- Email: [email protected]
Circular polarization with rotatable magnetic fields in crossed staggered undulator
Journal of Magnetism and Magnetic Materials 239 (2002) 363–366
Circular polarization with rotatable magnetic fields in crossed staggered undulator C.H. Chang*, Ch. Wang, C.S. Hwang, T.C. Fan, G.H. Luo Synchrotron Radiation Research Center, No. 1, R&D Road VI, Hsinchu Science-Based Industrial Park, Hsinchu 30077, Taiwan
Abstract This work presents a novel crossed staggered undulator (CSU) capable of producing circular polarization photon with higher photon energies and higher brightness. The CSU includes two 1-m long staggered undulators with 20-mm periodic length, to achieve high vertical field strength of 0.9 T and longitudinal field strength of 0.7 T at a 5.5-mm gap width. During beam injection, the staggered magnetic arrays in vacuum can be rotated within 7451 to accommodate the horizontal aperture limitation. The identical crossed magnetic fields can also be orientated to create the ideally circular or linear polarized light in any direction. The optimal merit flux is pointed at higher harmonics that allow circular polarized light to be used over the 1.4–4 KeV range in the SRRC 1.5 GeV storage ring. This paper also proposes an outline for the design of an entire system. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Circular polarization; Crossed undulator; Staggered undulator
Recently, Apple II type undulators have been used to generate linear, elliptical and circular polarized light in synchrotron radiation facilities [1]. A similar type of elliptically polarizing undulator (EPU), 3.9 m long with a 5.6 cm magnetic period length has also been in operation to produce variably polarized light in a range of 80–1400 eV at the Synchrotron Radiation Research Center (SRRC). Circular polarized light with higher flux intensity in the higher photon energy range has received increasing interest. A polarizing undulator with a short period and a small gap must be employed to obtain circular polarized light over the 1.4–4 KeV ranges in a 1.5 GeV energy machine. However, in a short period undulator, higher field strengths cannot be easily realized, as the volume of the permanent magnet is limited. The thickness of the vacuum chamber significantly reduces the field strength. The electron beam lifetime is subjected to the smallest gap width. Therefore, the undulator must be integrated into the vacuum system to optimize the gap width. The Apple II type *Corresponding author. Tel.: +886-35-780281ext.6304; fax: +886-35-783-890. E-mail address: [email protected] (C.H. Chang).
undulator cannot be used in the vacuum system due to mechanical complexity. A traditional crossed undulator has been considered as a polarizing undulator, consisting of two planar undulators in series with one modulator in between. These two planar undulators are configured with magnetic fields such that the electric field emitted from one undulator is orthogonal to that from the other. This crossed field design tends to be limited by the horizontal physical aperture [2]. This work seeks to develop a new type of polarizing undulator. The magnetic field strength must be enhanced by optimization of the periodic magnetic circuit of the undulator to maintain a reasonable gap and tuneability of the photon energy. The staggered undulator has several advantages: a high field is attainable even at short periods; field strength is tunable by varying the solenoid current and random field errors are reduced remarkably at a fixed gap width [3]. In the staggered hybrid undulator [4], only saturation fields of vanadium permendur pole materials limit the highest field of the staggered array undulator. Hence, the staggered hybrid undulator can achieve a higher magnetic field than can the hybrid and the pure magnet in the short period
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 6 0 2 - 3
364
C.H. Chang et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 363–366
1
Opera-3D, Vector Field Ltd., Oxford, England.
Bz = 0.0 T Bz = 0.6 T
0.8 0.4 0.0 -0.4 -0.8
-10
-5
0
5
10
Z-axis (mm) By Field Strength (T)
undulator. A crossed staggered undulator (CSU) with rotatable magnetic arrays in series is proposed to produce higher brightness with arbitrary polarization states at higher photon energies. A short period 20-mm undulator with a 0.9 T magnetic field is selected to produce 1.4–4.0 KeV photons in the SRRC 1.5 GeV ring. Fig. 1 displays the configuration of the 1-m long staggered undulator. The alternating sinusoidal field was derived from the staggered hybrid magnetic array inside a solenoid coil. The iron blocks are constructed from vanadium permendur. The solenoid field is deflected vertically into each vanadium permendur face to form an alternating vertical field owing to the high permeability of vanadium permendur pole. A wedge pole was designed to achieve higher field strength. The NdFeB permanent magnet blocks placed between the wedge pole are arranged to enhance the alternating vertical magnetic field strength. Three-dimensional field analysis optimized the period magnetic structure on the permanent magnet and pole parameters. Magnetic field calculations were performed with TOSCA/OPERA-3D computer code.1 A notably high vertical magnetic field of 0.9 T was achieved by driving a longitudinal solenoid field of 0.7 T at a 5.5-mm gap width. The permanent magnet could not exceed 1.25 Hc to ensure reproducible magnet operation. The largest reverse solenoid field was limited to avert the
By Field Strength (T)
Fig. 1. Schematic diagram of 1-m long staggered hybrid undulator.
1.0 0.8 0.6 0.4 0.2 0.0 -20
-15
-10
-5
0
5
10
15
20
X-axis (mm)
Fig. 2. The measured vertical and transverse field profiles of one period mockup at 5.5 mm gap.
irreversible demagnetization of the permanent magnet. The field performance was examined using a one-period mockup. Fig. 2 presents the measured vertical field and transverse field profiles at a 5.5-mm gap, as determined by the field design. An anti-symmetric field configuration was designed under stringent magnetic field requirements to increase the effective magnetic pole. The configuration includes an adiabatic section at both ends of the undulator. Fig. 1
By Field Strength (T)
C.H. Chang et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 363–366 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0
Modulator Staggerd Undulator Bx
Staggerd Undulator By
e−
0
Bz Field Strength (T)
365
50
100
150
200
250
300
350
400
450
500
0.8
Fig. 4. Conceptual illustration of the proposed staggered undulator with rotating magnet arrays at 7451 in crossed configuration.
0.6 0.4 0.2 0.0 0
50
100
150
200
250
300
350
400
450
500
Z-axis (mm)
Fig. 3. The calculated vertical and longitudinal field distribution of half staggered undulator.
shows the proposed end configuration. The end pole field is analyzed using two-dimensional calculation approaches. The magnet blocks in the end pole can be partially adjusted to compensate the field integrals, and adjust the field distributions. Fig. 3 gives the calculated vertical and longitudinal field distribution of the half section of a staggered undulator. A total of 44 effective magnetic periods were predicted for a 1-m long undulator. The longitudinal field can be applied with the opposite polarity using the solenoid in two undulators to cancel the longitudinal field effect on the electron beam orbit. Accordingly, the integrated longitudinal fields from the two undulators cancel each other. To generate circular polarized radiation, one of these two staggered undulators must be rotated by 901 with respect to the other one such that the generated identical magnetic fields are mutually orthogonal [5]. The undulator requires a large acceptable horizontal aperture in the storage ring during the electron beam injection. This work offers both planar undulators with the null rotation to accommodate the geometrical limitation along the planar direction, and prevent the injected from being affected. Both magnet arrays in the undulator can be rotated after the electron beam has been stored in the storage ring, and the magnetic field can be then tuned to create the various polarized lights. The in-vacuum magnetic arrays were not constrained by the vacuum chamber on both horizontal and vertical planes simultaneously. The magnetic field amplitude in both undulators is identical. The linear and circular radiation on each harmonic can be produced by the CSU. The magnetic field on-axis can be adjusted to produce linear or circular polarization, as well as any intermediate orientation of magnetic arrays. When Bx ¼ By ;
the circular polarized radiation is maximized. The horizontal and vertical fields in crossed field must be maximized to extend the useful photon energy range. In our design with rotating magnetic arrays with a fixed gap width, the linear and circular polarization on-axis also can be rotated in any directions on the plane. Note that the rotatable feature of the CSU provides more useful polarizing states than does EPU. The CSU is rotated with respect to one another by 7451 about their common longitudinal axis and variable-phased along the same axis, as illustrated in Fig. 4. The time delay of two linear polarized radiations from the two staggered undulators is due to superposition of the coherent wavetrains in a monochromater to produce the desired polarized radiation. Scanning photon energy while maintaining a constant polarization state requires careful tuning of the modulator. A 3-pole electromagnetic modulator with a fixed gap is utilized as an optical phase shifter to manipulate the time delay between the radiation pulses from the upstream and downstream undulators [6]. The magnetic field within the modulator forces the electrons to be deflected on the same path as electromagnetic radiation, and produces a phase shift of at least 2p of phase at the lowest photon energy. The polarization state can be determined by setting the magnetic field of modulator. Experiments that make use of polarization often require a rapid switching of polarization orientation from left to right. The switching frequency can be as high as 10 Hz. As mentioned above, the circular polarized radiation generated from a CSU is achieved by temporal overlapping of two orthogonal radiation pulses generated from two in-series staggered undulators. Interference between the radiation pulses from the upstream and downstream staggered undulators leads to a variation which alters the circular polarization rate, even within the main spectral lob of the harmonics. Fig. 5 shows the first harmonic circular and linear spectral intensity of the CSU for a vertical field of 0.9 T. Note that the positive and negative values of the spectral intensity in Fig. 5 correspond to left and right circular polarization, respectively. The finite pinhole affected the interference conditions and led to depolarization [7]. The energy spread and finite emittance of the bunch beam
C.H. Chang et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 363–366
Fig. 5. First harmonic on-axis spectra of the crossed staggered undulator with a magnetic vertical field strength of 0.9 T. The dashed line displays the linear polarized spectrum. The solid line shows the circular polarized spectrum. The positive/ negative value of spectra intensity corresponds to the left/right circular polarized.
may contribute to the depolarization. A trade-off to optimize polarizing spectral property will be discussed elsewhere. Circular polarized radiation can be generated from a CSU at higher harmonics, as shown in Fig. 6 for the first, third and fifth harmonic for a vertical field from 0.9 to 0.4 T. The corresponding circular polarized spectral intensity will be twice that of the linear polarization from a single device. However, the CSU can also be used to generate linear polarized radiation in an arbitrary spatial orientation by rotating the two staggered undulators to the same angle. The effective linear spectral intensity is then four times of that from a single undulator. The merit flux is proportional to the square of the degree of circular polarization. Consequently, a CSU generates ideally circular polarized radiation at higher harmonics and a higher degree of polarization. An Apple II EPU generates circular polarized radiation only at the fundamental harmonic, but poorer polarization at higher harmonics. The CPU thus compares very favorably to the EPU. The CSU generates the optimal
Spectral Intensity [Photons/sec/m rad^2/0.1% BW /200 m A]
366
1E18
1E17
1E16
linear polarized: 1st linear polarized: 3rd linear polarized: 5th circular polarized: 1st circular polarized: 3rd circular polarized: 5th
1E15
500
1000
2000
3000
4000
Photon energy [eV]
Fig. 6. Spectral intensity of the crossed staggered undulator: linear (solid points) and circular (dot point) polarization at first, third and fifth harmonics. The solenoids are powered to generate a vertical magnetic field from 0.9 to 0.4 T.
merit flux at higher harmonics at higher photon energies. The authors would like to thank the National Science Council of the Republic of China for financially supporting this research under Contract No. 89-2112M-213-014.
References [1] S. Sasaki, Nucl. Instrum. Methods A 347 (1994) 83. [2] J. Bahrdt, et al., Rev. Sci. Instrum. 63 (1) (1992) 339. [3] Y.C. Huang, et al., Nucl. Instrum. Methods A 341 (1994) 431. [4] C.H. Chang, et al., Proceedings of the Seventh European Particle Accelerator Conference, pp. 2313–2315. [5] Kwang-Je Kim, Nucl. Instrum. Methods 219 (1984) 425. [6] R. Savoy, K. Halbach, Proceedings of the Particle Accelerator Conference, 1991, pp. 2718–2720. [7] P. Elleaume, Proceeding of the Fourth European Particle Accelerator Conference, pp. 1083–1087.
Circular polarization with rotatable magnetic fields in crossed staggered undulator C.H. Chang*, Ch. Wang, C.S. Hwang, T.C. Fan, G.H. Luo Synchrotron Radiation Research Center, No. 1, R&D Road VI, Hsinchu Science-Based Industrial Park, Hsinchu 30077, Taiwan
Abstract This work presents a novel crossed staggered undulator (CSU) capable of producing circular polarization photon with higher photon energies and higher brightness. The CSU includes two 1-m long staggered undulators with 20-mm periodic length, to achieve high vertical field strength of 0.9 T and longitudinal field strength of 0.7 T at a 5.5-mm gap width. During beam injection, the staggered magnetic arrays in vacuum can be rotated within 7451 to accommodate the horizontal aperture limitation. The identical crossed magnetic fields can also be orientated to create the ideally circular or linear polarized light in any direction. The optimal merit flux is pointed at higher harmonics that allow circular polarized light to be used over the 1.4–4 KeV range in the SRRC 1.5 GeV storage ring. This paper also proposes an outline for the design of an entire system. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Circular polarization; Crossed undulator; Staggered undulator
Recently, Apple II type undulators have been used to generate linear, elliptical and circular polarized light in synchrotron radiation facilities [1]. A similar type of elliptically polarizing undulator (EPU), 3.9 m long with a 5.6 cm magnetic period length has also been in operation to produce variably polarized light in a range of 80–1400 eV at the Synchrotron Radiation Research Center (SRRC). Circular polarized light with higher flux intensity in the higher photon energy range has received increasing interest. A polarizing undulator with a short period and a small gap must be employed to obtain circular polarized light over the 1.4–4 KeV ranges in a 1.5 GeV energy machine. However, in a short period undulator, higher field strengths cannot be easily realized, as the volume of the permanent magnet is limited. The thickness of the vacuum chamber significantly reduces the field strength. The electron beam lifetime is subjected to the smallest gap width. Therefore, the undulator must be integrated into the vacuum system to optimize the gap width. The Apple II type *Corresponding author. Tel.: +886-35-780281ext.6304; fax: +886-35-783-890. E-mail address: [email protected] (C.H. Chang).
undulator cannot be used in the vacuum system due to mechanical complexity. A traditional crossed undulator has been considered as a polarizing undulator, consisting of two planar undulators in series with one modulator in between. These two planar undulators are configured with magnetic fields such that the electric field emitted from one undulator is orthogonal to that from the other. This crossed field design tends to be limited by the horizontal physical aperture [2]. This work seeks to develop a new type of polarizing undulator. The magnetic field strength must be enhanced by optimization of the periodic magnetic circuit of the undulator to maintain a reasonable gap and tuneability of the photon energy. The staggered undulator has several advantages: a high field is attainable even at short periods; field strength is tunable by varying the solenoid current and random field errors are reduced remarkably at a fixed gap width [3]. In the staggered hybrid undulator [4], only saturation fields of vanadium permendur pole materials limit the highest field of the staggered array undulator. Hence, the staggered hybrid undulator can achieve a higher magnetic field than can the hybrid and the pure magnet in the short period
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 6 0 2 - 3
364
C.H. Chang et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 363–366
1
Opera-3D, Vector Field Ltd., Oxford, England.
Bz = 0.0 T Bz = 0.6 T
0.8 0.4 0.0 -0.4 -0.8
-10
-5
0
5
10
Z-axis (mm) By Field Strength (T)
undulator. A crossed staggered undulator (CSU) with rotatable magnetic arrays in series is proposed to produce higher brightness with arbitrary polarization states at higher photon energies. A short period 20-mm undulator with a 0.9 T magnetic field is selected to produce 1.4–4.0 KeV photons in the SRRC 1.5 GeV ring. Fig. 1 displays the configuration of the 1-m long staggered undulator. The alternating sinusoidal field was derived from the staggered hybrid magnetic array inside a solenoid coil. The iron blocks are constructed from vanadium permendur. The solenoid field is deflected vertically into each vanadium permendur face to form an alternating vertical field owing to the high permeability of vanadium permendur pole. A wedge pole was designed to achieve higher field strength. The NdFeB permanent magnet blocks placed between the wedge pole are arranged to enhance the alternating vertical magnetic field strength. Three-dimensional field analysis optimized the period magnetic structure on the permanent magnet and pole parameters. Magnetic field calculations were performed with TOSCA/OPERA-3D computer code.1 A notably high vertical magnetic field of 0.9 T was achieved by driving a longitudinal solenoid field of 0.7 T at a 5.5-mm gap width. The permanent magnet could not exceed 1.25 Hc to ensure reproducible magnet operation. The largest reverse solenoid field was limited to avert the
By Field Strength (T)
Fig. 1. Schematic diagram of 1-m long staggered hybrid undulator.
1.0 0.8 0.6 0.4 0.2 0.0 -20
-15
-10
-5
0
5
10
15
20
X-axis (mm)
Fig. 2. The measured vertical and transverse field profiles of one period mockup at 5.5 mm gap.
irreversible demagnetization of the permanent magnet. The field performance was examined using a one-period mockup. Fig. 2 presents the measured vertical field and transverse field profiles at a 5.5-mm gap, as determined by the field design. An anti-symmetric field configuration was designed under stringent magnetic field requirements to increase the effective magnetic pole. The configuration includes an adiabatic section at both ends of the undulator. Fig. 1
By Field Strength (T)
C.H. Chang et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 363–366 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0
Modulator Staggerd Undulator Bx
Staggerd Undulator By
e−
0
Bz Field Strength (T)
365
50
100
150
200
250
300
350
400
450
500
0.8
Fig. 4. Conceptual illustration of the proposed staggered undulator with rotating magnet arrays at 7451 in crossed configuration.
0.6 0.4 0.2 0.0 0
50
100
150
200
250
300
350
400
450
500
Z-axis (mm)
Fig. 3. The calculated vertical and longitudinal field distribution of half staggered undulator.
shows the proposed end configuration. The end pole field is analyzed using two-dimensional calculation approaches. The magnet blocks in the end pole can be partially adjusted to compensate the field integrals, and adjust the field distributions. Fig. 3 gives the calculated vertical and longitudinal field distribution of the half section of a staggered undulator. A total of 44 effective magnetic periods were predicted for a 1-m long undulator. The longitudinal field can be applied with the opposite polarity using the solenoid in two undulators to cancel the longitudinal field effect on the electron beam orbit. Accordingly, the integrated longitudinal fields from the two undulators cancel each other. To generate circular polarized radiation, one of these two staggered undulators must be rotated by 901 with respect to the other one such that the generated identical magnetic fields are mutually orthogonal [5]. The undulator requires a large acceptable horizontal aperture in the storage ring during the electron beam injection. This work offers both planar undulators with the null rotation to accommodate the geometrical limitation along the planar direction, and prevent the injected from being affected. Both magnet arrays in the undulator can be rotated after the electron beam has been stored in the storage ring, and the magnetic field can be then tuned to create the various polarized lights. The in-vacuum magnetic arrays were not constrained by the vacuum chamber on both horizontal and vertical planes simultaneously. The magnetic field amplitude in both undulators is identical. The linear and circular radiation on each harmonic can be produced by the CSU. The magnetic field on-axis can be adjusted to produce linear or circular polarization, as well as any intermediate orientation of magnetic arrays. When Bx ¼ By ;
the circular polarized radiation is maximized. The horizontal and vertical fields in crossed field must be maximized to extend the useful photon energy range. In our design with rotating magnetic arrays with a fixed gap width, the linear and circular polarization on-axis also can be rotated in any directions on the plane. Note that the rotatable feature of the CSU provides more useful polarizing states than does EPU. The CSU is rotated with respect to one another by 7451 about their common longitudinal axis and variable-phased along the same axis, as illustrated in Fig. 4. The time delay of two linear polarized radiations from the two staggered undulators is due to superposition of the coherent wavetrains in a monochromater to produce the desired polarized radiation. Scanning photon energy while maintaining a constant polarization state requires careful tuning of the modulator. A 3-pole electromagnetic modulator with a fixed gap is utilized as an optical phase shifter to manipulate the time delay between the radiation pulses from the upstream and downstream undulators [6]. The magnetic field within the modulator forces the electrons to be deflected on the same path as electromagnetic radiation, and produces a phase shift of at least 2p of phase at the lowest photon energy. The polarization state can be determined by setting the magnetic field of modulator. Experiments that make use of polarization often require a rapid switching of polarization orientation from left to right. The switching frequency can be as high as 10 Hz. As mentioned above, the circular polarized radiation generated from a CSU is achieved by temporal overlapping of two orthogonal radiation pulses generated from two in-series staggered undulators. Interference between the radiation pulses from the upstream and downstream staggered undulators leads to a variation which alters the circular polarization rate, even within the main spectral lob of the harmonics. Fig. 5 shows the first harmonic circular and linear spectral intensity of the CSU for a vertical field of 0.9 T. Note that the positive and negative values of the spectral intensity in Fig. 5 correspond to left and right circular polarization, respectively. The finite pinhole affected the interference conditions and led to depolarization [7]. The energy spread and finite emittance of the bunch beam
C.H. Chang et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 363–366
Fig. 5. First harmonic on-axis spectra of the crossed staggered undulator with a magnetic vertical field strength of 0.9 T. The dashed line displays the linear polarized spectrum. The solid line shows the circular polarized spectrum. The positive/ negative value of spectra intensity corresponds to the left/right circular polarized.
may contribute to the depolarization. A trade-off to optimize polarizing spectral property will be discussed elsewhere. Circular polarized radiation can be generated from a CSU at higher harmonics, as shown in Fig. 6 for the first, third and fifth harmonic for a vertical field from 0.9 to 0.4 T. The corresponding circular polarized spectral intensity will be twice that of the linear polarization from a single device. However, the CSU can also be used to generate linear polarized radiation in an arbitrary spatial orientation by rotating the two staggered undulators to the same angle. The effective linear spectral intensity is then four times of that from a single undulator. The merit flux is proportional to the square of the degree of circular polarization. Consequently, a CSU generates ideally circular polarized radiation at higher harmonics and a higher degree of polarization. An Apple II EPU generates circular polarized radiation only at the fundamental harmonic, but poorer polarization at higher harmonics. The CPU thus compares very favorably to the EPU. The CSU generates the optimal
Spectral Intensity [Photons/sec/m rad^2/0.1% BW /200 m A]
366
1E18
1E17
1E16
linear polarized: 1st linear polarized: 3rd linear polarized: 5th circular polarized: 1st circular polarized: 3rd circular polarized: 5th
1E15
500
1000
2000
3000
4000
Photon energy [eV]
Fig. 6. Spectral intensity of the crossed staggered undulator: linear (solid points) and circular (dot point) polarization at first, third and fifth harmonics. The solenoids are powered to generate a vertical magnetic field from 0.9 to 0.4 T.
merit flux at higher harmonics at higher photon energies. The authors would like to thank the National Science Council of the Republic of China for financially supporting this research under Contract No. 89-2112M-213-014.
References [1] S. Sasaki, Nucl. Instrum. Methods A 347 (1994) 83. [2] J. Bahrdt, et al., Rev. Sci. Instrum. 63 (1) (1992) 339. [3] Y.C. Huang, et al., Nucl. Instrum. Methods A 341 (1994) 431. [4] C.H. Chang, et al., Proceedings of the Seventh European Particle Accelerator Conference, pp. 2313–2315. [5] Kwang-Je Kim, Nucl. Instrum. Methods 219 (1984) 425. [6] R. Savoy, K. Halbach, Proceedings of the Particle Accelerator Conference, 1991, pp. 2718–2720. [7] P. Elleaume, Proceeding of the Fourth European Particle Accelerator Conference, pp. 1083–1087.