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Novel free electron laser named photon storage ring
700
Nuclear Instruments and Methods in Physics Research A304 (1991) 700-702 North-Holland
Novel free electron laser named photon storage ring Hironari Yamada
Quantum Technology Research Section, Sumitomo Heavy Industries, Ltd, 2-1-1 Yato-cho, Tanashi-city, Tokyo 188, Japan
Observed features of the smallest synchrotron radiation (SR) source AURORA are presented A novel free electron laser named photon storage ring (PhSR) which is based on this SR source is proposed, and the lasing mechanism is described. In this scheme the SR is confined within a coaxial mirror surrounding the electron orbit. The simulation indicates 10 kW of continuous output power for sub-mm wavelength with the present scheme of AURORA . 1 . Introduction The compact synchrotron radiation (SR) source [1,2] is opening up a new era of particle accelerator science. Since the invention of the accelerator it was predominantly utilized for high energy physics and nuclear physics. But synchrotron radiation which was useless from the accelerator technology point of view is now demonstrated to offer a new means for research in a variety of fields such as material science, biology, medicine, etc. The compact SR source has extended its field of application to industry. X-ray lithography is, for instance, a field demanding the use of intense X-ray source of 1 nm range wavelength to fabricate very large scale integrated circuits . In future the compact SR source dedicated to X-ray microscopy might be controlled like an electron microscope. The compactness seems to offer a new opportunity to SR users. Furthermore the application field of the compact SR source can be greatly extended if it generates coherent radiation. The "photon storage ring" (PhSR) is a novel free electron laser based on a compact SR source that has an exactly circular electron orbit [3] . In section 2 we describe the compact SR source briefly, and in section 3 the principle for laser oscillation in the PhSR is discussed . 2. The smallest synchrotron radiation source We have succeeded in the commissioning of a compact synchrotron light source AURORA [2], which is composed of a unique electron storage ring made of a single weak focussing magnet, and a 150 MeV racetrack microtron injector . The ring magnet uses a pair of superconducting coils with an iron yoke, which is capable of storing a 650 MeV electron beam in a 1 m diameter orbit. The exactly circular machine, which must be the smallest, is realized by a new injection
method called the half-integer resonance injection method [4]. In the new infection scheme electron beams are injected at 150 MeV into a distorted orbit with a tune value of 0.5 generated with the help of an air core perturbator . When the perturbator is turned off the beam orbit becomes normal and the beam cross section is reduced by the radiation damping (damping time in the radial direction is - 14 ms). The injection process can be repeated many times within a lifetime, which is about 60 s at 300 mA stored current, since the nonlinear field generated by the perturbator does not disturb the beam in the central orbit. We have observed more than 60% injection efficiency . The electron energy is successfully boosted up to 650 MeV . The magnet current is increased at a speed of 2 A/s on average. It takes about 7 min to ramp up to 650 MeV. Ten major resonances appear in the course of the ramping because the field index is changed, but without exciting the resonance dumper, these are passed without current losses . So far 300 mA of beam is accumulated. Note that the infected beam current is less than 1 mA at the peak and with a 10 Hz duty cycle. The lifetime is still linuted to 1 h when the stored current is 300 mA . A very uniform and equal beam profile is observed throughout the circumference as expected from the axially symmetric magnet of the ring. The typical beam profile obtained is 1 .2 mm to the radial and 0.14 mm in the vertical direction at 650 MeV. These measured beam sizes are in good agreement with the designed values . A remarkable feature of AURORA is that the observed beam position is stable within 0.1 mm all the time . 3. Principle for laser oscillation in the photon storage ring The PhSR compassed an electron storage ring and a cylindrical mirror surrounding its electron orbit (fig . 1).
0168-9002/91/$03 .50 © 1991 - Elsevier Science Publishers B.V (North-Holland)
H. Yamada / Novel FEL named photon storage ring
When the coherent radiation is generated in the PhSR, the radiation propagates along the off-tangential line indicated as path a in fig. 2 to prepare for acceleration or deceleration of the electrons. Once the interaction occurs at point A m the mode of decelerating electrons, the interaction should occur again at point B in the same mode for a successive coherent generation . For this mechanism, the phase of the coherent radiation must be reversed as the beam progresses from point A to B. The resonant wavelengths (X R) are given by the equation [4) (m+ z ) AR=2p(a/ße - sin a),
L--Photon Exit Opening
Fig. 1 . The photon storage ring is composed of a compact synchrotron light source with a cylindrical or barrel mirror surrounding its electron orbit. Here the electron orbit is exactly circular and the mirror is concentric to it . In this configuration, the synchrotron radiation is reflected back tangentially to the same electron orbit by the cylindrical mirror . This configuration is possible with AURORA since the beam duct and devices have a slit on their side throughout the circumference to let the radiation go out. The radius of the mirror curvature can be arranged so that the reflected radiation intercepts the electron orbit and one of the electron bunches (the original bunch) simultaneously. Because the electron bunches are spaced equally in the orbit, the coincidence of the radiation and the electron bunches takes place periodically. When the mirror radius is appropriately selected, the phase between the single electron and the radiation can be precisely adjusted . The PhSR has the best features of an undulator having effectively an infinite number of periods [3]. An essential mechanism of a free electron laser (FEL) is a periodic interaction of relativistic electrons and coherent radiation which leads to modulation of the electron density at the spacing of its wavelength . For this purpose, the coherent radiation must have an electric field component toward the electron velocity . To accomplish this scheme the coherent radiation and electrons are made to merge at some angle. An undulator is a device which wiggles electrons and makes the electron trajectory and the radiation path cross each other. We believe that, as long as the radiation path and the electron trajectory merge each other at some angle, it is not necessary for the electrons to be wiggled, but the radiation might be "wiggled". Of course the electromagnetic wave cannot be wiggled since it is not a charged particle, but it can be reflected so as to merge with electrons at an angle. The PhSR is a device which employs such a concept.
where m is an integer, p is the electron orbit radius, a indicates a deflection angle of the radiation from the tangential line as indicated in fig. 2, and ßB is the electron orbital velocity relative to the speed of light . This condition is essentially the same as that for the undulator-based FEL except that the beam trajectory is exactly circular in the case of the PhSR . The wavelength is, however, not uniquely determined by this equation since the photon path can be selected arbitrarily. If the angle a is appropriately selected any wavelength will satisfy the above equation . For this reason the wavelength must be selected by another mechanism. The wavelength is actually determined by the mirror radius relative to the electron orbit radius. The light pulses confined in the mirror cavity propagate along the single photon path finally leading to the exit opening, and form a pulse train with an exact time period . The inverse of this time period corresponds to the frequency
Fig. 2. The photon storage ring has an ideal feature of a FEL. In the PhSR all radiation contributes positively to the interference effect due to the focussing power of the cylmdrical mirror, while the mismatch of phase between the radiation and the electron is unavoidable m the undulator. IX . UNCONVENTIONAL SCHEMES
70 2
H. Yamada / Nouel FEL named photon storage ring
of the light wave. This time period can be set to any small value by adjusting the mirror radius or the electron orbit radius precisely. This wavelength is [4] rnÀ=2(0+nirt/2)p/ß a - (2p tos a tan 0+itÀ),
(2)
where m is a higher harmonic number, p, is the phase shift by the reflection, and n indicates the nth electron bunch which merges with the light pulse successively . This equation deals with the case where the number of bunches in the orbit is two, but we can easily extend the equation to the case that the number of bunches is more than two. n = 0 represents the case that the interaction of the radiation occurs always with the same electron bunch. It is easily shown that the phase between the light pulse and the electron is almost independent of a when it is much smaller than 0, because the variation in the photon path length due to a is compensated by the shift in the crossing point on the electron orbit. The shift of 0 by the deflection angle a to the tangential line can be expanded as 0-0°
_
1 az a4 tann°(2-24+ . . .),
and cos a tan 0 - tan 0° =
z
tan g° ( 2
(3a)
4
6 +
(3b)
where 0° is the value of 0 when a = 0. Substituting eqs. (3a) and (3b) in (2), one can see that eq. (2) is highly independent of a. Consequently the wavelength shift is negligibly small for small values of a. Indeed a is as small as 1/y, where y is the Lorentz factor . We can conclude that if the electron orbit is an exact circle, there are no factors which deteriorate the interference effect in the PhSR . Radiation emitted at any angle interferes coherently at the same wavelength, whereas the undulator inevitably involves some mismatching of the phase. The advantages of using the PhSR for an FEL are the following. (1) The radiation power is fully extracted through a simple exit opening in the cylindrical mirror. (2) All generated photons contribute positively to the interference effect because of the focusing power of the mirror . (3) The wavelength is tunable by changing the electron orbit radius . All that we need is a variablefrequency rf cavity. (4) The generated mode of the light wave in the cylindrical mirror cavity has a strong azimuthal electric field component along the electron orbit. This electric field is expressed by the TE mode with larger azimuthal mode number in the cylindrical cavity, which is known as a whispering gallery mode . The phase velocity of the azimuthal electric field coincides with the orbital electron velocity at the inside of the orbit. The interaction between the radiation and
electrons occurs continuously along the electron orbit. Also it is important to note that the electron energy is refreshed every revolution . The FEL power to be extracted depends upon the wavelength under consideration, its radial beam size and the accuracy of the mirror curvature . With today's advanced technologies one might fabricate the mirror curvature as accurately to within an order of 1 lim, which limits the minimum wavelength to about 10 p m [2]. The gain has been calculated in the case of n = 0 for the present scheme of AURORA [6]. The gain is a function of the wavelength and the radial beam size. If 100 wm wavelength is considered a 10% gain is expected in one revolution of the electrons [6]. The maximum FEL power obtainable from the PhSR is limited by the amount of phase shift due to the total energy loss of the electrons in one revolution (or in one acceleration period if the number of rf cavities is more than two). In the PhSR the electron energy loss results in a shift of the electron position inward, while in the undulator the electron position is shifted backward relative to the radiation pulse. The laser power saturates when the energy loss reaches the half wavelength ; Opa < X/21T . Then the corresponding total energy loss (AE) of one electron in one revolution is calculated as AE= q ( 2mp)
z/3
'
(4)
where q is a momentum compaction factor, and E is the electron energy . For 10 ltm wavelength, 66 keV energy loss per electron is obtained from 300 MeV electrons. In reality the total power is, however, linuted by the rf power which is 30 kW with the present scheme of AURORA .
Acknowledgements The author would like to express many thanks to Prof. K. Mima and Prof . K. Shimoda for their valuable discussions to understand the mechanism of the PhSR.
References [ll N. Takahasi, Nucl . Instr. and Meth. B24/25 (1987) 425, H. Yamada et al ., Rev. Sci. Instr. 60 (1989) 1786 . (2] H. Yamada, J. Vac. Sci. Technol . B8 (1990) 1682. [3] H. Yamada, Jpn. J. Appl . Phys . 28 (1989) L1665. [41 T. Takayama, Nucl . Instr. and Meth . B24/25 (1987) 420. [5) H. Yamada, Proc. Int. Symp . on Free Electron Laser, Tokyo, 1990 . [61 K. Mima, K. Shimoda and H. Yamada, to be published in J. Quantum Electron .
Nuclear Instruments and Methods in Physics Research A304 (1991) 700-702 North-Holland
Novel free electron laser named photon storage ring Hironari Yamada
Quantum Technology Research Section, Sumitomo Heavy Industries, Ltd, 2-1-1 Yato-cho, Tanashi-city, Tokyo 188, Japan
Observed features of the smallest synchrotron radiation (SR) source AURORA are presented A novel free electron laser named photon storage ring (PhSR) which is based on this SR source is proposed, and the lasing mechanism is described. In this scheme the SR is confined within a coaxial mirror surrounding the electron orbit. The simulation indicates 10 kW of continuous output power for sub-mm wavelength with the present scheme of AURORA . 1 . Introduction The compact synchrotron radiation (SR) source [1,2] is opening up a new era of particle accelerator science. Since the invention of the accelerator it was predominantly utilized for high energy physics and nuclear physics. But synchrotron radiation which was useless from the accelerator technology point of view is now demonstrated to offer a new means for research in a variety of fields such as material science, biology, medicine, etc. The compact SR source has extended its field of application to industry. X-ray lithography is, for instance, a field demanding the use of intense X-ray source of 1 nm range wavelength to fabricate very large scale integrated circuits . In future the compact SR source dedicated to X-ray microscopy might be controlled like an electron microscope. The compactness seems to offer a new opportunity to SR users. Furthermore the application field of the compact SR source can be greatly extended if it generates coherent radiation. The "photon storage ring" (PhSR) is a novel free electron laser based on a compact SR source that has an exactly circular electron orbit [3] . In section 2 we describe the compact SR source briefly, and in section 3 the principle for laser oscillation in the PhSR is discussed . 2. The smallest synchrotron radiation source We have succeeded in the commissioning of a compact synchrotron light source AURORA [2], which is composed of a unique electron storage ring made of a single weak focussing magnet, and a 150 MeV racetrack microtron injector . The ring magnet uses a pair of superconducting coils with an iron yoke, which is capable of storing a 650 MeV electron beam in a 1 m diameter orbit. The exactly circular machine, which must be the smallest, is realized by a new injection
method called the half-integer resonance injection method [4]. In the new infection scheme electron beams are injected at 150 MeV into a distorted orbit with a tune value of 0.5 generated with the help of an air core perturbator . When the perturbator is turned off the beam orbit becomes normal and the beam cross section is reduced by the radiation damping (damping time in the radial direction is - 14 ms). The injection process can be repeated many times within a lifetime, which is about 60 s at 300 mA stored current, since the nonlinear field generated by the perturbator does not disturb the beam in the central orbit. We have observed more than 60% injection efficiency . The electron energy is successfully boosted up to 650 MeV . The magnet current is increased at a speed of 2 A/s on average. It takes about 7 min to ramp up to 650 MeV. Ten major resonances appear in the course of the ramping because the field index is changed, but without exciting the resonance dumper, these are passed without current losses . So far 300 mA of beam is accumulated. Note that the infected beam current is less than 1 mA at the peak and with a 10 Hz duty cycle. The lifetime is still linuted to 1 h when the stored current is 300 mA . A very uniform and equal beam profile is observed throughout the circumference as expected from the axially symmetric magnet of the ring. The typical beam profile obtained is 1 .2 mm to the radial and 0.14 mm in the vertical direction at 650 MeV. These measured beam sizes are in good agreement with the designed values . A remarkable feature of AURORA is that the observed beam position is stable within 0.1 mm all the time . 3. Principle for laser oscillation in the photon storage ring The PhSR compassed an electron storage ring and a cylindrical mirror surrounding its electron orbit (fig . 1).
0168-9002/91/$03 .50 © 1991 - Elsevier Science Publishers B.V (North-Holland)
H. Yamada / Novel FEL named photon storage ring
When the coherent radiation is generated in the PhSR, the radiation propagates along the off-tangential line indicated as path a in fig. 2 to prepare for acceleration or deceleration of the electrons. Once the interaction occurs at point A m the mode of decelerating electrons, the interaction should occur again at point B in the same mode for a successive coherent generation . For this mechanism, the phase of the coherent radiation must be reversed as the beam progresses from point A to B. The resonant wavelengths (X R) are given by the equation [4) (m+ z ) AR=2p(a/ße - sin a),
L--Photon Exit Opening
Fig. 1 . The photon storage ring is composed of a compact synchrotron light source with a cylindrical or barrel mirror surrounding its electron orbit. Here the electron orbit is exactly circular and the mirror is concentric to it . In this configuration, the synchrotron radiation is reflected back tangentially to the same electron orbit by the cylindrical mirror . This configuration is possible with AURORA since the beam duct and devices have a slit on their side throughout the circumference to let the radiation go out. The radius of the mirror curvature can be arranged so that the reflected radiation intercepts the electron orbit and one of the electron bunches (the original bunch) simultaneously. Because the electron bunches are spaced equally in the orbit, the coincidence of the radiation and the electron bunches takes place periodically. When the mirror radius is appropriately selected, the phase between the single electron and the radiation can be precisely adjusted . The PhSR has the best features of an undulator having effectively an infinite number of periods [3]. An essential mechanism of a free electron laser (FEL) is a periodic interaction of relativistic electrons and coherent radiation which leads to modulation of the electron density at the spacing of its wavelength . For this purpose, the coherent radiation must have an electric field component toward the electron velocity . To accomplish this scheme the coherent radiation and electrons are made to merge at some angle. An undulator is a device which wiggles electrons and makes the electron trajectory and the radiation path cross each other. We believe that, as long as the radiation path and the electron trajectory merge each other at some angle, it is not necessary for the electrons to be wiggled, but the radiation might be "wiggled". Of course the electromagnetic wave cannot be wiggled since it is not a charged particle, but it can be reflected so as to merge with electrons at an angle. The PhSR is a device which employs such a concept.
where m is an integer, p is the electron orbit radius, a indicates a deflection angle of the radiation from the tangential line as indicated in fig. 2, and ßB is the electron orbital velocity relative to the speed of light . This condition is essentially the same as that for the undulator-based FEL except that the beam trajectory is exactly circular in the case of the PhSR . The wavelength is, however, not uniquely determined by this equation since the photon path can be selected arbitrarily. If the angle a is appropriately selected any wavelength will satisfy the above equation . For this reason the wavelength must be selected by another mechanism. The wavelength is actually determined by the mirror radius relative to the electron orbit radius. The light pulses confined in the mirror cavity propagate along the single photon path finally leading to the exit opening, and form a pulse train with an exact time period . The inverse of this time period corresponds to the frequency
Fig. 2. The photon storage ring has an ideal feature of a FEL. In the PhSR all radiation contributes positively to the interference effect due to the focussing power of the cylmdrical mirror, while the mismatch of phase between the radiation and the electron is unavoidable m the undulator. IX . UNCONVENTIONAL SCHEMES
70 2
H. Yamada / Nouel FEL named photon storage ring
of the light wave. This time period can be set to any small value by adjusting the mirror radius or the electron orbit radius precisely. This wavelength is [4] rnÀ=2(0+nirt/2)p/ß a - (2p tos a tan 0+itÀ),
(2)
where m is a higher harmonic number, p, is the phase shift by the reflection, and n indicates the nth electron bunch which merges with the light pulse successively . This equation deals with the case where the number of bunches in the orbit is two, but we can easily extend the equation to the case that the number of bunches is more than two. n = 0 represents the case that the interaction of the radiation occurs always with the same electron bunch. It is easily shown that the phase between the light pulse and the electron is almost independent of a when it is much smaller than 0, because the variation in the photon path length due to a is compensated by the shift in the crossing point on the electron orbit. The shift of 0 by the deflection angle a to the tangential line can be expanded as 0-0°
_
1 az a4 tann°(2-24+ . . .),
and cos a tan 0 - tan 0° =
z
tan g° ( 2
(3a)
4
6 +
(3b)
where 0° is the value of 0 when a = 0. Substituting eqs. (3a) and (3b) in (2), one can see that eq. (2) is highly independent of a. Consequently the wavelength shift is negligibly small for small values of a. Indeed a is as small as 1/y, where y is the Lorentz factor . We can conclude that if the electron orbit is an exact circle, there are no factors which deteriorate the interference effect in the PhSR . Radiation emitted at any angle interferes coherently at the same wavelength, whereas the undulator inevitably involves some mismatching of the phase. The advantages of using the PhSR for an FEL are the following. (1) The radiation power is fully extracted through a simple exit opening in the cylindrical mirror. (2) All generated photons contribute positively to the interference effect because of the focusing power of the mirror . (3) The wavelength is tunable by changing the electron orbit radius . All that we need is a variablefrequency rf cavity. (4) The generated mode of the light wave in the cylindrical mirror cavity has a strong azimuthal electric field component along the electron orbit. This electric field is expressed by the TE mode with larger azimuthal mode number in the cylindrical cavity, which is known as a whispering gallery mode . The phase velocity of the azimuthal electric field coincides with the orbital electron velocity at the inside of the orbit. The interaction between the radiation and
electrons occurs continuously along the electron orbit. Also it is important to note that the electron energy is refreshed every revolution . The FEL power to be extracted depends upon the wavelength under consideration, its radial beam size and the accuracy of the mirror curvature . With today's advanced technologies one might fabricate the mirror curvature as accurately to within an order of 1 lim, which limits the minimum wavelength to about 10 p m [2]. The gain has been calculated in the case of n = 0 for the present scheme of AURORA [6]. The gain is a function of the wavelength and the radial beam size. If 100 wm wavelength is considered a 10% gain is expected in one revolution of the electrons [6]. The maximum FEL power obtainable from the PhSR is limited by the amount of phase shift due to the total energy loss of the electrons in one revolution (or in one acceleration period if the number of rf cavities is more than two). In the PhSR the electron energy loss results in a shift of the electron position inward, while in the undulator the electron position is shifted backward relative to the radiation pulse. The laser power saturates when the energy loss reaches the half wavelength ; Opa < X/21T . Then the corresponding total energy loss (AE) of one electron in one revolution is calculated as AE= q ( 2mp)
z/3
'
(4)
where q is a momentum compaction factor, and E is the electron energy . For 10 ltm wavelength, 66 keV energy loss per electron is obtained from 300 MeV electrons. In reality the total power is, however, linuted by the rf power which is 30 kW with the present scheme of AURORA .
Acknowledgements The author would like to express many thanks to Prof. K. Mima and Prof . K. Shimoda for their valuable discussions to understand the mechanism of the PhSR.
References [ll N. Takahasi, Nucl . Instr. and Meth. B24/25 (1987) 425, H. Yamada et al ., Rev. Sci. Instr. 60 (1989) 1786 . (2] H. Yamada, J. Vac. Sci. Technol . B8 (1990) 1682. [3] H. Yamada, Jpn. J. Appl . Phys . 28 (1989) L1665. [41 T. Takayama, Nucl . Instr. and Meth . B24/25 (1987) 420. [5) H. Yamada, Proc. Int. Symp . on Free Electron Laser, Tokyo, 1990 . [61 K. Mima, K. Shimoda and H. Yamada, to be published in J. Quantum Electron .