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The Eindhoven linac–racetrack microtron combination
Nuclear Instruments and Methods in Physics Research B 139 (1998) 522±526
The Eindhoven linac±racetrack microtron combination W.H.C. Theuws *, J.I.M. Botman, H.L. Hagedoorn, C.J. Timmermans Eindhoven University of Technology, Cyclotron Laboratory, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Abstract The Eindhoven linac±race track microtron (RTM) combination has been designed to serve as injector for an electron storage ring. The linac is a 10 MeV travelling-wave linac (type M.E.L. SL75/10). In the RTM a 5 MeV standing-wave cavity, which is synchronized with the linac, accelerates the electron beam 13 times, such that the extraction energy is 75 MeV. The RTM end magnets are two-sector magnets tilted in their median planes, to provide strong focusing forces for optimal electron-optical properties. Closed-orbit conditions are ful®lled with the help of small correction dipoles located in the RTM drift space; the magnetic-®eld strengths of these correction dipoles are adjusted on the basis of beamposition measurements. Isochronous acceleration is accomplished by position- and phase-measurements. A low-cost elaborate diagnostic system will be used for ecient commissioning of the combination of the 10 MeV linac and the 10±75 MeV RTM. Ó 1998 Elsevier Science B.V. PACS: 29.20.Mr; 29.17.+w; 29.30.Dn Keywords: Linac; Racetrack microtron; Beam dynamics; Beam diagnostics; Spectrometer
1. Linac and microtron A 10 MeV 2998 MHz travelling-wave linac (type M.E.L. SL75/10), serves as injector for the Eindhoven race track microtron (RTM). Its main parameters are listed in Table 1. The 10±75 MeV RTM, which is shown in Fig. 1, has been designed as injector for an electron storage ring [1], because a microtron oers a beam with small energy spread at relatively low RF requirements. The RTM's 5 MeV standing-wave cavity, which is synchronized
* Corresponding author. Tel.: +31 40 2474864; fax: +31 40 2438060; e-mail: [email protected].
with the linac, accelerates the electrons in 13 times to their extraction energy of 75 MeV [2]. 2. Basic microtron design The RTM design is basically dictated by its two resonance conditions. First, the revolution time of the ®rst orbit, t1 , must be an integer multiple, l, of the RF-period 1=f0 t1 l=f0 . Second, each revolution time must exceed the preceding one by another integer multiple, m, of the RF-period Dt tn ÿ tnÿ1 m=f0 . From these two resonance conditions together with the assumption that bn bnÿ1 1 [3] two basic relations for an RTM are derived:
0168-583X/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 5 8 3 X ( 9 7 ) 0 0 9 6 1 - 0
W.H.C. Theuws et al. / Nucl. Instr. and Meth. in Phys. Res. B 139 (1998) 522±526 Table 1 Main linac parameters Length (m) Average gradient (MV/m) Output energy (MeV) FWHM energy spread (%) Macro pulse current (mA) Operating frequency (MHz) Pulse repetition rate (Hz) Pulse duration (ls) Filling time (ls)
Er
m Einj ; l ÿ m ÿ 2L=k
523
Table 2 Basic microtron parameters 2.25 4.4 10 3.5 47 2998 50, 150, 300 1.7 0.5
Kinetic energy at injection (MeV) Kinetic energy at extraction (MeV) Energy gain per turn (MeV) Number of orbits RF-frequency (MHz) Resonant magnetic ®eld (T) Mode number l Mode number m Distance between magnets (m)
1
2pf0 Er ; 2 ec2 m where k c=f0 , Einj is the injection energy, L is the ®eld-free region between the end magnets and Br is the resonant or isochronous magnetic ®eld, corresponding to the energy gain per turn, Er . The maximum output energy is given by NEr Einj , with N the number of cavity passages. The RF-frequency of the RTM cavity, f0 , must be the same as the RF-frequency of the 10 MeV linac. The mode number, m, and the number of orbits, N, should be as small as possible to maximize the phase acceptance and to minimize phase errors due to imperfections of the construction [4]. The value of m also determines the orbit separation, which must be large enough to place the diagnostic equipment and beam steerers. The Br
Fig. 1. The 10±75 MeV Eindhoven racetrack microtron.
10 75 5 13 2998 0.524 26 2 1
®eld-free region must be large enough to place the cavity. As we want to use normal conducting magnets, the magnetic-®eld strength in the air gaps is limited by the maximum ®eld strength in the iron (about 2 T for ordinary steel). The basic parameters that have been established for the RTM are summarized in Table 2. 3. Two-sector bending magnets The RTM end magnets have two magnetic-®eld sectors to provide strong focusing forces. Sectors 1 and 2 have magnetic-®eld strengths of BL and BH aBL (a > 1), respectively. The trajectories in the end magnets consist of two circular arcs, de®ned by their centres M1 and M2 , radii q and q/a and angles 2H and (p)2H), respectively (see Fig. 2). The tilt angle, s, is retrieved from geometrical considerations:
Fig. 2. Two-sector magnets.
524
W.H.C. Theuws et al. / Nucl. Instr. and Meth. in Phys. Res. B 139 (1998) 522±526
sin 2H : ÿ cos 2H aÿ1
tan s a1
The magnetic ®eld BL is to be chosen 1 1 1 1ÿ 2H sin 2H Br ; BL a p a
3
4
such that resonant acceleration is not violated. The parameters a and H, which are not prescribed so far, determine the focusing properties of the RTM. Therefore, the microtronÕs transverse acceptance has been calculated for many combinations of a and H, where estimations for the fringing ®elds of the end magnet with their ®eld clamps have been taken into account [5]. Consequently, a 1.17 and H 45° have been chosen, which gives a horizontal and vertical acceptance
of 40 and 10 mm mrad, respectively. With Eqs. (3) and (4) this yields s 4.48°, BL 0.51 T, and consequently BR 0.60 T. The RTM with two-sector end magnets has been compared with the same RTM with homogeneous magnets. For both types of microtrons the trajectories in the horizontal and vertical plane are plotted both for a parallel and a divergent beam at injection (see Fig. 3). The main dierence is the periodicity of the betatron oscillations. For the horizontal plane motion the tune of the twosector option is 1.15 for the ®rst and 1.07 for the ®nal orbit. For the homogeneous option these numbers are 1.10 and 1.04, respectively. This leads to a smaller beam size in case of the two-sector magnets.
Fig. 3. Trajectories in the horizontal and vertical plane for a parallel beam and for a divergent beam at injection. Homogeneous option: (a) x0 )1..+1 mm, x00 0; (b) x0 0, x00 )1..+1 mm; (c) z0 )1..+1 mm, z00 0; (d) z0 0, z00 )1..+1 mm. Two-sector option: (e) x0 )1..+1 mm, x00 0; (f) x0 0, x00 )1..+1 mm; (g) z0 )1..+1 mm, z00 0; (h) z0 0, z00 )1..+1 mm [2].
W.H.C. Theuws et al. / Nucl. Instr. and Meth. in Phys. Res. B 139 (1998) 522±526
The stronger focusing would also lead to smaller vertical beam sizes if the defocusing of the fringing ®elds would be less. However, the fringing ®elds lead to a blow-up of the beam in the ®rst turn (the trace of the matrix is larger than 2 [6]). The tune of the two-sector option is 0.22 for the second and 0.30 for the ®nal orbit. For the homogeneous option these numbers are 0.09 and 0.05, respectively. Hence the use of two-sector magnets make it possible to stay further away from integer resonances. 4. Misalignments and magnetic-®eld imperfections Because of the strong focusing forces provided by the two-sector end magnets the RTM operates further from integer resonances than conventional RTMs. Therefore the sensitivity for misalignments of the end magnets is smaller. It has been investigated that all alignment tolerances can be met by mechanical alignment except for the tilt angle, s. Furthermore, the magnetic-®eld maps of the end magnets have been measured. These ®eld maps have been used for numerical orbit calculations, which have shown that it is not possible to obtain 180° bends for all orbits, simultaneously. However, the eects of the alignment error of the tilt angle as well as the magnetic-®eld imperfections can both be counteracted by an array of correction dipoles that is located in the ®eld-free region halfway the two end magnets.
525
adjusting the quadrupoles in the beam-guiding system between the 10 MeV linac and RTM [9]. In the second stage the combination of the linac and RTM will further be assembled. Then the energy of the injected electrons, the cavity potential and the phase dierence between the accelerating voltage of the linac and the cavity are adjusted. The energy of the beam is measured by means of the left RTM end magnet, see Fig. 4. This is done for several dierent positions of the phase-shifter, which determines the phase dierence of the accelerating voltage between the linac and the RTM cavity. Consequently, the energy will appear as a sine-like function of the position of the phaseshifter: E Einj Ecav cos /;
5
where Einj is the energy of the injected beam, Ecav is the cavity potential and / is the phase dierence between linac and cavity. The mean of this function is the injection energy; the amplitude of the harmonic part is the cavity potential. Further, the measurement yields a calibration for the phase-shifter. In the microtron many stripline beam-position monitors are used to adjust the array of correction dipoles discussed in Section 4 [10]. A phase-probe measures the phase dierence between the cavity voltage and the ®rst harmonic of the electron bunches in the ®eld-free region of the microtron. This phase-probe can be placed in each of the 12 orbits. The phase-measurements as well as the beam-position measurements are used to optimize the adjustable microtron parameters.
5. Diagnostics A low-cost elaborate diagnostic system will be used for ecient commissioning of the combination of the 10 MeV linac and the 10±75 MeV RTM [7]. The commissioning will take place in two stages. In the ®rst stage the cavity will be replaced by a temporary beamline with a quadrupole and an OTR set-up, which are used to measure the shape of transverse emittances [8]. Consequently, the emittance of the injected beam can be matched to the calculated acceptance of the microtron by
Fig. 4. Left-hand RTME magnet used as spectrometer.
526
W.H.C. Theuws et al. / Nucl. Instr. and Meth. in Phys. Res. B 139 (1998) 522±526
References [1] J.I.M. Botman, B. Xi, C.J. Timmermans, H.L. Hagedoorn, Rev. Sci. Instr. 63 (1992) 1569. [2] G.A. Webers, Ph.D. Thesis, Eindhoven University of Technology, 1994. [3] W.H.C. Theuws, J.I.M. Botman, H.L. Hagedoorn, Part. Acc. Conf., submitted. [4] S. Rosander, M. Sadlacek, O. Wernholm, H. Babic, Nucl. Instr. and Meth. 204 (1982) 1. [5] G.A. Webers, J.L. Delhez, J.I.M. Botman, H.L. Hagedoorn, J. Hofman, C.J. Timmermans, Nucl. Instr. and Meth. B 69 (1992) 83. [6] W.T. Weng, S.R. Mane, in: M. Month, M. Dienes (Eds.), Proc. AIP Conference 249, Brookhaven National Laboratory, 1992, p. 4.
[7] W.H.C. Theuws, R.W. de Leeuw, L.W.A.M. Gossens, P.M. Spoek, J.I.M. Botman, C.J. Timmermans, H.L. Hagedoorn, Proc. European Part. Acc. Conference, Barcelona, 1996, p. 1615. [8] M.J. de Loos, S.B. van der Geer, W.P. Leemans, Proc. European Part. Acc. Conference, London, 1994, p. 1679. [9] R.W. de Leeuw, J.I.M. Botman, I.F. van Maanen, C.J. Timmermans, G.A. Webers, H.L. Hagedoorn, Proc. European Part. Acc. Conference, London, 1994, p. 2417. [10] W.H.C. Theuws, R.W. de Leeuw, G.A. Webers, J.I.M. Botman, C.J. Timmermans, H.L. Hagedoorn, Proc. Part. Acc. Conference, Dallas, 1995, p. 2738.
The Eindhoven linac±racetrack microtron combination W.H.C. Theuws *, J.I.M. Botman, H.L. Hagedoorn, C.J. Timmermans Eindhoven University of Technology, Cyclotron Laboratory, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Abstract The Eindhoven linac±race track microtron (RTM) combination has been designed to serve as injector for an electron storage ring. The linac is a 10 MeV travelling-wave linac (type M.E.L. SL75/10). In the RTM a 5 MeV standing-wave cavity, which is synchronized with the linac, accelerates the electron beam 13 times, such that the extraction energy is 75 MeV. The RTM end magnets are two-sector magnets tilted in their median planes, to provide strong focusing forces for optimal electron-optical properties. Closed-orbit conditions are ful®lled with the help of small correction dipoles located in the RTM drift space; the magnetic-®eld strengths of these correction dipoles are adjusted on the basis of beamposition measurements. Isochronous acceleration is accomplished by position- and phase-measurements. A low-cost elaborate diagnostic system will be used for ecient commissioning of the combination of the 10 MeV linac and the 10±75 MeV RTM. Ó 1998 Elsevier Science B.V. PACS: 29.20.Mr; 29.17.+w; 29.30.Dn Keywords: Linac; Racetrack microtron; Beam dynamics; Beam diagnostics; Spectrometer
1. Linac and microtron A 10 MeV 2998 MHz travelling-wave linac (type M.E.L. SL75/10), serves as injector for the Eindhoven race track microtron (RTM). Its main parameters are listed in Table 1. The 10±75 MeV RTM, which is shown in Fig. 1, has been designed as injector for an electron storage ring [1], because a microtron oers a beam with small energy spread at relatively low RF requirements. The RTM's 5 MeV standing-wave cavity, which is synchronized
* Corresponding author. Tel.: +31 40 2474864; fax: +31 40 2438060; e-mail: [email protected].
with the linac, accelerates the electrons in 13 times to their extraction energy of 75 MeV [2]. 2. Basic microtron design The RTM design is basically dictated by its two resonance conditions. First, the revolution time of the ®rst orbit, t1 , must be an integer multiple, l, of the RF-period 1=f0 t1 l=f0 . Second, each revolution time must exceed the preceding one by another integer multiple, m, of the RF-period Dt tn ÿ tnÿ1 m=f0 . From these two resonance conditions together with the assumption that bn bnÿ1 1 [3] two basic relations for an RTM are derived:
0168-583X/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 8 - 5 8 3 X ( 9 7 ) 0 0 9 6 1 - 0
W.H.C. Theuws et al. / Nucl. Instr. and Meth. in Phys. Res. B 139 (1998) 522±526 Table 1 Main linac parameters Length (m) Average gradient (MV/m) Output energy (MeV) FWHM energy spread (%) Macro pulse current (mA) Operating frequency (MHz) Pulse repetition rate (Hz) Pulse duration (ls) Filling time (ls)
Er
m Einj ; l ÿ m ÿ 2L=k
523
Table 2 Basic microtron parameters 2.25 4.4 10 3.5 47 2998 50, 150, 300 1.7 0.5
Kinetic energy at injection (MeV) Kinetic energy at extraction (MeV) Energy gain per turn (MeV) Number of orbits RF-frequency (MHz) Resonant magnetic ®eld (T) Mode number l Mode number m Distance between magnets (m)
1
2pf0 Er ; 2 ec2 m where k c=f0 , Einj is the injection energy, L is the ®eld-free region between the end magnets and Br is the resonant or isochronous magnetic ®eld, corresponding to the energy gain per turn, Er . The maximum output energy is given by NEr Einj , with N the number of cavity passages. The RF-frequency of the RTM cavity, f0 , must be the same as the RF-frequency of the 10 MeV linac. The mode number, m, and the number of orbits, N, should be as small as possible to maximize the phase acceptance and to minimize phase errors due to imperfections of the construction [4]. The value of m also determines the orbit separation, which must be large enough to place the diagnostic equipment and beam steerers. The Br
Fig. 1. The 10±75 MeV Eindhoven racetrack microtron.
10 75 5 13 2998 0.524 26 2 1
®eld-free region must be large enough to place the cavity. As we want to use normal conducting magnets, the magnetic-®eld strength in the air gaps is limited by the maximum ®eld strength in the iron (about 2 T for ordinary steel). The basic parameters that have been established for the RTM are summarized in Table 2. 3. Two-sector bending magnets The RTM end magnets have two magnetic-®eld sectors to provide strong focusing forces. Sectors 1 and 2 have magnetic-®eld strengths of BL and BH aBL (a > 1), respectively. The trajectories in the end magnets consist of two circular arcs, de®ned by their centres M1 and M2 , radii q and q/a and angles 2H and (p)2H), respectively (see Fig. 2). The tilt angle, s, is retrieved from geometrical considerations:
Fig. 2. Two-sector magnets.
524
W.H.C. Theuws et al. / Nucl. Instr. and Meth. in Phys. Res. B 139 (1998) 522±526
sin 2H : ÿ cos 2H aÿ1
tan s a1
The magnetic ®eld BL is to be chosen 1 1 1 1ÿ 2H sin 2H Br ; BL a p a
3
4
such that resonant acceleration is not violated. The parameters a and H, which are not prescribed so far, determine the focusing properties of the RTM. Therefore, the microtronÕs transverse acceptance has been calculated for many combinations of a and H, where estimations for the fringing ®elds of the end magnet with their ®eld clamps have been taken into account [5]. Consequently, a 1.17 and H 45° have been chosen, which gives a horizontal and vertical acceptance
of 40 and 10 mm mrad, respectively. With Eqs. (3) and (4) this yields s 4.48°, BL 0.51 T, and consequently BR 0.60 T. The RTM with two-sector end magnets has been compared with the same RTM with homogeneous magnets. For both types of microtrons the trajectories in the horizontal and vertical plane are plotted both for a parallel and a divergent beam at injection (see Fig. 3). The main dierence is the periodicity of the betatron oscillations. For the horizontal plane motion the tune of the twosector option is 1.15 for the ®rst and 1.07 for the ®nal orbit. For the homogeneous option these numbers are 1.10 and 1.04, respectively. This leads to a smaller beam size in case of the two-sector magnets.
Fig. 3. Trajectories in the horizontal and vertical plane for a parallel beam and for a divergent beam at injection. Homogeneous option: (a) x0 )1..+1 mm, x00 0; (b) x0 0, x00 )1..+1 mm; (c) z0 )1..+1 mm, z00 0; (d) z0 0, z00 )1..+1 mm. Two-sector option: (e) x0 )1..+1 mm, x00 0; (f) x0 0, x00 )1..+1 mm; (g) z0 )1..+1 mm, z00 0; (h) z0 0, z00 )1..+1 mm [2].
W.H.C. Theuws et al. / Nucl. Instr. and Meth. in Phys. Res. B 139 (1998) 522±526
The stronger focusing would also lead to smaller vertical beam sizes if the defocusing of the fringing ®elds would be less. However, the fringing ®elds lead to a blow-up of the beam in the ®rst turn (the trace of the matrix is larger than 2 [6]). The tune of the two-sector option is 0.22 for the second and 0.30 for the ®nal orbit. For the homogeneous option these numbers are 0.09 and 0.05, respectively. Hence the use of two-sector magnets make it possible to stay further away from integer resonances. 4. Misalignments and magnetic-®eld imperfections Because of the strong focusing forces provided by the two-sector end magnets the RTM operates further from integer resonances than conventional RTMs. Therefore the sensitivity for misalignments of the end magnets is smaller. It has been investigated that all alignment tolerances can be met by mechanical alignment except for the tilt angle, s. Furthermore, the magnetic-®eld maps of the end magnets have been measured. These ®eld maps have been used for numerical orbit calculations, which have shown that it is not possible to obtain 180° bends for all orbits, simultaneously. However, the eects of the alignment error of the tilt angle as well as the magnetic-®eld imperfections can both be counteracted by an array of correction dipoles that is located in the ®eld-free region halfway the two end magnets.
525
adjusting the quadrupoles in the beam-guiding system between the 10 MeV linac and RTM [9]. In the second stage the combination of the linac and RTM will further be assembled. Then the energy of the injected electrons, the cavity potential and the phase dierence between the accelerating voltage of the linac and the cavity are adjusted. The energy of the beam is measured by means of the left RTM end magnet, see Fig. 4. This is done for several dierent positions of the phase-shifter, which determines the phase dierence of the accelerating voltage between the linac and the RTM cavity. Consequently, the energy will appear as a sine-like function of the position of the phaseshifter: E Einj Ecav cos /;
5
where Einj is the energy of the injected beam, Ecav is the cavity potential and / is the phase dierence between linac and cavity. The mean of this function is the injection energy; the amplitude of the harmonic part is the cavity potential. Further, the measurement yields a calibration for the phase-shifter. In the microtron many stripline beam-position monitors are used to adjust the array of correction dipoles discussed in Section 4 [10]. A phase-probe measures the phase dierence between the cavity voltage and the ®rst harmonic of the electron bunches in the ®eld-free region of the microtron. This phase-probe can be placed in each of the 12 orbits. The phase-measurements as well as the beam-position measurements are used to optimize the adjustable microtron parameters.
5. Diagnostics A low-cost elaborate diagnostic system will be used for ecient commissioning of the combination of the 10 MeV linac and the 10±75 MeV RTM [7]. The commissioning will take place in two stages. In the ®rst stage the cavity will be replaced by a temporary beamline with a quadrupole and an OTR set-up, which are used to measure the shape of transverse emittances [8]. Consequently, the emittance of the injected beam can be matched to the calculated acceptance of the microtron by
Fig. 4. Left-hand RTME magnet used as spectrometer.
526
W.H.C. Theuws et al. / Nucl. Instr. and Meth. in Phys. Res. B 139 (1998) 522±526
References [1] J.I.M. Botman, B. Xi, C.J. Timmermans, H.L. Hagedoorn, Rev. Sci. Instr. 63 (1992) 1569. [2] G.A. Webers, Ph.D. Thesis, Eindhoven University of Technology, 1994. [3] W.H.C. Theuws, J.I.M. Botman, H.L. Hagedoorn, Part. Acc. Conf., submitted. [4] S. Rosander, M. Sadlacek, O. Wernholm, H. Babic, Nucl. Instr. and Meth. 204 (1982) 1. [5] G.A. Webers, J.L. Delhez, J.I.M. Botman, H.L. Hagedoorn, J. Hofman, C.J. Timmermans, Nucl. Instr. and Meth. B 69 (1992) 83. [6] W.T. Weng, S.R. Mane, in: M. Month, M. Dienes (Eds.), Proc. AIP Conference 249, Brookhaven National Laboratory, 1992, p. 4.
[7] W.H.C. Theuws, R.W. de Leeuw, L.W.A.M. Gossens, P.M. Spoek, J.I.M. Botman, C.J. Timmermans, H.L. Hagedoorn, Proc. European Part. Acc. Conference, Barcelona, 1996, p. 1615. [8] M.J. de Loos, S.B. van der Geer, W.P. Leemans, Proc. European Part. Acc. Conference, London, 1994, p. 1679. [9] R.W. de Leeuw, J.I.M. Botman, I.F. van Maanen, C.J. Timmermans, G.A. Webers, H.L. Hagedoorn, Proc. European Part. Acc. Conference, London, 1994, p. 2417. [10] W.H.C. Theuws, R.W. de Leeuw, G.A. Webers, J.I.M. Botman, C.J. Timmermans, H.L. Hagedoorn, Proc. Part. Acc. Conference, Dallas, 1995, p. 2738.