDOI
TL;DR: A review of various methods for generation of ultrashort X-ray pulses using relativistic electron beam from conventional accelerators is presented in this article, where spontaneous and coherent emission of electrons are considered.
Abstract: A review of various methods for generation of ultrashort X-ray pulses using relativistic electron beam from conventional accelerators is presented. Both spontaneous and coherent emission of electrons are considered.

12 citations