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Optics and beam transport in energy-recovery linacs
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Nuclear Instruments and Methods in Physics Research A 557 (2006) 45–50 www.elsevier.com/locate/nima
Optics and beam transport in energy-recovery linacs R. Hajima Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319–1195, Japan Available online 16 November 2005
Abstract An energy-recovery linac (ERL), which produces an electron beam of high-brightness and ultrashort pulse, is expected to play an important role in future accelerators. We review the following optics and beam dynamics issues relevant to ERLs: design of a recirculation loop and merger, suppression of beam-breakup, compensation of emittance growth, etc. r 2005 Elsevier B.V. All rights reserved. PACS: 29.27.Bd; 41.85.Ja Keywords: Energy-recovery linac; Optics; Beam transport
1. Introduction The combination of same-cell energy recovery and superconducting technology will have a great impact on future accelerators. The concept of energy-recovery linac (ERL) makes it possible to accelerate an electron beam of high power without requiring a large amount of RF-power. In an ERL, the energy of accelerated electrons is reconverted into RF energy and recycled to accelerate succeeding electrons. Therefore, it enables us to accelerate an electron beam of high-average current using RF generators of small capacity. Adding to this excellent efficiency is the fact that an ERL has advantages essential to future accelerators. Since an electron bunch in an ERL is directed to a beam dump after deceleration and another fresh electron bunch is accelerated, an ERL is free from degradation of electron beam brightness. This property of an ERL is rather different from that of a storage ring, in which the emittance and temporal duration of bunches are restricted by bunch thermalization during a number of turns. Dumping an electron beam after deceleration also simplifies the radiation shield required for ERLs. ERLs have been employed in high-power free-electron lasers (FEL) [1–3] owing to their capability of accelerating high-power, high-brightness electron beams. There are also Tel.: +81 29 282 6315; fax: +81 29 282 6057.
E-mail address: [email protected]. 0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.10.050
several proposals to develop ERL-based next-generation light sources, which unveil several possibilities for application in coherent X-ray science and ultrafast X-ray science [4]. High-power electron beams from ERLs will be utilized in accelerators for high-energy physics such as an electron cooler for an ion collider [5] and an electron–ion collider [6,7]. In these ERL applications, electron beam optics and transport design are the key technologies employed in order to make the most optimal use of high-brightness and ultrashort electron bunches generated by ERLs. The optics and beam transport have been a core subject in all accelerators with a number of studies being compiled. Since we cannot summarize all the earlier studies, we focus only on ERL-relevant issues in the present paper. 2. Design of recirculation loops In the design of a recirculation loop of an ERL, we should take into account the following items: footprint, energy acceptance, path-length tunability, bunch compression and stretching, emittance growth and aberrations, operation flexibility, etc. Fig. 1 shows the recirculation loop of ERLs in operation and under proposal. Energy acceptance is a critical parameter in ERL-FELs because FEL oscillation introduces a large energy spread in the electron bunch. Full energy spread may become 5–10% for a typical FEL operation with 1% conversion
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R. Hajima / Nuclear Instruments and Methods in Physics Research A 557 (2006) 45–50
Fig. 1. Recirculation loop for existing and proposed ERLs. (a) JLAB IR-demo and IR-upgrade, (b) JAERI ERL and Daresbury ERLP, (c) BINP ERLFEL, (d) BNL ERL for an electron cooler.
efficiency [8,9]. Transporting such an electron beam without any loss requires large energy acceptance in a recirculation loop. In the JLAB IR-demo and the IR-upgrade, a Bates-type arc is used, which is an isochronous arc consisting of a 1801 bending magnet inserted in the middle of a four-dipole chicane. This arc was originally developed for the energydoubling of a normal conducting linac, MIT Bates [10]. Since the energy acceptance in this arc is determined by the horizontal aperture size of the bending magnets, it is easy to maintain a large energy acceptance. The energy acceptance is 8% in the IR-demo and 15% in the IRupgrade [8]. Path-length tunability is achieved in a Batestype arc by a small horizontal steering of an electron beam before and after the 1801 bending magnet. A nonisochronous operation is also possible by inserting trim quadrupole magnets in the arc [11]. A recirculation loop consisting of triple-bend achromat (TBA) is utilized in the JAERI-ERL and the Daresbury ERL Prototype (ERLP) [12,13]. TBA is the minimum configuration required to realize an isochronous cell and has a smaller footprint than a Bates-type arc. Both ERLs
are equipped with two families of quadrupole magnets in the TBA cell for tuning a momentum compaction factor from negative values to positive values. In order to compensate for the second-order aberrations caused by a large energy spread, sextupole magnets are installed inside the TBA cell. Three major aberrations T 166 , T 266 , and T 566 can be compensated by two families of sextupole magnets. Since the total path length cannot be altered in TBA cells, they installed the arc on a movable table to control the path length, which is similar to the Darmstadt multi-pass linac [14]. BINP ERL (accelerator–recuperator) has a unique compact arc as shown in Fig. 1. In the design of recirculation loops for ERL light sources, relevant issues include maintaining a small emittance during recirculation, achieving small transverse beam size at an undulator for radiation of high brilliance and high coherence, and bunch compression availability for generating femtosecond X-ray pulses. In order to achieve flexible operation to switch an isochronous mode and a bunch compression mode while maintaining zero momentum dispersion at every straight section, we need TBA rather than double-bend achromat (DBA).
ARTICLE IN PRESS R. Hajima / Nuclear Instruments and Methods in Physics Research A 557 (2006) 45–50
3. Beam dynamics in the recirculation loop 3.1. Transverse dynamics In the study of transverse beam dynamics in a recirculation loop, emittance growth and its compensation is a matter of concern. The sources of emittance growth are incoherent synchrotron radiation (ISR), coherent synchrotron radiation (CSR), and higher-order aberrations. When an electron emits synchrotron radiation inside a bending magnet of an achromatic cell, the electron loses a portion of its energy—recoil of radiation—and strays from its intended trajectory. Consequently, the electron has a non-zero momentum dispersion at the exit of the achromatic cell. This chromaticity violation results in increase of horizontal emittance. Photon emission occurs as a stochastic process for ISR, which has a radiation peak at the X-ray wavelength. The emittance growth, hence, should be discussed by means of a stochastic approach. On the other hand, the CSR recoil can be analyzed in a deterministic manner because the radiation has a peak at a wavelength around the far-infrared or millimeter region and a number of photons are emitted from a single electron through a bending magnet. It is observed that the amount of energy change for each electron is a function of its position in the electron bunch. In the ultrarelativistic regime, a one-dimensional model gives a good approximation and the CSR effects are represented by a longitudinal wake potential. The emittance growth in this regime appears as a displacement of bunch slices correlated to the longitudinal position in the bunch where slice emittance is preserved. The CSR-induced emittance growth has been a topic of interest in the design of bunch compressors for SASEFELs ever since the first suggestion of this phenomenon [15,16]. In order to solve this problem, extensive numerical and experimental work have been carried out. For the compensation of the CSR-induced emittance growth in an ERL recirculation loop, two design strategies have been proposed. One is by applying multiple CSR kicks to cancel each other by setting the cell-to-cell betatron phase advance to an appropriate value [17,18]. The other is by matching the CSR kick to the orientation of the phase ellipse at the cell exit [19]. These optimizations of an ERL loop can be carried out by using first-order beam transport analysis [19,20]. 3.2. Longitudinal dynamics In the case of the longitudinal beam dynamics, the compression and stretch of an electron bunch and the compression of energy spread after FEL lasing are the issues that need to be discussed. In the general design of ERL light sources, femtosecond electron bunches are generated by magnetic bunch compression during a recirculation loop [21–23] for the following reasons: (1) bunch length at the injection must be
47
sufficiently long to avoid emittance growth in a merger, (2) bunch length at the main linac must be sufficiently long so as not to excite large higher-order mode (HOM) power, (3) installation of a chicane-type bunch compressor inside the main linac causes difficulty in the ERL operation due to the path-length variation for the two beams. In a typical design, the bunch length during acceleration is chosen as 2–3 ps for the L-band linac to manage both moderate HOM power and the small energy spread induced by the RF curvature. This electron bunch is then compressed to 100 fs in the recirculation loop. An alternative scheme for the bunch compression— velocity bunching in a main linac—has been proposed [24]. In ERL light sources for femtosecond X-ray radiation, velocity bunching provides higher brilliance than magnetic compression because the residual energy spread of an electron bunch has a smaller value in the velocity bunching. In the recirculation loop for an ERL-FEL, the compression of energy spread induced by the FEL interaction is also an important issue as is the bunch compression to obtain a high FEL gain. When an electron bunch with energy spread is decelerated, the relative spread increases by the ratio of the initial to final energy. The energy spread, therefore, may become as large as 100% at the beam dump after deceleration, and a complete energy recovery operation is rather difficult. Reduction of the energy spread after deceleration can be achieved by rotating the electron bunch in the longitudinal phase space; this is also referred to as energy compression. In the JLAB IR-demo, the energy compression is realized by a non-isochronous setting of the return arc, and the nonlinear effect due to the curvature of the RF is compensated by tuning sextupoles at the return arc [11]. The return arc of JAERI-ERL is based on the same principle [9]. In the recirculation loop of an electron cooler, an electron bunch accelerated by the linac is stretched and transported to a cooling channel and compressed again before its reinjection into the linac. The energy spread in the stretched bunch is reduced by a harmonic cavity for effective cooling [5]. 4. Beam dynamics in the linac 4.1. HOM-BBU A critical subject of beam dynamics in an ERL main linac is the multi-bunch multi-pass instability driven by transverse HOMs, which restricts the average current in an ERL. There exist higher-order eigenmodes having transverse electric fields in an accelerating cavity, which are referred to as dipole modes or deflecting modes. These modes are excited by an electron beam injected off-axis or even excited without an electron beam due to the asymmetric structure in the cavity such as couplers. This transverse HOM applies a transverse kick upon an electron bunch which is injected off-axis. If the
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R. Hajima / Nuclear Instruments and Methods in Physics Research A 557 (2006) 45–50
kicked electron bunch returns after recirculation at the position and the phase exciting the HOM, the HOM power grows exponentially and finally leads to beam breakup (BBU). In a simple configuration comprising a single cavity and single HOM, the threshold current of HOM-BBU is derived based on analytical theory [25]. The threshold current for practical ERLs with multi-cavity and multiHOMs must be estimated by numerical simulations. The algorithm for HOM-BBU simulation is classified into two categories. One is a particle tracking method, in which the HOM fields and position of electron bunches are refreshed at every time step by taking into account HOM excitation and damping [26,27]. The other method is based on eigenvalue equations [28]. In the JLAB IR-upgrade, HOM-BBU was observed experimentally at a beam current of 3 mA, which restricts the performance of the ERL-FEL [29]. Since the acceleration of a large current beam is an essential advantage of an ERL, the suppression of the HOM-BBU is absolutely important in the ERL development. The threshold current of HOM-BBU can be increased by using a superconducting cavity driven at lower frequency, which has a smaller transverse impedance and larger damping for HOMs. The ERL for the RHIC electron cooler uses 700 MHz superconducting cavities, which will be operated at an average current of over 1 A [30,31]. Tuning a beam envelope through the linac is also effective in suppressing the HOM-BBU. The threshold current is proportional to the inverse of the first-order matrix elements R12 and R34 [25]; these parameters can be controlled by beam envelopes of accelerating and decelerating beams. However, in a long linac such as an ERL light source, it is difficult to maintain small values of R12 and R34 throughout in the linac because of a large difference in the electron energy of two beams. The design studies of ERL light sources show that the threshold current of HOM-BBU after the optimization of the beam envelope along the linac is approximately 200 mA for moderate parameters, an accelerating gradient of 20 MV/m and HOM randomization of 1 MHz [21,27]. The beam instability arising from HOM can also be suppressed by rotating an electron bunch in the transverse space during the recirculation loop [32]. Each deflecting HOM has a specific polarization in the transverse space, ðx; yÞ and kicks an electron bunch in this direction. If the kicked bunch is rotated by 901 in the transverse space through the recirculation loop, the bunch is decoupled with the deflecting mode after the recirculation and we can suppress the exponential growth of the mode. The manipulation of an electron bunch in such a manner can be achieved using a skewed quadrupole magnet or a solenoid magnet installed in a recirculation loop. In the JLAB IR-upgrade, skewed quadrupole magnets have been installed in the recirculation loop for this purpose. The threshold current of the IR-upgrade is expected to increase by 10 times or more [29].
4.2. Longitudinal wakefield An electron bunch passing through an accelerating cavity induces a wakefield in the cavity. For the acceleration of a high-average current beam by a superconducting accelerator, the excitation of a longitudinal wakefield— longitudinal HOMs—is a critical phenomenon. Longitudinal HOMs have large power in the wavelength around the bunch length—1 mm typically. According to the BCS theory of superconductivity, the surface resistivity of a superconducting material increases with the square of the RF frequency. The longitudinal HOMs, therefore, may result in an additional heat load in the cavity. As an example pertaining to TESLA 9-cell cavities [33], the dissipated HOM power for ERL operation at 100 mA (77 pC, 1.3 GHz) is calculated as 170 W for 3 ps bunches, and 275 W for 100 fs bunches. Since these two values of HOM power are significantly higher than the original design of TESLA—2 W for collider-mode operation—the cavity should be modified for the efficient extraction of excited HOM. A large portion of the longitudinal wakefield is distributed over untrapped modes, which have frequencies higher than the cut-off frequency of cavity’s beam pipe and travels through the beam pipe. These untrapped modes can be absorbed by lossy material such as ferrite loads installed in a beam pipe. This type of a HOM coupler has been developed for high-average current storage rings, and maximum outcoupled power higher than 1 kW has been demonstrated [34]. We consider that similar on-axis couplers can be applied to accelerating cavities for ERLs. The HOMs trapped in the cavity should be damped by off-axis couplers installed close to the cavity cells. Several designs have been proposed for this purpose [35]. The operation of an L-band ERL with average current over 100 mA is reasonably attainable by an appropriate combination of on-axis and off-axis couplers. 5. Beam dynamics in the merger Another component specific to ERL beam transport is a merger, which merges two beams—a low-energy injection beam and a high-energy recirculation beam—into the same trajectory. An ERL merger consists of an achromatic bending path, which is a combination of dipole magnets. Fig. 2 shows the merger configuration of ERLs in operation and under proposal. In an ERL merger, the emittance dilution may occur by transverse space charge force, longitudinal space charge force, and CSR. The emittance growth due to the transverse space charge force can be compensated in the same manner as the emittance compensation at a photocathode RF gun and a solenoid magnet [36]. In an ERL merger, the beam envelope is asymmetric in the horizontal and vertical plane because of the bending magnets, while a beam maintains an axisymmetric envelope in the case of the RF gun and solenoid magnet. This asymmetric envelope in an ERL merger complicates
ARTICLE IN PRESS R. Hajima / Nuclear Instruments and Methods in Physics Research A 557 (2006) 45–50
(a)
(b)
(c)
(d)
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Fig. 2. Mergers for existing and proposed ERLs. (a) JLAB IR-demo, IR-upgrade, Daresbury ERLP, (b) JAERI-ERL, (c) BINP-ERL, (d) BNL-ERL (proposed).
emittance compensation. However, an optimum beam envelope for minimum emittance growth can be obtained by numerical simulation by scanning the Courant–Snyder parameters at the merger entrance [37]. Longitudinal space charge force is also a source of emittance growth in a merger. The process of emittance growth here is similar to the CSR-induced emittance growth, which can be explained as a violation of the achromatic condition after the redistribution of electron energy inside a bunch traveling via a dispersive path. The emittance growth by longitudinal space charge force has been studied since the early development of a highbrightness electron beam from a photocathode RF gun [38]. This emittance growth can be compensated by the envelope matching technique as well as the CSR case. The matched envelope, in general, is not consistent with emittance compensation for transverse space charge force, and we cannot simultaneously compensate two sources of emittance growth [37]. A novel type of ERL merger—a zigzag merger—was recently proposed [39]. The zigzag merger shows a better fitting to the emittance compensation. The transverse emittance growth is efficiently suppressed by optimizing the solenoid magnet before the merger. The effects of CSR in an ERL merger are subtle problems because a one-dimensional pencil beam approximation does not hold in a low-energy regime. Although a three-dimensional CSR simulation code based on particle tracking such as TraFiC4 [40] is applicable to the analysis, the simulation requires a huge calculation time. An alternative simulation technique based on mesh calculation was recently developed for the CSR analysis [41]. This mesh calculation can be adapted to the low-energy regime after minor modification.
beam motion affected by wakefields, etc. However, we have also seen research subjects that are unique to ERLs, such as suppression of HOM-BBU and emittance compensation in a merger. These subjects should be investigated intensively for realizing an ERL that produces an electron beam of high-brightness, high-average current, and ultrashort pulses. It is highly recommended to construct an ERL prototype for carrying out these research activities.
6. Summary
[18]
We have reviewed optics and beam dynamics issues relevant to ERLs. Some of them are general subjects in accelerator development, such as the design of achromatic cells, emittance growth by space charge force and CSR,
[19] [20]
Acknowledgements The author acknowledges JPPS-15360507 for financial support. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
[21]
G.R. Neil, et al., Phys. Rev. Lett. 84 (2000) 662. R. Hajima, et al., Nucl. Instr. and Meth. A 507 (2003) 115. E.A. Antokhin, et al., Nucl. Instr. and Meth. A 528 (2004) 15. Sol M. Gruner, et al., Rev. Sci. Instr. 73 (2002) 1402. Jo¨rg Kewisch, et al., in: Proceedings of 2003 Particle Accelerator Conference, p. 2005. Ya. Derbenev, et al., in: Proceedings of European Particle Accelerator Conference 2004, p. 893. V. Ptitsyn, et al., in: Proceedings of European Particle Accelerator Conference 2004, p. 923. S.V. Benson, Nucl. Instr. and Meth. A 483 (2002) 1. R. Hajima, E.J. Minehara, Nucl. Instr. and Meth. A 507 (2003) 141. J.B. Flanz, C.P. Sargent, Nucl. Instr. and Meth. A 241 (1985) 325. P. Piot, D.R. Douglas, G.A. Krafft, Phys. Rev. ST Accel. Beams 6 (2003) 030702. R. Hajima, et al., Nucl. Instr. and Meth. A 445 (2000) 384. B. Muratori, H.L. Owen, J.A. Varley, in: Proceedings of European Particle Accelerator Conference 2004, p. 449. V. Aab, et al., Nucl. Instr. and Meth. A 272 (1988) 53. Y.S. Derbenev, et al., TESLA-95-05, 1995. B.E. Carlsten, Phys. Rev. E 54 (1996) 838. D. Douglas, Thomas Jefferson National Accelerator Laboratory Technical Note, JLAB-TN-98-012, 1998. J.H. Wu, et al., in: Proceedings of 2001 Particle Accelerator Conference, p. 2866. R. Hajima, Jpn. J. Appl. Phys. 42 (2003) L974. R. Hajima, in: Proceedings of the Third Asian Particle Accelerator Conference, 2004. S.M. Gruner, M. Tigner, CHESS Technical Memo 01-003/JLABACT-01-004, 2001.
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[22] V. Yakimenko, et al., in: Proceedings of 2001 Particle Accelerator Conference, p. 3344. [23] M. Sawamura, et al., in: Proceedings of 2003 Particle Accelerator Conference, p. 2117. [24] H. Iijima, R. Hajima, Nucl. Instr. and Meth. A, in these Proceedings, doi: 10.1016/j.nima.2005.10.071. [25] G.H. Hoffstaetter, I.V. Bazarov, Phys. Rev. Spec. Top-Ac. 7 (2004) 054401. [26] G.A. Krafft, J.J. Bisognano, in: Proceedings of 1987 Particle Accelerator Conference, p. 1356. [27] R.Nagai, et al., in: Proceedings of 2003 Particle Accelerator Conference, p. 3443. [28] K. Beard, L. Merminga, B. Yunn, in: Proceedings of 2003 Particle Accelerator Conference, p. 332. [29] C. Tennant, et al., in: Proceedings of the 26th International FEL Conference, 2004, p. 590. [30] I. Ben-Zvi, et al., in: Proceedings of 2003 Particle Accelerator Conference, p. 39.
[31] D. Wang, et al., in: Proceedings of 2003 Particle Accelerator Conference, p. 1300. [32] R. Rand, T. Smith, Part. Accel. 2 (1980) 1. [33] F. Richard, et al., TESLA Technical Design Report, 2001. [34] T. Tajima, et al., in: Proceedings of Sixth Workshop on RF Superconductivity, 1993. [35] R.A. Rimmer, et al., in: Proceedings of 2003 Particle Accelerator Conference, p. 1389. [36] B.E. Carlsten, Nucl. Instr. and Meth. A 285 (1989) 313. [37] R. Hajima, Nucl. Instr. and Meth. A, in these Proceedings, doi: 10.1016/j.nima.2005.10.065. [38] B.E. Carlsten, et al., IEEE QE 27 (1991) 2580. [39] V.N. Litvinenko, et al., in: Proceedings of the 26th International FEL Conference, 2004, p. 570. [40] A. Kabel, M. Dohlus, T. Limberg, Nucl. Instr. and Meth. A 455 (2000) 185. [41] T. Agoh, K. Yokoya, Phys. Rev. ST Accel. Beams 7 (2004) 054403.
Nuclear Instruments and Methods in Physics Research A 557 (2006) 45–50 www.elsevier.com/locate/nima
Optics and beam transport in energy-recovery linacs R. Hajima Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319–1195, Japan Available online 16 November 2005
Abstract An energy-recovery linac (ERL), which produces an electron beam of high-brightness and ultrashort pulse, is expected to play an important role in future accelerators. We review the following optics and beam dynamics issues relevant to ERLs: design of a recirculation loop and merger, suppression of beam-breakup, compensation of emittance growth, etc. r 2005 Elsevier B.V. All rights reserved. PACS: 29.27.Bd; 41.85.Ja Keywords: Energy-recovery linac; Optics; Beam transport
1. Introduction The combination of same-cell energy recovery and superconducting technology will have a great impact on future accelerators. The concept of energy-recovery linac (ERL) makes it possible to accelerate an electron beam of high power without requiring a large amount of RF-power. In an ERL, the energy of accelerated electrons is reconverted into RF energy and recycled to accelerate succeeding electrons. Therefore, it enables us to accelerate an electron beam of high-average current using RF generators of small capacity. Adding to this excellent efficiency is the fact that an ERL has advantages essential to future accelerators. Since an electron bunch in an ERL is directed to a beam dump after deceleration and another fresh electron bunch is accelerated, an ERL is free from degradation of electron beam brightness. This property of an ERL is rather different from that of a storage ring, in which the emittance and temporal duration of bunches are restricted by bunch thermalization during a number of turns. Dumping an electron beam after deceleration also simplifies the radiation shield required for ERLs. ERLs have been employed in high-power free-electron lasers (FEL) [1–3] owing to their capability of accelerating high-power, high-brightness electron beams. There are also Tel.: +81 29 282 6315; fax: +81 29 282 6057.
E-mail address: [email protected]. 0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.10.050
several proposals to develop ERL-based next-generation light sources, which unveil several possibilities for application in coherent X-ray science and ultrafast X-ray science [4]. High-power electron beams from ERLs will be utilized in accelerators for high-energy physics such as an electron cooler for an ion collider [5] and an electron–ion collider [6,7]. In these ERL applications, electron beam optics and transport design are the key technologies employed in order to make the most optimal use of high-brightness and ultrashort electron bunches generated by ERLs. The optics and beam transport have been a core subject in all accelerators with a number of studies being compiled. Since we cannot summarize all the earlier studies, we focus only on ERL-relevant issues in the present paper. 2. Design of recirculation loops In the design of a recirculation loop of an ERL, we should take into account the following items: footprint, energy acceptance, path-length tunability, bunch compression and stretching, emittance growth and aberrations, operation flexibility, etc. Fig. 1 shows the recirculation loop of ERLs in operation and under proposal. Energy acceptance is a critical parameter in ERL-FELs because FEL oscillation introduces a large energy spread in the electron bunch. Full energy spread may become 5–10% for a typical FEL operation with 1% conversion
ARTICLE IN PRESS 46
R. Hajima / Nuclear Instruments and Methods in Physics Research A 557 (2006) 45–50
Fig. 1. Recirculation loop for existing and proposed ERLs. (a) JLAB IR-demo and IR-upgrade, (b) JAERI ERL and Daresbury ERLP, (c) BINP ERLFEL, (d) BNL ERL for an electron cooler.
efficiency [8,9]. Transporting such an electron beam without any loss requires large energy acceptance in a recirculation loop. In the JLAB IR-demo and the IR-upgrade, a Bates-type arc is used, which is an isochronous arc consisting of a 1801 bending magnet inserted in the middle of a four-dipole chicane. This arc was originally developed for the energydoubling of a normal conducting linac, MIT Bates [10]. Since the energy acceptance in this arc is determined by the horizontal aperture size of the bending magnets, it is easy to maintain a large energy acceptance. The energy acceptance is 8% in the IR-demo and 15% in the IRupgrade [8]. Path-length tunability is achieved in a Batestype arc by a small horizontal steering of an electron beam before and after the 1801 bending magnet. A nonisochronous operation is also possible by inserting trim quadrupole magnets in the arc [11]. A recirculation loop consisting of triple-bend achromat (TBA) is utilized in the JAERI-ERL and the Daresbury ERL Prototype (ERLP) [12,13]. TBA is the minimum configuration required to realize an isochronous cell and has a smaller footprint than a Bates-type arc. Both ERLs
are equipped with two families of quadrupole magnets in the TBA cell for tuning a momentum compaction factor from negative values to positive values. In order to compensate for the second-order aberrations caused by a large energy spread, sextupole magnets are installed inside the TBA cell. Three major aberrations T 166 , T 266 , and T 566 can be compensated by two families of sextupole magnets. Since the total path length cannot be altered in TBA cells, they installed the arc on a movable table to control the path length, which is similar to the Darmstadt multi-pass linac [14]. BINP ERL (accelerator–recuperator) has a unique compact arc as shown in Fig. 1. In the design of recirculation loops for ERL light sources, relevant issues include maintaining a small emittance during recirculation, achieving small transverse beam size at an undulator for radiation of high brilliance and high coherence, and bunch compression availability for generating femtosecond X-ray pulses. In order to achieve flexible operation to switch an isochronous mode and a bunch compression mode while maintaining zero momentum dispersion at every straight section, we need TBA rather than double-bend achromat (DBA).
ARTICLE IN PRESS R. Hajima / Nuclear Instruments and Methods in Physics Research A 557 (2006) 45–50
3. Beam dynamics in the recirculation loop 3.1. Transverse dynamics In the study of transverse beam dynamics in a recirculation loop, emittance growth and its compensation is a matter of concern. The sources of emittance growth are incoherent synchrotron radiation (ISR), coherent synchrotron radiation (CSR), and higher-order aberrations. When an electron emits synchrotron radiation inside a bending magnet of an achromatic cell, the electron loses a portion of its energy—recoil of radiation—and strays from its intended trajectory. Consequently, the electron has a non-zero momentum dispersion at the exit of the achromatic cell. This chromaticity violation results in increase of horizontal emittance. Photon emission occurs as a stochastic process for ISR, which has a radiation peak at the X-ray wavelength. The emittance growth, hence, should be discussed by means of a stochastic approach. On the other hand, the CSR recoil can be analyzed in a deterministic manner because the radiation has a peak at a wavelength around the far-infrared or millimeter region and a number of photons are emitted from a single electron through a bending magnet. It is observed that the amount of energy change for each electron is a function of its position in the electron bunch. In the ultrarelativistic regime, a one-dimensional model gives a good approximation and the CSR effects are represented by a longitudinal wake potential. The emittance growth in this regime appears as a displacement of bunch slices correlated to the longitudinal position in the bunch where slice emittance is preserved. The CSR-induced emittance growth has been a topic of interest in the design of bunch compressors for SASEFELs ever since the first suggestion of this phenomenon [15,16]. In order to solve this problem, extensive numerical and experimental work have been carried out. For the compensation of the CSR-induced emittance growth in an ERL recirculation loop, two design strategies have been proposed. One is by applying multiple CSR kicks to cancel each other by setting the cell-to-cell betatron phase advance to an appropriate value [17,18]. The other is by matching the CSR kick to the orientation of the phase ellipse at the cell exit [19]. These optimizations of an ERL loop can be carried out by using first-order beam transport analysis [19,20]. 3.2. Longitudinal dynamics In the case of the longitudinal beam dynamics, the compression and stretch of an electron bunch and the compression of energy spread after FEL lasing are the issues that need to be discussed. In the general design of ERL light sources, femtosecond electron bunches are generated by magnetic bunch compression during a recirculation loop [21–23] for the following reasons: (1) bunch length at the injection must be
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sufficiently long to avoid emittance growth in a merger, (2) bunch length at the main linac must be sufficiently long so as not to excite large higher-order mode (HOM) power, (3) installation of a chicane-type bunch compressor inside the main linac causes difficulty in the ERL operation due to the path-length variation for the two beams. In a typical design, the bunch length during acceleration is chosen as 2–3 ps for the L-band linac to manage both moderate HOM power and the small energy spread induced by the RF curvature. This electron bunch is then compressed to 100 fs in the recirculation loop. An alternative scheme for the bunch compression— velocity bunching in a main linac—has been proposed [24]. In ERL light sources for femtosecond X-ray radiation, velocity bunching provides higher brilliance than magnetic compression because the residual energy spread of an electron bunch has a smaller value in the velocity bunching. In the recirculation loop for an ERL-FEL, the compression of energy spread induced by the FEL interaction is also an important issue as is the bunch compression to obtain a high FEL gain. When an electron bunch with energy spread is decelerated, the relative spread increases by the ratio of the initial to final energy. The energy spread, therefore, may become as large as 100% at the beam dump after deceleration, and a complete energy recovery operation is rather difficult. Reduction of the energy spread after deceleration can be achieved by rotating the electron bunch in the longitudinal phase space; this is also referred to as energy compression. In the JLAB IR-demo, the energy compression is realized by a non-isochronous setting of the return arc, and the nonlinear effect due to the curvature of the RF is compensated by tuning sextupoles at the return arc [11]. The return arc of JAERI-ERL is based on the same principle [9]. In the recirculation loop of an electron cooler, an electron bunch accelerated by the linac is stretched and transported to a cooling channel and compressed again before its reinjection into the linac. The energy spread in the stretched bunch is reduced by a harmonic cavity for effective cooling [5]. 4. Beam dynamics in the linac 4.1. HOM-BBU A critical subject of beam dynamics in an ERL main linac is the multi-bunch multi-pass instability driven by transverse HOMs, which restricts the average current in an ERL. There exist higher-order eigenmodes having transverse electric fields in an accelerating cavity, which are referred to as dipole modes or deflecting modes. These modes are excited by an electron beam injected off-axis or even excited without an electron beam due to the asymmetric structure in the cavity such as couplers. This transverse HOM applies a transverse kick upon an electron bunch which is injected off-axis. If the
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kicked electron bunch returns after recirculation at the position and the phase exciting the HOM, the HOM power grows exponentially and finally leads to beam breakup (BBU). In a simple configuration comprising a single cavity and single HOM, the threshold current of HOM-BBU is derived based on analytical theory [25]. The threshold current for practical ERLs with multi-cavity and multiHOMs must be estimated by numerical simulations. The algorithm for HOM-BBU simulation is classified into two categories. One is a particle tracking method, in which the HOM fields and position of electron bunches are refreshed at every time step by taking into account HOM excitation and damping [26,27]. The other method is based on eigenvalue equations [28]. In the JLAB IR-upgrade, HOM-BBU was observed experimentally at a beam current of 3 mA, which restricts the performance of the ERL-FEL [29]. Since the acceleration of a large current beam is an essential advantage of an ERL, the suppression of the HOM-BBU is absolutely important in the ERL development. The threshold current of HOM-BBU can be increased by using a superconducting cavity driven at lower frequency, which has a smaller transverse impedance and larger damping for HOMs. The ERL for the RHIC electron cooler uses 700 MHz superconducting cavities, which will be operated at an average current of over 1 A [30,31]. Tuning a beam envelope through the linac is also effective in suppressing the HOM-BBU. The threshold current is proportional to the inverse of the first-order matrix elements R12 and R34 [25]; these parameters can be controlled by beam envelopes of accelerating and decelerating beams. However, in a long linac such as an ERL light source, it is difficult to maintain small values of R12 and R34 throughout in the linac because of a large difference in the electron energy of two beams. The design studies of ERL light sources show that the threshold current of HOM-BBU after the optimization of the beam envelope along the linac is approximately 200 mA for moderate parameters, an accelerating gradient of 20 MV/m and HOM randomization of 1 MHz [21,27]. The beam instability arising from HOM can also be suppressed by rotating an electron bunch in the transverse space during the recirculation loop [32]. Each deflecting HOM has a specific polarization in the transverse space, ðx; yÞ and kicks an electron bunch in this direction. If the kicked bunch is rotated by 901 in the transverse space through the recirculation loop, the bunch is decoupled with the deflecting mode after the recirculation and we can suppress the exponential growth of the mode. The manipulation of an electron bunch in such a manner can be achieved using a skewed quadrupole magnet or a solenoid magnet installed in a recirculation loop. In the JLAB IR-upgrade, skewed quadrupole magnets have been installed in the recirculation loop for this purpose. The threshold current of the IR-upgrade is expected to increase by 10 times or more [29].
4.2. Longitudinal wakefield An electron bunch passing through an accelerating cavity induces a wakefield in the cavity. For the acceleration of a high-average current beam by a superconducting accelerator, the excitation of a longitudinal wakefield— longitudinal HOMs—is a critical phenomenon. Longitudinal HOMs have large power in the wavelength around the bunch length—1 mm typically. According to the BCS theory of superconductivity, the surface resistivity of a superconducting material increases with the square of the RF frequency. The longitudinal HOMs, therefore, may result in an additional heat load in the cavity. As an example pertaining to TESLA 9-cell cavities [33], the dissipated HOM power for ERL operation at 100 mA (77 pC, 1.3 GHz) is calculated as 170 W for 3 ps bunches, and 275 W for 100 fs bunches. Since these two values of HOM power are significantly higher than the original design of TESLA—2 W for collider-mode operation—the cavity should be modified for the efficient extraction of excited HOM. A large portion of the longitudinal wakefield is distributed over untrapped modes, which have frequencies higher than the cut-off frequency of cavity’s beam pipe and travels through the beam pipe. These untrapped modes can be absorbed by lossy material such as ferrite loads installed in a beam pipe. This type of a HOM coupler has been developed for high-average current storage rings, and maximum outcoupled power higher than 1 kW has been demonstrated [34]. We consider that similar on-axis couplers can be applied to accelerating cavities for ERLs. The HOMs trapped in the cavity should be damped by off-axis couplers installed close to the cavity cells. Several designs have been proposed for this purpose [35]. The operation of an L-band ERL with average current over 100 mA is reasonably attainable by an appropriate combination of on-axis and off-axis couplers. 5. Beam dynamics in the merger Another component specific to ERL beam transport is a merger, which merges two beams—a low-energy injection beam and a high-energy recirculation beam—into the same trajectory. An ERL merger consists of an achromatic bending path, which is a combination of dipole magnets. Fig. 2 shows the merger configuration of ERLs in operation and under proposal. In an ERL merger, the emittance dilution may occur by transverse space charge force, longitudinal space charge force, and CSR. The emittance growth due to the transverse space charge force can be compensated in the same manner as the emittance compensation at a photocathode RF gun and a solenoid magnet [36]. In an ERL merger, the beam envelope is asymmetric in the horizontal and vertical plane because of the bending magnets, while a beam maintains an axisymmetric envelope in the case of the RF gun and solenoid magnet. This asymmetric envelope in an ERL merger complicates
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(a)
(b)
(c)
(d)
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Fig. 2. Mergers for existing and proposed ERLs. (a) JLAB IR-demo, IR-upgrade, Daresbury ERLP, (b) JAERI-ERL, (c) BINP-ERL, (d) BNL-ERL (proposed).
emittance compensation. However, an optimum beam envelope for minimum emittance growth can be obtained by numerical simulation by scanning the Courant–Snyder parameters at the merger entrance [37]. Longitudinal space charge force is also a source of emittance growth in a merger. The process of emittance growth here is similar to the CSR-induced emittance growth, which can be explained as a violation of the achromatic condition after the redistribution of electron energy inside a bunch traveling via a dispersive path. The emittance growth by longitudinal space charge force has been studied since the early development of a highbrightness electron beam from a photocathode RF gun [38]. This emittance growth can be compensated by the envelope matching technique as well as the CSR case. The matched envelope, in general, is not consistent with emittance compensation for transverse space charge force, and we cannot simultaneously compensate two sources of emittance growth [37]. A novel type of ERL merger—a zigzag merger—was recently proposed [39]. The zigzag merger shows a better fitting to the emittance compensation. The transverse emittance growth is efficiently suppressed by optimizing the solenoid magnet before the merger. The effects of CSR in an ERL merger are subtle problems because a one-dimensional pencil beam approximation does not hold in a low-energy regime. Although a three-dimensional CSR simulation code based on particle tracking such as TraFiC4 [40] is applicable to the analysis, the simulation requires a huge calculation time. An alternative simulation technique based on mesh calculation was recently developed for the CSR analysis [41]. This mesh calculation can be adapted to the low-energy regime after minor modification.
beam motion affected by wakefields, etc. However, we have also seen research subjects that are unique to ERLs, such as suppression of HOM-BBU and emittance compensation in a merger. These subjects should be investigated intensively for realizing an ERL that produces an electron beam of high-brightness, high-average current, and ultrashort pulses. It is highly recommended to construct an ERL prototype for carrying out these research activities.
6. Summary
[18]
We have reviewed optics and beam dynamics issues relevant to ERLs. Some of them are general subjects in accelerator development, such as the design of achromatic cells, emittance growth by space charge force and CSR,
[19] [20]
Acknowledgements The author acknowledges JPPS-15360507 for financial support. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
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