- Email: [email protected]
A SASE free electron laser optimization based on new generation in-vacuum undulators
Optics & Laser Technology 44 (2012) 1083–1088
Contents lists available at SciVerse ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
A SASE free electron laser optimization based on new generation in-vacuum undulators ¨ . YavasB. Keteno˘glu n, O Department of Engineering Physics, Ankara University, 06100 Tandog˘ an, Ankara, Turkey
a r t i c l e i n f o
abstract
Article history: Received 19 September 2011 Received in revised form 4 October 2011 Accepted 9 October 2011 Available online 27 October 2011
Optimization studies for an accelerator based light source, namely self-amplified spontaneous emission (SASE) free electron laser (FEL), based on new generation in-vacuum hybrid and superconducting undulator configurations, are compared and discussed. It is shown that the FEL wavelength should be down to soft X-rays ( 3 nm) part of the spectrum while keeping the same linear accelerator (linac) energy about 1 GeV. On the other hand, numerical calculations and simulation results of the main performance parameters for SASE operation (1D gain length, saturation power and saturation length), are optimized. Finally, technological advantages and challenges for both cases, are briefly mentioned. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Linac In-vacuum hybrid and superconducting undulators SASE FEL
1. Introduction In the early 20th century, by discovery of X-ray tubes, high brightness radiation requirements of users have been scaled up year after year. By the beginning of 1970s, scientist discovered bending magnet radiation obtained from positron synchrotrons which were originally designed for particle physics experiments (see Fig. 1). These parasitic radiations were called 1st generation sources. Afterwards, by the development of wiggler and undulator magnets, 2nd generation sources were improved based on electron synchrotrons. Because of the higher emittance of electron beams ( 4 100 mm), the radiation obtained from those magnetic structures was not qualified enough. Flux and brightness values were still poor. After 1980s, by developing technology, emittance of the electron beam was reduced (20 mm o e o 100 mm) and flux and brightness of these radiations were relatively raised. This group is called 3rd generation light sources. Finally, by the beginning of 2000s, scientists proved that emittance of the electron beam should be less than 20 mm via modern linear accelerators. Thus, linac based 4th generation light sources have still been operating and developing day by day. In the present time, there are several operating SASE FEL facilities and proposals around the World. In Fig. 2, the blue facilities, e.g. TTF (later on upgraded to FLASH [1] and still operating), 4GLS (modified to the NLS project [2]), are based on superconducting linacs. The blacks, e.g. FERMI@Elettra [3], SCSS
n
Corresponding author. E-mail address: [email protected] (B. Keteno˘glu).
0030-3992/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2011.10.006
[4] (operated and upgraded to higher energies), SPARC/SPARX/ SPARXINO [5] are based on normal conducting linacs. Furthermore, the European XFEL project [6] should be exemplified as a future X-ray free electron laser source. This research facility is currently under construction and will generate extremely intense X-ray flashes to be used by researchers from all over the World. Additionally, more information about technical and design issues of the facilities and proposals mentioned above, can be found out from the Refs. [1–6]. Today, accelerator based 4th generation light sources, namely free electron lasers, are quite in demand because of their high power ( GW), coherent and ultra short ( fs) pulse characteristics. In addition, FELs have many applications in a broad wavelength range from infrared to soft X-rays. Considering longer (i.e. infrared) wavelengths, namely conventional FEL oscillator, lasing process is achieved by using two reflecting mirrors to confine the laser beam in an optical resonator which enables the interaction repetition of the electron beam with the radiation inside the undulator resulting a laser. But assuming shorter (i.e. VUV, soft X-rays and even X-rays) wavelengths, no reflecting mirror is available. In this case, when a longer undulator is designed without any mirrors, electron beam injected to the undulator keeps interaction with undulator and radiations fields relatively in a long time, the noise signal is amplified and finally reaches saturation, hence the self-amplified spontaneous emission concept comes out (see Fig. 3). Finally, conventional out-vacuum undulators are technologically well known components of operating facilities around the World. But, because of the narrow gap requirements of most facilities, new generation in-vacuum undulators have largely been
1084
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O
Fig. 1. Development of light sources by their brightness values in the 20th century.
Fig. 2. Operating SASE FEL facilities and proposals around the World.
operated in recent years and rapidly developing day by day. Additionally, these new generation configurations are also quite in demand because of the fact that they are much more compact than conventional out-vacuum undulators. In this respect, following sections cover SASE FEL optimizations based on in-vacuum hybrid and superconducting undulators. Actually, hybrid with iron and vanadium permendur options will result similar laser characteristics (Tables 3 and 5), but a main reason for choosing these options is, their out-vacuum designs are troubleless operating devices and they are quite stable than other configurations.
2. Electron beam parameters based on a 1 GeV linac As known, an L-band (1.3 GHz) superconducting, or a C-band (5.7 GHz) normal conducting, or evenmore an S-band (3 GHZ) normal conducting linac can be operated as a driver for SASE
undulators at the present time. In this respect, a typical electron beam given in Table 1, should interact with the fields inside the undulator during lasing. In addition, transverse emittances, peak current and beam peak power given in Table 1, are calculated by the following equations respectively:
ex,y ¼
s2x,y bx,y
ð1Þ
Q tm
ð2Þ
Pbeam ¼ Ebeam Ipeak
ð3Þ
Ipeak ¼
Some of the well known electron parameters given in Table 1, can briefly be defined in concept. The most important one is, the transverse emittance. It is the area of the ellipse in phase space, where the electrons are occupied in a bunch. In some notations,
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O
1085
Fig. 4. Ebeam (GeV) vs lu (cm) and g (cm) for hybrid with iron (lFEL ¼ 3:18 nm).
Fig. 3. Schematic view of SASE FEL power saturation.
Table 1 Typical 1 GeV electron beam parameters at undulator entrance. Parameter
Unit
Value
Electron beam energy, Ebeam Bunch charge, Q Transverse emittances, ex,y FWHM bunch length, t m Transverse bunch sizes, sx,y Peak current, Ipeak Beta functions, bx,y
GeV nC nm ps mm kA m
1 1 1.021 0.5 101.09 2 10
Energy spread, DE=E Beam peak power, Pbeam
– TW
2 10 4 2
normalized emittances are given by multiplying the transverse emittance with the Lorentz factor, g. On the other hand, sx and sy are real transverse sizes of a bunch in the linac. Furthermore, t m is the bunch length in time domain, which is also known as sz (in units of meters), obtained by dividing sz to the speed of light.
3. In-vacuum hybrid undulator based SASE FEL optimization In this section, SASE FEL optimizations are carried out based on two different types of in-vacuum hybrid undulators [7]. First is hybrid-with-iron planar, and the second one is hybrid-withvanadium permendur planar configurations. Additionally, it is shown that two stand-alone undulator lines should asynchronously be operated to go down soft X-rays ( 3 nm) while keeping the same beam energy (1 GeV) for each case (see Fig. 4 for hybrid with iron and Fig. 5 for hybrid with vanadium permendur). On the other hand, undulator gaps (g) and periods (lu ) are optimized as 0.5 cm and 1.5 cm respectively for both. Furthermore, peak magnetic field (Bpeak) and the K parameter of the undulators are calculated by Eqs. (4) and (5). In Eq. (4), coefficient a is in units of Tesla, where b and c are dimensionless [7]. In general, K parameter given in Eq. (7) is typically less than 3 for undulator magnets as well. Finally, one has to keep the restriction in mind on g/lu ratio as: 0:1o g=lu o 1 for both types of dedicated hybrid options [7]: " 2 # g g Bpeak ¼ aExp b þc ð4Þ
lu
lu
Fig. 5. Ebeam (GeV) vs lu (cm) and g (cm) for hybrid with vanadium permendur (lFEL ¼ 3.21 nm).
K ¼ 0:934lu ½cmBpeak ½T
ð5Þ
On the other hand, a critical parameter, namely Pierce (r) parameter defined in Eq. (8) [8], which directly affects the performance and quality of the free electron laser, has to carefully been optimized. In Eq. (8), g is Lorentz factor of the electron beam, J0 and J1 are 0th and 1st order Bessel functions:
r¼
8 > > > > >
FEL Þ
2
r e ne
8p
> > > > > :
91=3 1 0 132 > > > K2 K2 > > 6 B 4 C B 4 C7 = K2 B B 6 C C 7 J1 @ !2 4J 0 @ A A 5 2 2 > K K > K2 > > 1þ 1þ > 1þ ; 2 2 2 2 0
ð6Þ where, re is electron classical radius and ne is the electron density in a bunch. Finally, wavelength of the laser (lFEL ) is calculated for a planar undulator by Eq. (9):
lFEL ¼
lu 2g2
1þ
K2 2
! ð7Þ
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O
1086
From now on, hybrid with iron planar undulator based SASE free electron laser optimization will be considered. In Table 2, dedicated undulator parameters (g¼ 0.5 cm and lu ¼ 1:5 cm) are given. Here, it is shown that 3:18 nm wavelength should be achievable by this configuration. Pierce (r) parameter is contour-plotted vs undulator period and gap in Fig. 6 for dedicated electron beam (Table 1) and undulator configurations (Table 2). Additionally, three more parameters, namely 1D and 3D gain lengths (LG,1D and LG,3D ) and Rayleigh length (LR), which enable to optimize the saturation length (Lsat), are given in Eqs. (8)–(10) respectively, where Z is the universal scaling function [9]: LG,1D ¼
l
puffiffiffi 4p 3r
ð8Þ
LG,3D ¼ ð1 þ ZÞLG,1D
LR ¼
ð9Þ
4ps2x
ð10Þ
lFEL
Saturation length of the undulator [9], which approximately gives the length of the undulator (Lu), is calculated by Eq. (11) and contour-plotted vs energy spread (DE (MeV)) and peak current (Ipeak (kA)) for 1.021 nm transverse emittance in Fig. 7, where P sat rP beam ¼ 1:6rðLG,1D =LG,3D Þ2 P beam : 9lFEL P sat Lsat ¼ LG,1D ln 2 r cEbeam
ð11Þ
Table 2 Hybrid with iron planar undulator parameters. Parameter
Unit
Value
Undulator gap, g Undulator period, lu Peak magnetic field, Bpeak K parameter Number of undulator periods, Nu Undulator length, Lu
cm cm T – – m
0.5 1.5 0.798 1.118 1065 16
Fig. 7. Lsat (m) vs DE (MeV) and Ipeak (kA) for 1.021 nm transverse emittance.
Table 3 Hybrid with iron planar undulator based SASE FEL parameters. Parameter
Unit
Value
Pierce parameter, r 1D gain length, LG,1D 3D gain length, LG,3D Rayleigh length, LR Saturation length, Lsat FEL wavelength, lFEL Saturation power#, Psat FEL energy, EFEL Photons per pulse# Energy per pulse# Peak flux# Peak brilliance#
– m m m m nm GW keV – J photons/s photons/s/mm2/mrad2/0.1%bw
9.364 10 4 0.735 0.886 40.349 15.501 3.182 1.653 0.388 1.325 1013 8.272 10 4 1.472 1025 5.812 1030
Table 4 Hybrid with vanadium permendur planar undulator parameters. Parameter
Unit
Value
Undulator gap, g Undulator period, lu Peak magnetic field, Bpeak K parameter Number of undulator periods, Nu Undulator length, Lu
cm cm T – – m
0.5 1.5 0.807 1.131 1065 16
Additionally, laser energy of the fundamental harmonic (EFEL) given in Tables 3 and 5, is calculated by the following equation: EFEL ½keV ¼
Fig. 6. Pierce (r) parameter vs lu (cm) and g (cm) for hybrid with iron configuration.
0:947ðEbeam ðGeVÞÞ2 ! K2 lu ½cm 1 þ 2
ð12Þ
Laser parameters based on dedicated electron beam (Table 1) and undulator (Table 2) configurations, are summarized in Table 3. In addition, parameters in Tables 3 and 5 with superscripts (#), are obtained by SIMPLEX 1.3 simulation code [10]. Eventually, hybrid with iron planar undulator based laser optimization has been considered as yet. From now on, a new undulator configuration (hybrid with vanadium permendur), will be considered. Hybrid with vanadium permendur planar undulator parameters based on Table 1 are summarized in Table 4.
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O Table 5 Hybrid with vanadium permendur planar undulator based SASE FEL parameters. Parameter
Unit
Value
Pierce parameter, r 1D gain length, LG,1D 3D gain length, LG,3D Rayleigh length, LR Saturation length, Lsat FEL wavelength, lFEL Saturation power#, Psat FEL energy, EFEL Photons per pulse# Energy per pulse# Peak flux# Peak brilliance#
– m m m m nm GW keV J photons/s photons/s/mm2/mrad2/0.1%bw
9.425 10 4 0.731 0.878 39.986 15.405 3.211 1.676 0.384 1.356 1013 8.386 10 4 1.496 1025 5.802 1030
1087
spread and peak current for 1.021 nm transverse emittance, is shown in Fig. 9.
4. Comparison of in-vacuum hybrid undulator based optimization with a superconducting design Here, optimization and simulation studies carried out in Section 3, are compared with a superconducting undulator based design [11]. In Ref. [11], it was proved that numerical calculations and simulation results are fairly well consistent (see Tables 6 and 7) for the dedicated undulator (g¼0.8 cm and lu ¼1.5 cm). One can easily check that peak brilliance values of the lasers (Section 3 and Table 6) are about 1030 photons/s/mm2/mrad2/0.1%bw around 3 nm wavelength. On the other hand, saturation powers are about 1.6 GW for the three different (Section 3 and Table 7) undulator configurations.
5. Conclusion In this study, optimization studies for a SASE free electron laser based on new generation in-vacuum hybrid and superconducting undulator configurations are discussed and compared. It is shown that the FEL wavelength should be down to soft X-rays ( 3 nm) part of the spectrum while keeping the same linac energy (1 GeV) for both. Consequently, it is proved that numerical calculations and simulation results are fairly well consistent for the dedicated hybrid undulators. As known, a main goal of the Turkish Accelerator Center (TAC) project [12,13] is a 1 GeV SASE FEL facility proposal. In this respect, conceptual design studies have still been considering by supports and recommendations of the International Scientific Advisory Committee (ISAC) of TAC for 3 years. On the other hand, technical design studies [14] are also planned to be completed by the end of 2017. In addition, construction of the whole SASE FEL facility is estimated to be accomplished between 2018 and 2022. Fig. 8. Pierce (r) parameter vs lu (cm) and g (cm) for hybrid with vanadium permendur configuration.
Table 6 Superconducting undulator based SASE FEL parameters of [11] (g ¼ 0.8 cm and lu ¼ 1:5 cm). Parameter
Unit
Value
Pierce parameter, r 1D gain length, LG,1D 3D gain length, LG,3D Rayleigh length, LR Saturation length, Lsat FEL wavelength, lFEL Saturation power, Psat FEL energy, EFEL Photons per pulse# Energy per pulse# Peak flux# Peak brilliance#
– m m m m nm GW keV – J photons/s photons/s/mm2/mrad2/0.1%bw
6.327 10 4 1.089 2.659 129.2 21.8 3.15 1.265 0.392 1.29 1013 8.15 10 4 1.45 1025 5.82 1030
Table 7 Simulation results of [11] obtained by SIMPLEX 1.3 code [10] for the dedicated superconducting undulator (g ¼ 0.8 cm).
Fig. 9. Lsat (m) vs DE (MeV) and Ipeak (kA) for 1.021 nm transverse emittance.
Laser parameters based on dedicated electron beam (Table 1) and undulator (Table 4) configurations are summarized in Table 5. Furthermore, Pierce parameter of the laser vs lu and g, is shown in Fig. 8. On the other hand, saturation length vs energy
Parameter
Unit
Value
Peak magnetic field, Bpeak Pierce parameter, r 1D gain length, LG,1D 3D gain length, LG,3D Saturation length, Lsat FEL wavelength, lFEL Saturation power, Psat FEL energy, EFEL
T – m m m nm GW keV
0.788 8.117 10 4 0.85 1.072 22.6 3.15 1.628 0.393
1088
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O
Finally, results of the optimization studies carried out in previous sections, will act as a complementary contribution to design issues of new generation in-vacuum undulator technologies around the World, and evenmore, will be considered under technical design studies of the TAC SASE FEL proposal.
Acknowledgments This work is supported by the Turkish Accelerator Center (TAC) project [12] funded by Turkish State Planning Organization under grant number DPT2006K–120470. References [1] Schreiber S, Faatz B, Honkavaara K. Operation of FLASH at 6.5 nm wavelength, in: Proceedings of the EPAC; 2008. p. 133–5. [2] New light source (NLS) Project conceptual design report; 2010.
[3] FERMI@Elettra conceptual design report; 2007. [4] Shintake T, et al. Status of SPring-8 compact SASE source FEL project. Nuclear Instruments and Methods in Physics Research Section A 2003;507:382–7. [5] Renieri A, et al., Contributions to FEL 2004 (SPARC-GE-04/003). In: Proceedings of the FEL; 2004. [6] Abela R, et al., The European X-ray free-electron laser technical design report; 2007. [7] Elleaume P, Chavanne J, Faatz B. Design considerations for a 1 A˚ SASE undulator. Nuclear Instruments and Methods in Physics Research Section A 2000;455:503–23. [8] SCSS X-FEL conceptual design report; 2005. [9] Xie M. Design optimization for an X-ray free electron laser driven by SLAC linac. In: Proceedings of the PAC; 1995. p. 183. [10] /http://radiant.harima.riken.go.jp/simplex/S. ¨ . Optimization considerations for a SASE free electron [11] Keteno˘glu B, Yavas- O laser based on a superconducting undulator. Optik – International Journal for Light and Electron Optics, doi:10.1016/j.ijleo.2011.07.018. In press. [12] /http://thm.ankara.edu.trS. ¨ zkorucuklu S, et al., The status of Turkish accelerator center project. In: [13] O Proceedings of the IPAC; 2010. p. 4419–21. [14] Keteno˘glu B, et al., Technical design studies of TAC SASE FEL proposal. In: Proceedings of the FEL; 2009. p. 325–8.
Contents lists available at SciVerse ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
A SASE free electron laser optimization based on new generation in-vacuum undulators ¨ . YavasB. Keteno˘glu n, O Department of Engineering Physics, Ankara University, 06100 Tandog˘ an, Ankara, Turkey
a r t i c l e i n f o
abstract
Article history: Received 19 September 2011 Received in revised form 4 October 2011 Accepted 9 October 2011 Available online 27 October 2011
Optimization studies for an accelerator based light source, namely self-amplified spontaneous emission (SASE) free electron laser (FEL), based on new generation in-vacuum hybrid and superconducting undulator configurations, are compared and discussed. It is shown that the FEL wavelength should be down to soft X-rays ( 3 nm) part of the spectrum while keeping the same linear accelerator (linac) energy about 1 GeV. On the other hand, numerical calculations and simulation results of the main performance parameters for SASE operation (1D gain length, saturation power and saturation length), are optimized. Finally, technological advantages and challenges for both cases, are briefly mentioned. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Linac In-vacuum hybrid and superconducting undulators SASE FEL
1. Introduction In the early 20th century, by discovery of X-ray tubes, high brightness radiation requirements of users have been scaled up year after year. By the beginning of 1970s, scientist discovered bending magnet radiation obtained from positron synchrotrons which were originally designed for particle physics experiments (see Fig. 1). These parasitic radiations were called 1st generation sources. Afterwards, by the development of wiggler and undulator magnets, 2nd generation sources were improved based on electron synchrotrons. Because of the higher emittance of electron beams ( 4 100 mm), the radiation obtained from those magnetic structures was not qualified enough. Flux and brightness values were still poor. After 1980s, by developing technology, emittance of the electron beam was reduced (20 mm o e o 100 mm) and flux and brightness of these radiations were relatively raised. This group is called 3rd generation light sources. Finally, by the beginning of 2000s, scientists proved that emittance of the electron beam should be less than 20 mm via modern linear accelerators. Thus, linac based 4th generation light sources have still been operating and developing day by day. In the present time, there are several operating SASE FEL facilities and proposals around the World. In Fig. 2, the blue facilities, e.g. TTF (later on upgraded to FLASH [1] and still operating), 4GLS (modified to the NLS project [2]), are based on superconducting linacs. The blacks, e.g. FERMI@Elettra [3], SCSS
n
Corresponding author. E-mail address: [email protected] (B. Keteno˘glu).
0030-3992/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2011.10.006
[4] (operated and upgraded to higher energies), SPARC/SPARX/ SPARXINO [5] are based on normal conducting linacs. Furthermore, the European XFEL project [6] should be exemplified as a future X-ray free electron laser source. This research facility is currently under construction and will generate extremely intense X-ray flashes to be used by researchers from all over the World. Additionally, more information about technical and design issues of the facilities and proposals mentioned above, can be found out from the Refs. [1–6]. Today, accelerator based 4th generation light sources, namely free electron lasers, are quite in demand because of their high power ( GW), coherent and ultra short ( fs) pulse characteristics. In addition, FELs have many applications in a broad wavelength range from infrared to soft X-rays. Considering longer (i.e. infrared) wavelengths, namely conventional FEL oscillator, lasing process is achieved by using two reflecting mirrors to confine the laser beam in an optical resonator which enables the interaction repetition of the electron beam with the radiation inside the undulator resulting a laser. But assuming shorter (i.e. VUV, soft X-rays and even X-rays) wavelengths, no reflecting mirror is available. In this case, when a longer undulator is designed without any mirrors, electron beam injected to the undulator keeps interaction with undulator and radiations fields relatively in a long time, the noise signal is amplified and finally reaches saturation, hence the self-amplified spontaneous emission concept comes out (see Fig. 3). Finally, conventional out-vacuum undulators are technologically well known components of operating facilities around the World. But, because of the narrow gap requirements of most facilities, new generation in-vacuum undulators have largely been
1084
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O
Fig. 1. Development of light sources by their brightness values in the 20th century.
Fig. 2. Operating SASE FEL facilities and proposals around the World.
operated in recent years and rapidly developing day by day. Additionally, these new generation configurations are also quite in demand because of the fact that they are much more compact than conventional out-vacuum undulators. In this respect, following sections cover SASE FEL optimizations based on in-vacuum hybrid and superconducting undulators. Actually, hybrid with iron and vanadium permendur options will result similar laser characteristics (Tables 3 and 5), but a main reason for choosing these options is, their out-vacuum designs are troubleless operating devices and they are quite stable than other configurations.
2. Electron beam parameters based on a 1 GeV linac As known, an L-band (1.3 GHz) superconducting, or a C-band (5.7 GHz) normal conducting, or evenmore an S-band (3 GHZ) normal conducting linac can be operated as a driver for SASE
undulators at the present time. In this respect, a typical electron beam given in Table 1, should interact with the fields inside the undulator during lasing. In addition, transverse emittances, peak current and beam peak power given in Table 1, are calculated by the following equations respectively:
ex,y ¼
s2x,y bx,y
ð1Þ
Q tm
ð2Þ
Pbeam ¼ Ebeam Ipeak
ð3Þ
Ipeak ¼
Some of the well known electron parameters given in Table 1, can briefly be defined in concept. The most important one is, the transverse emittance. It is the area of the ellipse in phase space, where the electrons are occupied in a bunch. In some notations,
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O
1085
Fig. 4. Ebeam (GeV) vs lu (cm) and g (cm) for hybrid with iron (lFEL ¼ 3:18 nm).
Fig. 3. Schematic view of SASE FEL power saturation.
Table 1 Typical 1 GeV electron beam parameters at undulator entrance. Parameter
Unit
Value
Electron beam energy, Ebeam Bunch charge, Q Transverse emittances, ex,y FWHM bunch length, t m Transverse bunch sizes, sx,y Peak current, Ipeak Beta functions, bx,y
GeV nC nm ps mm kA m
1 1 1.021 0.5 101.09 2 10
Energy spread, DE=E Beam peak power, Pbeam
– TW
2 10 4 2
normalized emittances are given by multiplying the transverse emittance with the Lorentz factor, g. On the other hand, sx and sy are real transverse sizes of a bunch in the linac. Furthermore, t m is the bunch length in time domain, which is also known as sz (in units of meters), obtained by dividing sz to the speed of light.
3. In-vacuum hybrid undulator based SASE FEL optimization In this section, SASE FEL optimizations are carried out based on two different types of in-vacuum hybrid undulators [7]. First is hybrid-with-iron planar, and the second one is hybrid-withvanadium permendur planar configurations. Additionally, it is shown that two stand-alone undulator lines should asynchronously be operated to go down soft X-rays ( 3 nm) while keeping the same beam energy (1 GeV) for each case (see Fig. 4 for hybrid with iron and Fig. 5 for hybrid with vanadium permendur). On the other hand, undulator gaps (g) and periods (lu ) are optimized as 0.5 cm and 1.5 cm respectively for both. Furthermore, peak magnetic field (Bpeak) and the K parameter of the undulators are calculated by Eqs. (4) and (5). In Eq. (4), coefficient a is in units of Tesla, where b and c are dimensionless [7]. In general, K parameter given in Eq. (7) is typically less than 3 for undulator magnets as well. Finally, one has to keep the restriction in mind on g/lu ratio as: 0:1o g=lu o 1 for both types of dedicated hybrid options [7]: " 2 # g g Bpeak ¼ aExp b þc ð4Þ
lu
lu
Fig. 5. Ebeam (GeV) vs lu (cm) and g (cm) for hybrid with vanadium permendur (lFEL ¼ 3.21 nm).
K ¼ 0:934lu ½cmBpeak ½T
ð5Þ
On the other hand, a critical parameter, namely Pierce (r) parameter defined in Eq. (8) [8], which directly affects the performance and quality of the free electron laser, has to carefully been optimized. In Eq. (8), g is Lorentz factor of the electron beam, J0 and J1 are 0th and 1st order Bessel functions:
r¼
8 > > > > >
FEL Þ
2
r e ne
8p
> > > > > :
91=3 1 0 132 > > > K2 K2 > > 6 B 4 C B 4 C7 = K2 B B 6 C C 7 J1 @ !2 4J 0 @ A A 5 2 2 > K K > K2 > > 1þ 1þ > 1þ ; 2 2 2 2 0
ð6Þ where, re is electron classical radius and ne is the electron density in a bunch. Finally, wavelength of the laser (lFEL ) is calculated for a planar undulator by Eq. (9):
lFEL ¼
lu 2g2
1þ
K2 2
! ð7Þ
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O
1086
From now on, hybrid with iron planar undulator based SASE free electron laser optimization will be considered. In Table 2, dedicated undulator parameters (g¼ 0.5 cm and lu ¼ 1:5 cm) are given. Here, it is shown that 3:18 nm wavelength should be achievable by this configuration. Pierce (r) parameter is contour-plotted vs undulator period and gap in Fig. 6 for dedicated electron beam (Table 1) and undulator configurations (Table 2). Additionally, three more parameters, namely 1D and 3D gain lengths (LG,1D and LG,3D ) and Rayleigh length (LR), which enable to optimize the saturation length (Lsat), are given in Eqs. (8)–(10) respectively, where Z is the universal scaling function [9]: LG,1D ¼
l
puffiffiffi 4p 3r
ð8Þ
LG,3D ¼ ð1 þ ZÞLG,1D
LR ¼
ð9Þ
4ps2x
ð10Þ
lFEL
Saturation length of the undulator [9], which approximately gives the length of the undulator (Lu), is calculated by Eq. (11) and contour-plotted vs energy spread (DE (MeV)) and peak current (Ipeak (kA)) for 1.021 nm transverse emittance in Fig. 7, where P sat rP beam ¼ 1:6rðLG,1D =LG,3D Þ2 P beam : 9lFEL P sat Lsat ¼ LG,1D ln 2 r cEbeam
ð11Þ
Table 2 Hybrid with iron planar undulator parameters. Parameter
Unit
Value
Undulator gap, g Undulator period, lu Peak magnetic field, Bpeak K parameter Number of undulator periods, Nu Undulator length, Lu
cm cm T – – m
0.5 1.5 0.798 1.118 1065 16
Fig. 7. Lsat (m) vs DE (MeV) and Ipeak (kA) for 1.021 nm transverse emittance.
Table 3 Hybrid with iron planar undulator based SASE FEL parameters. Parameter
Unit
Value
Pierce parameter, r 1D gain length, LG,1D 3D gain length, LG,3D Rayleigh length, LR Saturation length, Lsat FEL wavelength, lFEL Saturation power#, Psat FEL energy, EFEL Photons per pulse# Energy per pulse# Peak flux# Peak brilliance#
– m m m m nm GW keV – J photons/s photons/s/mm2/mrad2/0.1%bw
9.364 10 4 0.735 0.886 40.349 15.501 3.182 1.653 0.388 1.325 1013 8.272 10 4 1.472 1025 5.812 1030
Table 4 Hybrid with vanadium permendur planar undulator parameters. Parameter
Unit
Value
Undulator gap, g Undulator period, lu Peak magnetic field, Bpeak K parameter Number of undulator periods, Nu Undulator length, Lu
cm cm T – – m
0.5 1.5 0.807 1.131 1065 16
Additionally, laser energy of the fundamental harmonic (EFEL) given in Tables 3 and 5, is calculated by the following equation: EFEL ½keV ¼
Fig. 6. Pierce (r) parameter vs lu (cm) and g (cm) for hybrid with iron configuration.
0:947ðEbeam ðGeVÞÞ2 ! K2 lu ½cm 1 þ 2
ð12Þ
Laser parameters based on dedicated electron beam (Table 1) and undulator (Table 2) configurations, are summarized in Table 3. In addition, parameters in Tables 3 and 5 with superscripts (#), are obtained by SIMPLEX 1.3 simulation code [10]. Eventually, hybrid with iron planar undulator based laser optimization has been considered as yet. From now on, a new undulator configuration (hybrid with vanadium permendur), will be considered. Hybrid with vanadium permendur planar undulator parameters based on Table 1 are summarized in Table 4.
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O Table 5 Hybrid with vanadium permendur planar undulator based SASE FEL parameters. Parameter
Unit
Value
Pierce parameter, r 1D gain length, LG,1D 3D gain length, LG,3D Rayleigh length, LR Saturation length, Lsat FEL wavelength, lFEL Saturation power#, Psat FEL energy, EFEL Photons per pulse# Energy per pulse# Peak flux# Peak brilliance#
– m m m m nm GW keV J photons/s photons/s/mm2/mrad2/0.1%bw
9.425 10 4 0.731 0.878 39.986 15.405 3.211 1.676 0.384 1.356 1013 8.386 10 4 1.496 1025 5.802 1030
1087
spread and peak current for 1.021 nm transverse emittance, is shown in Fig. 9.
4. Comparison of in-vacuum hybrid undulator based optimization with a superconducting design Here, optimization and simulation studies carried out in Section 3, are compared with a superconducting undulator based design [11]. In Ref. [11], it was proved that numerical calculations and simulation results are fairly well consistent (see Tables 6 and 7) for the dedicated undulator (g¼0.8 cm and lu ¼1.5 cm). One can easily check that peak brilliance values of the lasers (Section 3 and Table 6) are about 1030 photons/s/mm2/mrad2/0.1%bw around 3 nm wavelength. On the other hand, saturation powers are about 1.6 GW for the three different (Section 3 and Table 7) undulator configurations.
5. Conclusion In this study, optimization studies for a SASE free electron laser based on new generation in-vacuum hybrid and superconducting undulator configurations are discussed and compared. It is shown that the FEL wavelength should be down to soft X-rays ( 3 nm) part of the spectrum while keeping the same linac energy (1 GeV) for both. Consequently, it is proved that numerical calculations and simulation results are fairly well consistent for the dedicated hybrid undulators. As known, a main goal of the Turkish Accelerator Center (TAC) project [12,13] is a 1 GeV SASE FEL facility proposal. In this respect, conceptual design studies have still been considering by supports and recommendations of the International Scientific Advisory Committee (ISAC) of TAC for 3 years. On the other hand, technical design studies [14] are also planned to be completed by the end of 2017. In addition, construction of the whole SASE FEL facility is estimated to be accomplished between 2018 and 2022. Fig. 8. Pierce (r) parameter vs lu (cm) and g (cm) for hybrid with vanadium permendur configuration.
Table 6 Superconducting undulator based SASE FEL parameters of [11] (g ¼ 0.8 cm and lu ¼ 1:5 cm). Parameter
Unit
Value
Pierce parameter, r 1D gain length, LG,1D 3D gain length, LG,3D Rayleigh length, LR Saturation length, Lsat FEL wavelength, lFEL Saturation power, Psat FEL energy, EFEL Photons per pulse# Energy per pulse# Peak flux# Peak brilliance#
– m m m m nm GW keV – J photons/s photons/s/mm2/mrad2/0.1%bw
6.327 10 4 1.089 2.659 129.2 21.8 3.15 1.265 0.392 1.29 1013 8.15 10 4 1.45 1025 5.82 1030
Table 7 Simulation results of [11] obtained by SIMPLEX 1.3 code [10] for the dedicated superconducting undulator (g ¼ 0.8 cm).
Fig. 9. Lsat (m) vs DE (MeV) and Ipeak (kA) for 1.021 nm transverse emittance.
Laser parameters based on dedicated electron beam (Table 1) and undulator (Table 4) configurations are summarized in Table 5. Furthermore, Pierce parameter of the laser vs lu and g, is shown in Fig. 8. On the other hand, saturation length vs energy
Parameter
Unit
Value
Peak magnetic field, Bpeak Pierce parameter, r 1D gain length, LG,1D 3D gain length, LG,3D Saturation length, Lsat FEL wavelength, lFEL Saturation power, Psat FEL energy, EFEL
T – m m m nm GW keV
0.788 8.117 10 4 0.85 1.072 22.6 3.15 1.628 0.393
1088
¨ . Yavas- / Optics & Laser Technology 44 (2012) 1083–1088 B. Ketenog˘ lu, O
Finally, results of the optimization studies carried out in previous sections, will act as a complementary contribution to design issues of new generation in-vacuum undulator technologies around the World, and evenmore, will be considered under technical design studies of the TAC SASE FEL proposal.
Acknowledgments This work is supported by the Turkish Accelerator Center (TAC) project [12] funded by Turkish State Planning Organization under grant number DPT2006K–120470. References [1] Schreiber S, Faatz B, Honkavaara K. Operation of FLASH at 6.5 nm wavelength, in: Proceedings of the EPAC; 2008. p. 133–5. [2] New light source (NLS) Project conceptual design report; 2010.
[3] FERMI@Elettra conceptual design report; 2007. [4] Shintake T, et al. Status of SPring-8 compact SASE source FEL project. Nuclear Instruments and Methods in Physics Research Section A 2003;507:382–7. [5] Renieri A, et al., Contributions to FEL 2004 (SPARC-GE-04/003). In: Proceedings of the FEL; 2004. [6] Abela R, et al., The European X-ray free-electron laser technical design report; 2007. [7] Elleaume P, Chavanne J, Faatz B. Design considerations for a 1 A˚ SASE undulator. Nuclear Instruments and Methods in Physics Research Section A 2000;455:503–23. [8] SCSS X-FEL conceptual design report; 2005. [9] Xie M. Design optimization for an X-ray free electron laser driven by SLAC linac. In: Proceedings of the PAC; 1995. p. 183. [10] /http://radiant.harima.riken.go.jp/simplex/S. ¨ . Optimization considerations for a SASE free electron [11] Keteno˘glu B, Yavas- O laser based on a superconducting undulator. Optik – International Journal for Light and Electron Optics, doi:10.1016/j.ijleo.2011.07.018. In press. [12] /http://thm.ankara.edu.trS. ¨ zkorucuklu S, et al., The status of Turkish accelerator center project. In: [13] O Proceedings of the IPAC; 2010. p. 4419–21. [14] Keteno˘glu B, et al., Technical design studies of TAC SASE FEL proposal. In: Proceedings of the FEL; 2009. p. 325–8.