- Email: [email protected]
Ultrashort high-brightness pulses from storage rings
Nuclear Instruments and Methods in Physics Research A ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Ultrashort high-brightness pulses from storage rings Shaukat Khan Zentrum für Synchrotronstrahlung (DELTA), TU Dortmund University, Maria-Goeppert-Mayer-Str. 2, 44227 Dortmund, Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 15 June 2016 Received in revised form 25 July 2016 Accepted 27 July 2016
The brightness of short-wavelength radiation from accelerator-based sources can be increased by coherent emission in which the radiation intensity scales with the number of contributing electrons squared. This requires a microbunched longitudinal electron distribution, which is the case in freeelectron lasers. The brightness of light sources based on electron storage rings was steadily improved, but could profit further from coherent emission. The modulation of the electron energy by a continuouswave laser field may provide steady-state microbunching in the infrared regime. For shorter wavelengths, the energy modulation can be converted into a temporary density modulation by a dispersive chicane. One particular goal is coherent emission from a very short “slice” within an electron bunch in order to produce ultrashort radiation pulses with high brightness. & 2016 Elsevier B.V. All rights reserved.
Keywords: Synchrotron radiation Storage rings Microbunching Ultrashort pulses High brightness
rate [1]
1. Introduction The spectral brightness of a photon source is defined by [1]
B=
ΔN /Δt , 4π 2·σx·σ x′·σy·σ y′·dω/ω
ΔN ΔNe = · Δt Δt (1)
where ΔN is the number of photons in an extended time interval Δt (average brightness) or in an infinitesimal interval at the pulse maximum (peak brightness), and s is the rms value of the quantity in the subscript: horizontal ( x, x′) or vertical ( y, y′) source size and divergence. The usual convention for the frequency interval dω/ω is 0.1%. In storage rings, progress has been made in different directions. The photon rate ΔN /Δt was improved by increasing the beam current, requiring feedback systems to counteract collective instabilities, by keeping the beam current nearly constant with top-up injection, and by employing novel insertion devices such as in-vacuum undulators. For an undulator source, the photon rate within the interval dω/ω increases with the number of undulator periods. Progress has also been made in reducing the horizontal beam emittance ε ∼ σx·σ x′, reaching 1 nm rad with a large ring and damping wigglers (PETRA III in Hamburg, Germany [2]) and 0.3 nm rad with a multi-bend magnetic lattice based on a very compact mechanical design (MAX IV in Lund, Sweden [3]). With careful alignment and tuning of the magnets, a vertical beam emittance εy ∼ σy·σ y′ of 2 pm or less has been reported from different sources (SLS in Switzerland, ESRF in France, DIAMOND in the UK, ALS in USA). The Australian Light Source ASLS claims to have reached the quantum limit of 0.35 pm [4]. So far, the photon E-mail address: [email protected]
=
ne
ne
∑ eiωt j · ∑ e−iωtk j=1
k=1
ΔNe ΔNe ·ne + · Δt Δt
ne
ne
∑ ∑ eiω (t j− tk ) j=1 k≠j
(2)
with ΔNe/Δt being the photon rate from a single electron was assumed to be proportional to the number of electrons ne, which is true for a random temporal separation (t j − tk ) between any two electrons. The second term of the equation provides coherent emission with a rate proportional to the number of electrons squared for Fourier components of the electron distribution, e.g., for wavelengths being an integer fraction of the distance between so-called microbunches, as in the case of free-electron lasers (FELs) [5]. To date, only four short-wavelength FELs are in user operation: FLASH in Hamburg, Germany [6], LCLS at SLAC, Menlo Park, USA [7], SACLA at Harima, Japan [8], and FERMI near Trieste, Italy [9]. On the other hand, about 50 electron storage rings are operated as synchrotron light sources [10] and serve multiple beamlines, often in 24/7 operation, with a high repetition rate given by the radiofrequency (RF), where 500 MHz is a typical value. It would therefore be advantageous for a large user community if the intensity of synchrotron radiation could be enhanced by microbunching. An additional benefit is the generation of short radiation pulses, if only a short “slice” at the center of the electron distribution is microbunched.
http://dx.doi.org/10.1016/j.nima.2016.07.048 0168-9002/& 2016 Elsevier B.V. All rights reserved.
Please cite this article as: S. Khan, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.07.048i
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2. Steady-state microbunching in storage rings The stochastic nature of synchrotron radiation results in an energy spread of typically σΔE / E ≈ 10−3, which translates into a ′ , where α is the momentum compaction bunch length σz ∼ α ·VRF factor and VRF ′ is the RF gradient. With typical values, a bunch length of several 10 ps is obtained, but various facilities have adopted a “low-α” mode of operation, in which a strongly reduced momentum compaction factor leads to a bunch length of about 1 ps, allowing for the coherent emission of terahertz (THz) radiation [11]. An increase of the RF frequency would reduce the bunch length as well as the bunch separation while increasing the number of RF buckets along the circumference of the storage ring. Here, a factor of 10 can be envisioned, but beyond that—leaving aside engineering issues—the reduced size of the RF resonators would be at variance with the required transverse aperture. The RF system provides bunching and recovers the energy lost due to synchrotron radiation. As sketched in the left part of Fig. 1, the force from the RF field is parallel to the electron path. Another way to create a succession of equidistant buckets is the interaction of electrons with a light wave co-propagating in an undulator. The right part of Fig. 1 illustrates that this interaction is not very effi→ cient, because the electric field , of the light is perpendicular to its propagation direction and, compared to the RF case, the transferred energy [5]
→→ dE = − e , · v dt = − e , x′c dt ,
(3)
is reduced by a factor x′, the angular coordinate of the electron. Nevertheless, the sinusoidal energy modulation can in principle assume the role of the RF voltage and create buckets on a much smaller wavelength scale. To cite give a few examples, the wavelength may be a few 100 μm in the case of a continuous-wave (cw) far-infrared FEL, 10 μm for a CO2 laser, or below 1 μm for lasers in the visible regime. An all-optical storage ring would be a fascinating device with 107 buckets in the case of the CO2 laser and a correspondingly high repetition rate of bunches with a length of a few femtoseconds. The beam current and the charge density would be similar to that of a conventional storage ring. The strong coherent emission in the whole infrared range would not change the total energy loss very much, since most of the spectral intensity is in the 100-eV to keV range, but will require further consideration in terms of collective effects and beam dynamics. Consider, as an example, a 10-kW CO2 laser in cw mode focused onto an area of 10 6 m2, as sketched in Fig. 2(a). The electric field amplitude is then , = 2I /(ε0 c ) , where I is the power density and ε0 is the vacuum permittivity. The result is 2.7 106 V/m, which is comparable to RF gradients. An undulator resonant to 10 μm will have a high strength parameter K. With K ¼20 (actually a wiggler, but here used as an undulator) and
1-GeV electrons (Lorentz factor γ ≈ 2000), the maximum angle is ′ xmax = K/γ ≈ 10−2 rad and—ignoring aberrations and other detrimental effects—the energy transfer over 4 m is 50 keV, which is in the regime of the energy loss per turn. Tighter focusing would not help to gain a larger overvoltage factor, because a smaller focus reduces the Rayleigh length [12] and thus the electric field averaged along the undulator. Furthermore, the size of the laser beam should be larger than the electron beam size in order to reduce the effect of the radial intensity variation. On the other hand, the electric field could be intensified by placing the undulator inside the optical cavity of the laser, see Fig. 2(b). Yet another possibility is to perform laser-electron interaction in more than one undulator by guiding the laser beam from one device to the next with mirrors, see Fig. 2(c). Replacing the RF voltage by a laser-induced energy modulation demands phase focusing within a fraction of the wavelength, i.e., a highly isochronous ring. Assuming a circumference of 100 m, the momentum compaction factor should be of the order of 10 4 for far-infrared wavelengths and below 10 5 for the CO2 laser, which is not impossible. However, the isochronicity of a storage ring is limited by the betatron motion [13] and by longitudinal radiation excitation [14] to the order of 100 fs (or several 10 μm), which would exclude any optical laser unless these limits can be overcome with a novel lattice design. Steady-state microbunching schemes in such a regime are discussed, e.g., in [15]. For a conventional lattice, it appears to be more realistic to employ a farinfrared FEL as proposed, e.g., in [16] to produce sub-mm buckets, which are still three orders of magnitude shorter than conventional RF buckets. If, on the other hand, electrons were allowed to jump between the short buckets from turn to turn, they would partly be on unbound trajectories outside the separatrix. It is conceivable that a conventional RF field takes care of the radiation losses, while an optical field provides steady-state bunching at a small wavelength with a continuous background of particles very much like the coasting-beam background in a proton ring (e.g., [17]).
3. Temporary microbuncing in storage rings While steady-state microbunching as shown in Fig. 3(a) can be envisioned in the infrared regime, a laser-induced energy modulation at shorter wavelengths is easily converted into a periodic density modulation by dispersive elements, see Fig. 3(b1) and (b2). In a chicane made of four dipole magnets, for example, electrons having gained (lost) energy E and momentum p ¼E/c slip forward (backward) by an amount Δz given by the transfer matrix element R56 = Δz /(Δp/p), while transverse-longitudinal coupling from the matrix elements R51 and R52 nearly cancels. This way, microbunches are temporarily created with a separation of one laser
Fig. 1. Schematic view of an electron inside an RF resonator (left) and co-propagating with a light wave in an undulator (right). The dashed lines represent the electron trajectory. The arrows indicate the force from an electric field acting on the electron.
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Fig. 2. Three scenarios for a storage ring driven by a continuous-wave laser. (a) The light wave emerging from an optical cavity interacts with the electron beam in an undulator. (b) The undulator is within the optical cavity. (c) The light wave from the cavity is deflected by mirrors and interacts with electrons in more than one undulator.
Fig. 3. Electrons in longitudinal phase space (energy deviation versus longitudinal coordinate in units of the wavelength λ) for three cases: (a) phase focusing under the influence of a sinusoidal accelerating voltage and radiation losses, (b1) laser-induced energy modulation, and (b2) microbunching of energy-modulated electrons after a dispersive chicane.
wavelength and give rise to coherent emission at harmonics of this wavelength. In 1984, coherent emission at the third harmonic of a Nd:YAG laser was demonstrated at the storage ring ACO in Orsay, France [18]. More recently, this technique, known as coherent
harmonic generation (CHG), was implemented using femtosecond Ti:sapphire lasers at the storage rings UVSOR in Okazaki, Japan [19], Elettra near Trieste, Italy [20], and DELTA in Dortmund, Germany [21]. Even though a femtosecond laser pulse interacts only
Please cite this article as: S. Khan, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.07.048i
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with a short “slice” within the electron bunch (about 1/1000 of the bunch length), the coherently emitted radiation up to typically the 5th harmonic exceeds the radiation from the whole bunch in brightness. The photon flux scales with the number of electrons squared, the transverse source size and divergence is smaller than from incoherent emission, and the spectrum is nearly Fourierlimited. In order to reach shorter wavelengths, the implementation of echo-enabled harmonic generation (EEHG) [22] is planned at DELTA after modifying the storage ring and creating a 20 m long straight section [23]. In the EEGH scheme, a two-fold energy modulation generates a more complex microbunch pattern with Fourier components at very high harmonics. At NLCTA, a linear accelerator facility at SLAC in Menlo Park, USA, EEHG was recently demonstrated at the 75th harmonic [24]. Using laser-induced energy modulation with subsequent microbunching, the repetition rate of ultrashort high-brightness pulses is limited by the laser to typically several kHz for laser pulses in the mJ range. If the repetition rate of novel laser systems reaches the bunch revolution frequency, this type of microbunching may be considered as “steady state”, even though the structure is created anew with each laser pulse. In this case, the energy modulation would cause a significant increase of the electron energy spread, which can be avoided by either interacting with many bunches one after the other, or by undoing the energy change turn by turn with negative R56 and an opposite energy modulation. In conclusion, steady-state or temporary microbunching can be employed to increase the brightness and to reduce the pulse duration of synchrotron radiation in storage rings. This would add a new quality to the high bunch rate and excellent beam stability of these machines.
Acknowledgements The pleasant and constructive working atmosphere at DELTA is gratefully acknowledged. I thank P. Ungelenk for reading the manuscript. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
References [1] H. Wiedemann, Particle Accelerator Physics, 4th Edition, Springer 2015 http: //dx.doi.org/10.1007/978-3-319-18317-6. [2] K. Balewski, Commissioning of PETRA III, in: Proceedings of the International Particle Accelerator Conference, Kyoto, Japan, 2010, pp. 1280–1284, 〈http:// www.jacow.org〉. [3] M. Eriksson, Commissioning of the MAX IV light source, in: Proceedings of the International Particle Accelerator Conference, Busan, Korea, 2016, pp. 11–15, 〈http://www.jacow.org〉.
[4] R. Dowd, Y.-R.E. Tan, K.P. Wootton, Vertical emittance at the quantum limit, in: Proceedings of the International Particle Accelerator Conference, Dresden, Germany, 2014, pp. 1096–1098, 〈http://www.jacow.org〉. [5] P. Schmüser, M. Dohlus, J. Rossbach, Ultraviolet and Soft-X-ray Free-electron Lasers, Springer, Berlin Heidelberg 2008 http://dx.doi.org/10.1007/ 978-3-540-79572-8. [6] W. Ackermann, et al., Operation of a free-electron laser from the extreme ultraviolet to the water window, Nat. Photon. 1 (2007) 336, http://dx.doi.org/ 10.1038/nphoton.2007.76. [7] P. Emma, et al., First lasing and operation of an Angstrom-wavelength freeelectron laser, Nat. Photon. 4 (2010) 641, http://dx.doi.org/10.1038/ nphoton.2010.176. [8] T. Ishikawa, et al., A compact x-ray free-electron laser emitting in the subAngstrom region, Nat. Photon. 6 (2012) 540, http://dx.doi.org/10.1038/ nphoton.2012.141. [9] E. Allaria, et al., Highly coherent and stable pulses from the FERMI seeded freeelectron laser in the extreme ultraviolet, Nat. Photon. 6 (2012) 699, http://dx. doi.org/10.1038/nphoton.2012.233. [10] 〈http://www.lightsources.org〉. [11] M. Abo-Bakr, J. Feikes, K. Holldack, P. Kuske, W. Peatman, U. Schade, G. Wüstefeld, Brilliant, coherent far-infrared (THz) synchrotron radiation, Phys. Rev. Lett. 90 (2003) 094801, http://dx.doi.org/10.1103/ PhysRevLett.90.094801. [12] A. Siegman, Lasers, University Science Books, Sausalito, 1986. [13] Y. Shoji, Bunch lengthening by a betatron motion in quasi-isochronous storage rings, Phys. Rev. Spec. Top. - Accel. Beams 7 (2004) 090703, http://dx.doi.org/ 10.1103/PhysRevSTAB.7.090703. [14] Y. Shoji, H. Tanaka, M. Takao, K. Soutome, Longitudinal radiation excitation in an electron storage ring, Phys. Rev. E 54 (1996) R4556, http://dx.doi.org/ 10.1103/PhysRevE.54.R4556. [15] D. Ratner, A. Chao, Steady-state microbunching in a storage ring for generating coherent radiation, Phys. Rev. Lett. 105 (2010) 154801, http://dx.doi.org/ 10.1103/PhysRevLett.105.154801. [16] V. Litvinenko, O. Shevchenko, S. Mikhailov, Y. Wu, Project for generation of femtosecond x-ray beams from the Duke storage ring, in: Proceedings of the Particle Accelerator Conference, Chicago, USA, 2001, pp. 2614–2616, 〈http:// www.jacow.org〉. [17] K. Ehret, M. Funcke, S. Issever, T. Jagla, T. Lohse, S. Schaller, S. Spratte, M. Symalla, Y. Vassiliev, D. Wegener, J. Klute, C. Montag, Observation of coasting beam at the HERA proton-ring, Nucl. Instrum. Methods Phys. Res. A 456 (2001) 206. [18] B. Girard, Y. Lapierre, J.M. Ortega, C. Bazin, M. Billardon, P. Elleaume, M. Bergher, M. Velghe, Y. Petroff, Optical frequency multiplication by an optical klystron, Phys. Rev. Lett. 53 (1984) 2405, http://dx.doi.org/10.1103/ PhysRevLett.53.2405. [19] M. Labat, et al., Coherent harmonic generation on UVSOR-II storage ring, Eur. Phys. J. D 44 (2007) 187, http://dx.doi.org/10.1140/epjd/e2007-00177-6. [20] G.D. Ninno, et al., Generation of ultrashort coherent vacuum ultraviolet pulses using electron storage rings: a new bright light source for experiments, Phys. Rev. Lett. 101 (2008) 053902, http://dx.doi.org/10.1103/ PhysRevLett.101.053902. [21] S. Khan, et al., Generation of ultrashort and coherent synchrotron radiation pulses at delta, Sync. Rad. News 26 (3) (2013) 25, http://dx.doi.org/10.1080/ 08940886.2013.791213. [22] G. Stupakov, Using the beam-echo effect for generation of short-wavelength radiation, Phys. Rev. Lett. 102 (2009) 074801, http://dx.doi.org/10.1103/ PhysRevLett.102.074801. [23] S. Hilbrich, et al., Plans for an EEHG-based short-pulse facility at the DELTA storage ring, in: Proceedings of the Free-Electron Laser Conference, Daejeon, Korea, 2015, pp. 363–367, 〈http://www.jacow.org〉. [24] E. Hemsing, M. Dunning, B. Garcia, C. Hast, T. Raubenheimer, G. Stupakov, D. Xiang, Echo-enabled harmonics up to the 75th order from precisely tailored electron beams, Nat. Photon. 10 (2016) 512. 〈http://dx.doi.org/10.1038/npho ton.2016.101〉.
Please cite this article as: S. Khan, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.07.048i
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Ultrashort high-brightness pulses from storage rings Shaukat Khan Zentrum für Synchrotronstrahlung (DELTA), TU Dortmund University, Maria-Goeppert-Mayer-Str. 2, 44227 Dortmund, Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 15 June 2016 Received in revised form 25 July 2016 Accepted 27 July 2016
The brightness of short-wavelength radiation from accelerator-based sources can be increased by coherent emission in which the radiation intensity scales with the number of contributing electrons squared. This requires a microbunched longitudinal electron distribution, which is the case in freeelectron lasers. The brightness of light sources based on electron storage rings was steadily improved, but could profit further from coherent emission. The modulation of the electron energy by a continuouswave laser field may provide steady-state microbunching in the infrared regime. For shorter wavelengths, the energy modulation can be converted into a temporary density modulation by a dispersive chicane. One particular goal is coherent emission from a very short “slice” within an electron bunch in order to produce ultrashort radiation pulses with high brightness. & 2016 Elsevier B.V. All rights reserved.
Keywords: Synchrotron radiation Storage rings Microbunching Ultrashort pulses High brightness
rate [1]
1. Introduction The spectral brightness of a photon source is defined by [1]
B=
ΔN /Δt , 4π 2·σx·σ x′·σy·σ y′·dω/ω
ΔN ΔNe = · Δt Δt (1)
where ΔN is the number of photons in an extended time interval Δt (average brightness) or in an infinitesimal interval at the pulse maximum (peak brightness), and s is the rms value of the quantity in the subscript: horizontal ( x, x′) or vertical ( y, y′) source size and divergence. The usual convention for the frequency interval dω/ω is 0.1%. In storage rings, progress has been made in different directions. The photon rate ΔN /Δt was improved by increasing the beam current, requiring feedback systems to counteract collective instabilities, by keeping the beam current nearly constant with top-up injection, and by employing novel insertion devices such as in-vacuum undulators. For an undulator source, the photon rate within the interval dω/ω increases with the number of undulator periods. Progress has also been made in reducing the horizontal beam emittance ε ∼ σx·σ x′, reaching 1 nm rad with a large ring and damping wigglers (PETRA III in Hamburg, Germany [2]) and 0.3 nm rad with a multi-bend magnetic lattice based on a very compact mechanical design (MAX IV in Lund, Sweden [3]). With careful alignment and tuning of the magnets, a vertical beam emittance εy ∼ σy·σ y′ of 2 pm or less has been reported from different sources (SLS in Switzerland, ESRF in France, DIAMOND in the UK, ALS in USA). The Australian Light Source ASLS claims to have reached the quantum limit of 0.35 pm [4]. So far, the photon E-mail address: [email protected]
=
ne
ne
∑ eiωt j · ∑ e−iωtk j=1
k=1
ΔNe ΔNe ·ne + · Δt Δt
ne
ne
∑ ∑ eiω (t j− tk ) j=1 k≠j
(2)
with ΔNe/Δt being the photon rate from a single electron was assumed to be proportional to the number of electrons ne, which is true for a random temporal separation (t j − tk ) between any two electrons. The second term of the equation provides coherent emission with a rate proportional to the number of electrons squared for Fourier components of the electron distribution, e.g., for wavelengths being an integer fraction of the distance between so-called microbunches, as in the case of free-electron lasers (FELs) [5]. To date, only four short-wavelength FELs are in user operation: FLASH in Hamburg, Germany [6], LCLS at SLAC, Menlo Park, USA [7], SACLA at Harima, Japan [8], and FERMI near Trieste, Italy [9]. On the other hand, about 50 electron storage rings are operated as synchrotron light sources [10] and serve multiple beamlines, often in 24/7 operation, with a high repetition rate given by the radiofrequency (RF), where 500 MHz is a typical value. It would therefore be advantageous for a large user community if the intensity of synchrotron radiation could be enhanced by microbunching. An additional benefit is the generation of short radiation pulses, if only a short “slice” at the center of the electron distribution is microbunched.
http://dx.doi.org/10.1016/j.nima.2016.07.048 0168-9002/& 2016 Elsevier B.V. All rights reserved.
Please cite this article as: S. Khan, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.07.048i
S. Khan / Nuclear Instruments and Methods in Physics Research A ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
2. Steady-state microbunching in storage rings The stochastic nature of synchrotron radiation results in an energy spread of typically σΔE / E ≈ 10−3, which translates into a ′ , where α is the momentum compaction bunch length σz ∼ α ·VRF factor and VRF ′ is the RF gradient. With typical values, a bunch length of several 10 ps is obtained, but various facilities have adopted a “low-α” mode of operation, in which a strongly reduced momentum compaction factor leads to a bunch length of about 1 ps, allowing for the coherent emission of terahertz (THz) radiation [11]. An increase of the RF frequency would reduce the bunch length as well as the bunch separation while increasing the number of RF buckets along the circumference of the storage ring. Here, a factor of 10 can be envisioned, but beyond that—leaving aside engineering issues—the reduced size of the RF resonators would be at variance with the required transverse aperture. The RF system provides bunching and recovers the energy lost due to synchrotron radiation. As sketched in the left part of Fig. 1, the force from the RF field is parallel to the electron path. Another way to create a succession of equidistant buckets is the interaction of electrons with a light wave co-propagating in an undulator. The right part of Fig. 1 illustrates that this interaction is not very effi→ cient, because the electric field , of the light is perpendicular to its propagation direction and, compared to the RF case, the transferred energy [5]
→→ dE = − e , · v dt = − e , x′c dt ,
(3)
is reduced by a factor x′, the angular coordinate of the electron. Nevertheless, the sinusoidal energy modulation can in principle assume the role of the RF voltage and create buckets on a much smaller wavelength scale. To cite give a few examples, the wavelength may be a few 100 μm in the case of a continuous-wave (cw) far-infrared FEL, 10 μm for a CO2 laser, or below 1 μm for lasers in the visible regime. An all-optical storage ring would be a fascinating device with 107 buckets in the case of the CO2 laser and a correspondingly high repetition rate of bunches with a length of a few femtoseconds. The beam current and the charge density would be similar to that of a conventional storage ring. The strong coherent emission in the whole infrared range would not change the total energy loss very much, since most of the spectral intensity is in the 100-eV to keV range, but will require further consideration in terms of collective effects and beam dynamics. Consider, as an example, a 10-kW CO2 laser in cw mode focused onto an area of 10 6 m2, as sketched in Fig. 2(a). The electric field amplitude is then , = 2I /(ε0 c ) , where I is the power density and ε0 is the vacuum permittivity. The result is 2.7 106 V/m, which is comparable to RF gradients. An undulator resonant to 10 μm will have a high strength parameter K. With K ¼20 (actually a wiggler, but here used as an undulator) and
1-GeV electrons (Lorentz factor γ ≈ 2000), the maximum angle is ′ xmax = K/γ ≈ 10−2 rad and—ignoring aberrations and other detrimental effects—the energy transfer over 4 m is 50 keV, which is in the regime of the energy loss per turn. Tighter focusing would not help to gain a larger overvoltage factor, because a smaller focus reduces the Rayleigh length [12] and thus the electric field averaged along the undulator. Furthermore, the size of the laser beam should be larger than the electron beam size in order to reduce the effect of the radial intensity variation. On the other hand, the electric field could be intensified by placing the undulator inside the optical cavity of the laser, see Fig. 2(b). Yet another possibility is to perform laser-electron interaction in more than one undulator by guiding the laser beam from one device to the next with mirrors, see Fig. 2(c). Replacing the RF voltage by a laser-induced energy modulation demands phase focusing within a fraction of the wavelength, i.e., a highly isochronous ring. Assuming a circumference of 100 m, the momentum compaction factor should be of the order of 10 4 for far-infrared wavelengths and below 10 5 for the CO2 laser, which is not impossible. However, the isochronicity of a storage ring is limited by the betatron motion [13] and by longitudinal radiation excitation [14] to the order of 100 fs (or several 10 μm), which would exclude any optical laser unless these limits can be overcome with a novel lattice design. Steady-state microbunching schemes in such a regime are discussed, e.g., in [15]. For a conventional lattice, it appears to be more realistic to employ a farinfrared FEL as proposed, e.g., in [16] to produce sub-mm buckets, which are still three orders of magnitude shorter than conventional RF buckets. If, on the other hand, electrons were allowed to jump between the short buckets from turn to turn, they would partly be on unbound trajectories outside the separatrix. It is conceivable that a conventional RF field takes care of the radiation losses, while an optical field provides steady-state bunching at a small wavelength with a continuous background of particles very much like the coasting-beam background in a proton ring (e.g., [17]).
3. Temporary microbuncing in storage rings While steady-state microbunching as shown in Fig. 3(a) can be envisioned in the infrared regime, a laser-induced energy modulation at shorter wavelengths is easily converted into a periodic density modulation by dispersive elements, see Fig. 3(b1) and (b2). In a chicane made of four dipole magnets, for example, electrons having gained (lost) energy E and momentum p ¼E/c slip forward (backward) by an amount Δz given by the transfer matrix element R56 = Δz /(Δp/p), while transverse-longitudinal coupling from the matrix elements R51 and R52 nearly cancels. This way, microbunches are temporarily created with a separation of one laser
Fig. 1. Schematic view of an electron inside an RF resonator (left) and co-propagating with a light wave in an undulator (right). The dashed lines represent the electron trajectory. The arrows indicate the force from an electric field acting on the electron.
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Fig. 2. Three scenarios for a storage ring driven by a continuous-wave laser. (a) The light wave emerging from an optical cavity interacts with the electron beam in an undulator. (b) The undulator is within the optical cavity. (c) The light wave from the cavity is deflected by mirrors and interacts with electrons in more than one undulator.
Fig. 3. Electrons in longitudinal phase space (energy deviation versus longitudinal coordinate in units of the wavelength λ) for three cases: (a) phase focusing under the influence of a sinusoidal accelerating voltage and radiation losses, (b1) laser-induced energy modulation, and (b2) microbunching of energy-modulated electrons after a dispersive chicane.
wavelength and give rise to coherent emission at harmonics of this wavelength. In 1984, coherent emission at the third harmonic of a Nd:YAG laser was demonstrated at the storage ring ACO in Orsay, France [18]. More recently, this technique, known as coherent
harmonic generation (CHG), was implemented using femtosecond Ti:sapphire lasers at the storage rings UVSOR in Okazaki, Japan [19], Elettra near Trieste, Italy [20], and DELTA in Dortmund, Germany [21]. Even though a femtosecond laser pulse interacts only
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with a short “slice” within the electron bunch (about 1/1000 of the bunch length), the coherently emitted radiation up to typically the 5th harmonic exceeds the radiation from the whole bunch in brightness. The photon flux scales with the number of electrons squared, the transverse source size and divergence is smaller than from incoherent emission, and the spectrum is nearly Fourierlimited. In order to reach shorter wavelengths, the implementation of echo-enabled harmonic generation (EEHG) [22] is planned at DELTA after modifying the storage ring and creating a 20 m long straight section [23]. In the EEGH scheme, a two-fold energy modulation generates a more complex microbunch pattern with Fourier components at very high harmonics. At NLCTA, a linear accelerator facility at SLAC in Menlo Park, USA, EEHG was recently demonstrated at the 75th harmonic [24]. Using laser-induced energy modulation with subsequent microbunching, the repetition rate of ultrashort high-brightness pulses is limited by the laser to typically several kHz for laser pulses in the mJ range. If the repetition rate of novel laser systems reaches the bunch revolution frequency, this type of microbunching may be considered as “steady state”, even though the structure is created anew with each laser pulse. In this case, the energy modulation would cause a significant increase of the electron energy spread, which can be avoided by either interacting with many bunches one after the other, or by undoing the energy change turn by turn with negative R56 and an opposite energy modulation. In conclusion, steady-state or temporary microbunching can be employed to increase the brightness and to reduce the pulse duration of synchrotron radiation in storage rings. This would add a new quality to the high bunch rate and excellent beam stability of these machines.
Acknowledgements The pleasant and constructive working atmosphere at DELTA is gratefully acknowledged. I thank P. Ungelenk for reading the manuscript. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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Please cite this article as: S. Khan, Nuclear Instruments & Methods in Physics Research A (2016), http://dx.doi.org/10.1016/j. nima.2016.07.048i