- Email: [email protected]
Permanent magnet systems for free-electron lasers
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185
Permanent magnet systems for free-electron lasers Steve C. Gottschalka,*, David H. Dowellb, David C. Quimbya b
a STI Optronics Inc., 2755 Northup Way, Bellevue, WA 98004-1495, USA Stanford Linear Accelerator Center, Mail Stop 18, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
Abstract We review uses of permanent magnets (PMs) in free-electron lasers (FELs). Recently, PMs have been considered to replace many of the electromagnet (EM) dipoles, quadrupoles, and sextupoles in FEL beamlines and linear collider quadrupoles. PM beamline optics offer several advantages over EMs (Proceedings of the Particle Acceleration Conference, 2001, p. 3218). They are more compact, need no power, and do not require cooling water. In addition, adjustable-strength quadrupoles may have a precisely tuneable magnetic centerline. High pole tip fields (1.5 T in dipoles and 1.2 T in quadrupoles) are easily achieved. PM technology opens up new bend design possibilities. We describe a new, high performance, all-PM bend, the Ballard bend, that is first-order isochronous and doubly achromatic. It is suitable for use in the exhaust beam leg of an energy recovery FEL. We have designed and built a compact, high field sector PM dipole. Measured field profiles agree to 10 ppm of predictions. Compact PM quadrupoles were also designed and built. Measurements of field strength, axial profile, magnetic centerline tuning, and passive temperature compensation of strength and centerline shift agreed very well with predictions. Published by Elsevier Science B.V. PACS: 07.55.Db; 29.27.Eg; 41.85.L.c; 41.85.Ja Keywords: Free-electron lasers; Permanent magnets; Beamline optics; Dipoles; Quadrupoles; Sextupoles
1. Introduction The main advantage of permanent magnets (PMs) is that they do not waste power as heat to create a magnetic field. PMs are candidates to replace any room temperature DC electromagnet (EM) in accelerator or free-electron laser (FEL) systems. Recently, there has been interest in extending the use of PMs to include beamline optics [1–4], compact bends [5,6], pulse compressors and periodic permanent magnet klystrons [7]. PM quadrupoles are considered a viable alter*Corresponding author. E-mail address: [email protected] (S.C. Gottschalk). 0168-9002/03/$ - see front matter Published by Elsevier Science B.V. doi:10.1016/S0168-9002(03)00867-2
native for the Next Linear Collider (NLC) Main Line quadrupoles. PM multipoles are potentially more economical and reliable than EMs because of the elimination of high-current power supplies, cooling water and associated plumbing. Maintenance issues for EMs are well known. The relative long-term operating cost of PMs is essentially zero. The Fermilab Transfer line [8] and Recycler [9] use over 500 PM gradient dipoles, quadrupoles and sextupoles. Hybrid PM technology uses steel poles for high magnetic field strength and precision field shaping. Their compact size and simplicity allow new design approaches, including tuneable PM multipoles for improved electron beam (e-beam) quality
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S.C. Gottschalk et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185
preservation in beamlines that are smaller, more rugged, lower in cost, and lighter in weight compared to current EM designs. A unique feature of the PM quadrupole design we will discuss is the ability to adjust the magnetic centerline without the use of movers. NLC quadrupole designs have a 20 mechanical advantage: a 20 mm movement of magnets can produce a 1 mm centerline shift. This can allow accurate centerline control using lower resolution equipment.
Fig. 1. Hybrid quadrupole.
2. PM beamline optics There are a wide range of PM multipoles. The classic example is the Halbach design [10]. This is constructed from pie-shaped rare earth permanent magnet blocks (REPM) magnetized azimuthally and arranged to mimic the desired multipolar field distribution. Most applications of this style have fixed magnet strengths [11], but adjustablestrength versions have been made [12]. The adjustment process uses rotating and counterrotating REPM rings whose skew fields must precisely cancel. There are no means for keeping the multipole centers aligned as the magnets are rotated. Maximum pole tip fields are limited by demagnetization in the REPM wedges [11] to a level of 1.1 T. Since the magnets operate in the third quadrant they are more susceptible to radiation damage [13,14]. Hybrid PM multipoles use steel poles to establish a high-quality field. An early design by Halbach [15] was later used on the LANL compact FEL [16]. Later designs by Volk used rotating series rod magnets. Kashikin used axially translated shunts [3]. All these designs use a large number of magnets and do not adjust the magnetic centerline. An alternative design [1,2], Fig. 1, uses linear magnet retraction and can adjust field strength by 100%. The important points are the few number of magnets and the use of linear magnet retraction. The design is axially compact. Extensions to sextupoles, octupoles, etc. are obvious. The field strength adjustment method is shown in Fig. 1. Two or four magnets are moved in opposite directions relative to the center. In
Fig. 2. Centerline adjustment.
addition a means of adjusting the magnetic centerline is provided by moving two opposing magnets, such as the upper and lower in Fig. 2, in the same direction. This adjusts the centerline up. Finite element analysis (FEA) shows that the field isocontours remain linearly spaced and round over most of the beam tube region. Centerline shifts of 1–2% of the aperture diameter do not create appreciable sextupole. Two quadrupoles and one sector dipole prototype have been built and measured. A quadrupole with parameters suitable for a 25 MeV e-beam is shown in Fig. 3. Micrometer lead screws are used to retract or insert the magnets. As can be seen from Fig. 4 the predicted and measured fields are indistinguishable. Field strength is linear with magnet retraction and varied at a rate of 0.66%/ mm. Magnetic centerline shift is linear as well and varies at a rate of 0.2744 * Magnet retraction. All results agree with 3D FEA predictions. Integrated multipoles are below 0.1% at 80% aperture. A prototype NLC quadrupole was also built. The magnetic centerline was measured with a Hall probe attached to the magnet over a 2-week period. Typical centerline repeatability was 0.1 mm, Fig. 5, and long-term centerline drift was 3 mm, Fig. 6. Spinning coil tests will also be made.
ARTICLE IN PRESS S.C. Gottschalk et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185 3/5/02
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Centerline (microns)
0 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 -4
Date
Fig. 6. Long-term centerline drift on NLC prototype quadrupole.
Fig. 3. Compact quadrupole.
Measurement Prediction
B-field (T)
0.4
0.3
0.2
0.1
Fig. 7. Uniformity of compact sector dipole.
0.0 -4
-2
0
2
4
z (cm) Fig. 4. Measured field profile.
Day-to-Day Repeatability (µm)
0.4
0.3
0.2
0.1
0.0 0
5
10
15
Retraction (mm)
Fig. 5. NLC prototype quadrupole centerline repeatability.
A dipole for a 25 MeV e-beam was also designed, assembled, and tested. The measured field profile along a radial line at the middle of the poles is compared with 3D FEA in Fig. 7. The two profiles agree to within 710 ppm. For 100 MeV operation, the 100 ppm uniformity is 4 wider or 3.5 cm. Radiation damage is a potential concern for any PMs used on accelerator systems. Experience to date with NdFeB and SmCo used in wigglers and undulators has generally been favorable, particularly for stabilized, ultrahigh coercivity grades. Studies are underway in an effort to determine relative dose limits for various materials, grades and manufacturers [17]. Linear-retraction quadrupole magnets (Fig. 1) operate entirely in the second quadrant, thus reducing radiation damage susceptibility.
ARTICLE IN PRESS S.C. Gottschalk et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185
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3. Compact PM bends The exhaust bend of a high-power, energyrecovery FEL needs to efficiently transport a high current beam that has a much larger energy spread due to the FEL interaction in the wiggler. Some emittance growth or bunch lengthening is tolerable, but it cannot lead to any beam loss during deceleration in the main accelerator. Typically the desired energy acceptance is 10%. In order to build a bend with large energy acceptance and large bend angle, it is essential to keep the overall length of the bend as short as possible. The reason for this is simple: after bending a beam with a large energy spread in a dipole, its bend-plane size begins to grow rapidly, making it difficult to control in any of the subsequent optical elements. PM beamline optics are candidates for use in these compact designs. We originally considered using PMs in the compact Dundee bend [18]. However, for this application, it was found to require sextupoles with high pole tip fields located in close proximity to the quadrupoles. A new geometry, the Ballard bend shown in Fig. 8, was found to better satisfy the exhaust beam requirements. It has the same basic symmetry, but uses fewer elements and is much more compact. Pairs of defocusing quadrupoles, Q1 and Q3, are placed symmetrically on both sides of the dipole pairs. This arrangement establishes two planes of reflection symmetry, one about the center quadrupole, Q3, and another about the focusing quadrupole, Q2, for each 90 half of the bend. The sextupoles are mainly trim magnets used to maintain small emittance growth. Q3
D2
45°
S2
D3
45°
This high degree of symmetry helps to cancel various second-order aberrations to greatly improve the transmitted beam quality. The size bend shown can comfortably operate at 130 MeV. Performance estimates at 100 MeV are shown in Fig. 9. The lower curves illustrate that the Ballard bend design produces significantly less emittance growth even for a 10% energy spread in the beam. The upper curves illustrate that the improvement in the bunch length distortion is even more dramatic, showing negligible change from 0% to 10% energy spread. The bend is first-order isochronous and doubly achromatic. The Ballard bend has a large beam size in the quadrupoles and the required dipole uniformity is 100 ppm over a 1 cm aperture. This is because the e-beam is only turned 45 before it is refocused by a quadrupole (Q2 or Q3). The sector dipoles discussed previously have ample uniformity: 100 ppm over a 3.5 cm aperture.
S2
4. Conclusion
S1
S1 Q2
Fig. 9. Emittance growth (lower) and electron bunch length (upper) vs. energy spread for the Ballard (solid) and Dundee bends (dashed).
Q2 D4
D1
45°
45°
Q1
Q1
2.681 meters
Fig. 8. Ballard bend.
Recent work on PM systems for FELs has shown that high performance and compact size can be achieved with permanent magnet optics. A new bend, the Ballard bend, makes good use of the novel characteristics of a new class of PM optics based on linearly retracting magnets. A summary
ARTICLE IN PRESS S.C. Gottschalk et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185
of experimental results was presented that illustrate the performance of these designs.
Acknowledgements The authors acknowledge useful discussions with David Douglas, George Neil, George Biallas and Steve Benson of TJNAF, Dinh Nguyen of LANL and Edward Pogue of JTO. This work was supported in part by DOE Grant DE-FG03-01ER83305 and US Department of Interior Grant NBCHC010026.
References [1] S. Gottschalk, et al., Proceedings of the Particle Acceleration Conference, Chicago, IL, June 18–22, 2001, p. 3218. [2] S. Gottschalk, et al., Presented at Navy/JTO FEL Workshop, Newport News, VA, June 5–6, 2001. [3] J. Volk, et al., Proceedings of the Particle Acceleration Conference, Chicago, IL, June 18–22, 2001, p. 217.
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[4] www-project.slac.stanford.edu/nlc/home.html [5] D. Dowell, Proceedings of the Particle Acceleration Conference, Vancouver, B.C, Canada, May 12–16, 1997, p. 1888. [6] D. Dowell, et al., Presented at Navy/JTO FEL Workshop, Newport News, VA, June 5–6, 2001. [7] D. Sprehn, et al., SLAC Pub. 7321, July 1996. [8] S. Pruss, et al., Proceedings of the Particle Acceleration Conference, 1997, p. 3286. [9] M. Hu, Proceedings of the Particle Acceleration Conference, Chicago, IL, June 18–22, 2001, p. 30. [10] K. Halbach, Nucl. Instr. and Meth. 169 (1980) 1. [11] W. Lou, et al., Proceedings of the Particle Acceleration Conference, Vancouver, B.C, Canada, May 12–16, 1997, p. 3236. [12] R. Gluckstern, Proceedings of the Linear Acceleration Conference, Montauk, NY, Sept. 10–14, 1979, p. 245. [13] Y. Ito, et al., Nucl. Instr. and Meth. B 183 (2001) 323. [14] T. Ikeda, S. Okuda, Nucl. Instr. and Meth. A 407 (1998) 439. [15] K. Halbach, Nucl. Instr. and Meth. 206 (1983) 353. [16] K. Chan, et al., Proceedings of the Linear Acceleration Conference, Ottawa, Ont., Canada, Aug, 24–28, 1992, p. 37. [17] http://home.fnal.gov/Bvolk/ [18] W. Gillespie, Nucl. Instr. and Meth. A 374 (1996) 395.
Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185
Permanent magnet systems for free-electron lasers Steve C. Gottschalka,*, David H. Dowellb, David C. Quimbya b
a STI Optronics Inc., 2755 Northup Way, Bellevue, WA 98004-1495, USA Stanford Linear Accelerator Center, Mail Stop 18, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
Abstract We review uses of permanent magnets (PMs) in free-electron lasers (FELs). Recently, PMs have been considered to replace many of the electromagnet (EM) dipoles, quadrupoles, and sextupoles in FEL beamlines and linear collider quadrupoles. PM beamline optics offer several advantages over EMs (Proceedings of the Particle Acceleration Conference, 2001, p. 3218). They are more compact, need no power, and do not require cooling water. In addition, adjustable-strength quadrupoles may have a precisely tuneable magnetic centerline. High pole tip fields (1.5 T in dipoles and 1.2 T in quadrupoles) are easily achieved. PM technology opens up new bend design possibilities. We describe a new, high performance, all-PM bend, the Ballard bend, that is first-order isochronous and doubly achromatic. It is suitable for use in the exhaust beam leg of an energy recovery FEL. We have designed and built a compact, high field sector PM dipole. Measured field profiles agree to 10 ppm of predictions. Compact PM quadrupoles were also designed and built. Measurements of field strength, axial profile, magnetic centerline tuning, and passive temperature compensation of strength and centerline shift agreed very well with predictions. Published by Elsevier Science B.V. PACS: 07.55.Db; 29.27.Eg; 41.85.L.c; 41.85.Ja Keywords: Free-electron lasers; Permanent magnets; Beamline optics; Dipoles; Quadrupoles; Sextupoles
1. Introduction The main advantage of permanent magnets (PMs) is that they do not waste power as heat to create a magnetic field. PMs are candidates to replace any room temperature DC electromagnet (EM) in accelerator or free-electron laser (FEL) systems. Recently, there has been interest in extending the use of PMs to include beamline optics [1–4], compact bends [5,6], pulse compressors and periodic permanent magnet klystrons [7]. PM quadrupoles are considered a viable alter*Corresponding author. E-mail address: [email protected] (S.C. Gottschalk). 0168-9002/03/$ - see front matter Published by Elsevier Science B.V. doi:10.1016/S0168-9002(03)00867-2
native for the Next Linear Collider (NLC) Main Line quadrupoles. PM multipoles are potentially more economical and reliable than EMs because of the elimination of high-current power supplies, cooling water and associated plumbing. Maintenance issues for EMs are well known. The relative long-term operating cost of PMs is essentially zero. The Fermilab Transfer line [8] and Recycler [9] use over 500 PM gradient dipoles, quadrupoles and sextupoles. Hybrid PM technology uses steel poles for high magnetic field strength and precision field shaping. Their compact size and simplicity allow new design approaches, including tuneable PM multipoles for improved electron beam (e-beam) quality
ARTICLE IN PRESS 182
S.C. Gottschalk et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185
preservation in beamlines that are smaller, more rugged, lower in cost, and lighter in weight compared to current EM designs. A unique feature of the PM quadrupole design we will discuss is the ability to adjust the magnetic centerline without the use of movers. NLC quadrupole designs have a 20 mechanical advantage: a 20 mm movement of magnets can produce a 1 mm centerline shift. This can allow accurate centerline control using lower resolution equipment.
Fig. 1. Hybrid quadrupole.
2. PM beamline optics There are a wide range of PM multipoles. The classic example is the Halbach design [10]. This is constructed from pie-shaped rare earth permanent magnet blocks (REPM) magnetized azimuthally and arranged to mimic the desired multipolar field distribution. Most applications of this style have fixed magnet strengths [11], but adjustablestrength versions have been made [12]. The adjustment process uses rotating and counterrotating REPM rings whose skew fields must precisely cancel. There are no means for keeping the multipole centers aligned as the magnets are rotated. Maximum pole tip fields are limited by demagnetization in the REPM wedges [11] to a level of 1.1 T. Since the magnets operate in the third quadrant they are more susceptible to radiation damage [13,14]. Hybrid PM multipoles use steel poles to establish a high-quality field. An early design by Halbach [15] was later used on the LANL compact FEL [16]. Later designs by Volk used rotating series rod magnets. Kashikin used axially translated shunts [3]. All these designs use a large number of magnets and do not adjust the magnetic centerline. An alternative design [1,2], Fig. 1, uses linear magnet retraction and can adjust field strength by 100%. The important points are the few number of magnets and the use of linear magnet retraction. The design is axially compact. Extensions to sextupoles, octupoles, etc. are obvious. The field strength adjustment method is shown in Fig. 1. Two or four magnets are moved in opposite directions relative to the center. In
Fig. 2. Centerline adjustment.
addition a means of adjusting the magnetic centerline is provided by moving two opposing magnets, such as the upper and lower in Fig. 2, in the same direction. This adjusts the centerline up. Finite element analysis (FEA) shows that the field isocontours remain linearly spaced and round over most of the beam tube region. Centerline shifts of 1–2% of the aperture diameter do not create appreciable sextupole. Two quadrupoles and one sector dipole prototype have been built and measured. A quadrupole with parameters suitable for a 25 MeV e-beam is shown in Fig. 3. Micrometer lead screws are used to retract or insert the magnets. As can be seen from Fig. 4 the predicted and measured fields are indistinguishable. Field strength is linear with magnet retraction and varied at a rate of 0.66%/ mm. Magnetic centerline shift is linear as well and varies at a rate of 0.2744 * Magnet retraction. All results agree with 3D FEA predictions. Integrated multipoles are below 0.1% at 80% aperture. A prototype NLC quadrupole was also built. The magnetic centerline was measured with a Hall probe attached to the magnet over a 2-week period. Typical centerline repeatability was 0.1 mm, Fig. 5, and long-term centerline drift was 3 mm, Fig. 6. Spinning coil tests will also be made.
ARTICLE IN PRESS S.C. Gottschalk et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185 3/5/02
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Centerline (microns)
0 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 -4
Date
Fig. 6. Long-term centerline drift on NLC prototype quadrupole.
Fig. 3. Compact quadrupole.
Measurement Prediction
B-field (T)
0.4
0.3
0.2
0.1
Fig. 7. Uniformity of compact sector dipole.
0.0 -4
-2
0
2
4
z (cm) Fig. 4. Measured field profile.
Day-to-Day Repeatability (µm)
0.4
0.3
0.2
0.1
0.0 0
5
10
15
Retraction (mm)
Fig. 5. NLC prototype quadrupole centerline repeatability.
A dipole for a 25 MeV e-beam was also designed, assembled, and tested. The measured field profile along a radial line at the middle of the poles is compared with 3D FEA in Fig. 7. The two profiles agree to within 710 ppm. For 100 MeV operation, the 100 ppm uniformity is 4 wider or 3.5 cm. Radiation damage is a potential concern for any PMs used on accelerator systems. Experience to date with NdFeB and SmCo used in wigglers and undulators has generally been favorable, particularly for stabilized, ultrahigh coercivity grades. Studies are underway in an effort to determine relative dose limits for various materials, grades and manufacturers [17]. Linear-retraction quadrupole magnets (Fig. 1) operate entirely in the second quadrant, thus reducing radiation damage susceptibility.
ARTICLE IN PRESS S.C. Gottschalk et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185
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3. Compact PM bends The exhaust bend of a high-power, energyrecovery FEL needs to efficiently transport a high current beam that has a much larger energy spread due to the FEL interaction in the wiggler. Some emittance growth or bunch lengthening is tolerable, but it cannot lead to any beam loss during deceleration in the main accelerator. Typically the desired energy acceptance is 10%. In order to build a bend with large energy acceptance and large bend angle, it is essential to keep the overall length of the bend as short as possible. The reason for this is simple: after bending a beam with a large energy spread in a dipole, its bend-plane size begins to grow rapidly, making it difficult to control in any of the subsequent optical elements. PM beamline optics are candidates for use in these compact designs. We originally considered using PMs in the compact Dundee bend [18]. However, for this application, it was found to require sextupoles with high pole tip fields located in close proximity to the quadrupoles. A new geometry, the Ballard bend shown in Fig. 8, was found to better satisfy the exhaust beam requirements. It has the same basic symmetry, but uses fewer elements and is much more compact. Pairs of defocusing quadrupoles, Q1 and Q3, are placed symmetrically on both sides of the dipole pairs. This arrangement establishes two planes of reflection symmetry, one about the center quadrupole, Q3, and another about the focusing quadrupole, Q2, for each 90 half of the bend. The sextupoles are mainly trim magnets used to maintain small emittance growth. Q3
D2
45°
S2
D3
45°
This high degree of symmetry helps to cancel various second-order aberrations to greatly improve the transmitted beam quality. The size bend shown can comfortably operate at 130 MeV. Performance estimates at 100 MeV are shown in Fig. 9. The lower curves illustrate that the Ballard bend design produces significantly less emittance growth even for a 10% energy spread in the beam. The upper curves illustrate that the improvement in the bunch length distortion is even more dramatic, showing negligible change from 0% to 10% energy spread. The bend is first-order isochronous and doubly achromatic. The Ballard bend has a large beam size in the quadrupoles and the required dipole uniformity is 100 ppm over a 1 cm aperture. This is because the e-beam is only turned 45 before it is refocused by a quadrupole (Q2 or Q3). The sector dipoles discussed previously have ample uniformity: 100 ppm over a 3.5 cm aperture.
S2
4. Conclusion
S1
S1 Q2
Fig. 9. Emittance growth (lower) and electron bunch length (upper) vs. energy spread for the Ballard (solid) and Dundee bends (dashed).
Q2 D4
D1
45°
45°
Q1
Q1
2.681 meters
Fig. 8. Ballard bend.
Recent work on PM systems for FELs has shown that high performance and compact size can be achieved with permanent magnet optics. A new bend, the Ballard bend, makes good use of the novel characteristics of a new class of PM optics based on linearly retracting magnets. A summary
ARTICLE IN PRESS S.C. Gottschalk et al. / Nuclear Instruments and Methods in Physics Research A 507 (2003) 181–185
of experimental results was presented that illustrate the performance of these designs.
Acknowledgements The authors acknowledge useful discussions with David Douglas, George Neil, George Biallas and Steve Benson of TJNAF, Dinh Nguyen of LANL and Edward Pogue of JTO. This work was supported in part by DOE Grant DE-FG03-01ER83305 and US Department of Interior Grant NBCHC010026.
References [1] S. Gottschalk, et al., Proceedings of the Particle Acceleration Conference, Chicago, IL, June 18–22, 2001, p. 3218. [2] S. Gottschalk, et al., Presented at Navy/JTO FEL Workshop, Newport News, VA, June 5–6, 2001. [3] J. Volk, et al., Proceedings of the Particle Acceleration Conference, Chicago, IL, June 18–22, 2001, p. 217.
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[4] www-project.slac.stanford.edu/nlc/home.html [5] D. Dowell, Proceedings of the Particle Acceleration Conference, Vancouver, B.C, Canada, May 12–16, 1997, p. 1888. [6] D. Dowell, et al., Presented at Navy/JTO FEL Workshop, Newport News, VA, June 5–6, 2001. [7] D. Sprehn, et al., SLAC Pub. 7321, July 1996. [8] S. Pruss, et al., Proceedings of the Particle Acceleration Conference, 1997, p. 3286. [9] M. Hu, Proceedings of the Particle Acceleration Conference, Chicago, IL, June 18–22, 2001, p. 30. [10] K. Halbach, Nucl. Instr. and Meth. 169 (1980) 1. [11] W. Lou, et al., Proceedings of the Particle Acceleration Conference, Vancouver, B.C, Canada, May 12–16, 1997, p. 3236. [12] R. Gluckstern, Proceedings of the Linear Acceleration Conference, Montauk, NY, Sept. 10–14, 1979, p. 245. [13] Y. Ito, et al., Nucl. Instr. and Meth. B 183 (2001) 323. [14] T. Ikeda, S. Okuda, Nucl. Instr. and Meth. A 407 (1998) 439. [15] K. Halbach, Nucl. Instr. and Meth. 206 (1983) 353. [16] K. Chan, et al., Proceedings of the Linear Acceleration Conference, Ottawa, Ont., Canada, Aug, 24–28, 1992, p. 37. [17] http://home.fnal.gov/Bvolk/ [18] W. Gillespie, Nucl. Instr. and Meth. A 374 (1996) 395.