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The CR storage ring in an isochronous mode operation with nonlinear optics characteristics
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NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 4579–4582 www.elsevier.com/locate/nimb
The CR storage ring in an isochronous mode operation with nonlinear optics characteristics A. Dolinskii *, H. Geissel, S. Litvinov, F. Nolden, M. Steck, H. Weick GSI, Planckstrasse 1, 64291 Darmstadt, Germany Available online 6 June 2008
Abstract In the Facility for Antiproton and Ion Research (FAIR), which is presently designed at GSI (Darmstadt, Germany) a variety of new short-lived nuclides will be generated with the Super-FRS by using projectile fragmentation or uranium fission. The storage rings for the CR-RESR complex have been designed for efficient cooling and accumulation of antiprotons and cooling and deceleration of rare isotopes beams. A new Collector Ring (CR) is planned to be constructed, where one of the functions is devoted also to mass measurements of very short-lived nuclei when it is tuned to an isochronous mode. The structure of the ring lattice and its ion-optical properties in the isochronous mode are described. Nonlinear ion-optical characteristics and their influence on an achievable mass resolving power in an isochronous mode operation of the CR are discussed. Ó 2008 Elsevier B.V. All rights reserved. PACS: 29.20.Dh; 29.27.Fh; 41.85.p Keywords: CR; Storage ring; Isochronous optic; Mass measurements
1. Introduction Mass measurements of very exotic nuclei up to the limits of nuclear existence are essential for studies of nuclear structure allowing to discover new shell effects, nuclear shapes, decay properties, creation of the elements in stars. Mass measurements of exotic nuclei are a challenge because of the low production cross sections, the large transverse emittance and longitudinal momentum spread of radioactive ion beams separated in flight. A further challenge arises due to the limit in preparation and observation times because of the short life time of the secondary ions. Storage rings can be used as instruments for mass measurements of nuclei [1]. At GSI two methods have been developed for precise mass measurements of exotic nuclei at relativistic energies using the ESR storage ring: ‘Schottky Mass Spectometry (SMS)’ for longer-lived isotopes *
Corresponding author. Tel.: +49 06159 711511; fax: +49 06159 712044. E-mail address: [email protected] (A. Dolinskii). 0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.05.082
[2], and ‘Isochronous Mass Spectrometry (IMS)’ for short-lived isotopes [3]. Both methods are based on accurate measurements of the revolution frequency which characterizes the mass-to-charge ratio of the circulating ions. In SMS the velocity spread of the relativistic hot fragment beams is reduced by electron cooling. For IMS the ring optics is tuned to an isochronous mode such that the differences in velocities are compensated by different path lengths. The planned FAIR facility [4] will open unique opportunities for the production, accumulation and mass measurements of radioactive nuclides, which are very far from stability. The Super-FRS [5] – CR (Collector Ring) [6] will be a powerful tool to provide short-lived exotic nuclides for precise measurements at relativistic energies. Experiments involving nuclei with very short half-lives, down to the ls range will be performed in the CR operated in the isochronous mode. The experimental equipment in the CR will include two time-of-flight detectors, which enable precise revolution frequency measurements in a very short time. The goal for the mass resolving power is more than 105
4580
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4579–4582
with a mass accuracy better then 106. In this article the isochronous mode of the CR operation is discussed. 2. The CR characteristics in the first order design The general layout of the CR is shown in Fig. 1. The CR is dedicated to efficient cooling of rare isotope beams (RIB mode) as well as antiproton beams (PBAR mode). Tuning the CR to an isochronous mode (IMS) it will be used as a time-of-flight (TOF) mass spectrometer. The CR will accept the hot beams coming from the Super-FRS (in RIB and IMS modes) or antiproton separator (in PBAR mode) with acceptances given in Table 1. The lattice is designed as a racetrack-shaped storage ring, consisting of two 180o arc sections connected by two long straight sections. One straight section will be occupied by the injection/extraction system devices and three pick-up tanks for stochastic cooling. The other straight section will host five RF-cavities for bunch rotation and three kicker tanks for stochastic cooling. Pick-
Fig. 1. Layout of the CR lattice. SCP – stochastic cooling pick-ups; SCK – stochastic cooling kickers; dipol – dipole magnet, quad – quadrupole magnet; RF – cavities – rf-cavities for bunch rotations; ink-n – injection kicker; exk-n – extraction kicker; TOF – time-of-flight detector; sx-n – sextupole magnets (n-number of family).
Table 1 The CR parameters Mode operation
RIB
PBAR
IMS
Ion energy (MeV/u) Hor. acceptance (mm mrad) Ver. acceptance (mm mrad) Momentum acceptance (%)
740 200 200 3
3000 240 240 6
790 100 100 1
Betatron tunes Hor. Qx Ver. Qy Transition energy, ctr
3.18 3.17 3.52
4.45 4.43 2.91
3.56 4.41 1.84
up and kicker tanks for stochastic cooling are located close to one of the arcs. Special requirements for the lattice are the following: (a) dispersion-free straight sections; (b) certain betatron phase advances between pick-ups and kickers for stochastic cooling (Dlh,v = (2n + 1)p/2); (c) the ctr (transition energies) given in Table 1 must be provided. All CR (RIB, PBAR ans IMS) modes will be operated at constant magnetic field level close to the maximum bending power of Bq = 13 Tm. Hence the velocity of the ions in each operation mode is different. To achieve efficient stochastic cooling only in RIB and PBAR modes one has to optimize the frequency slip factor g = |1/c2 1/ctr2| for each beam velocity. In IMS mode one has to achieve the condition when the circulation time of a particle is independent of their velocity. In this case the quadrupole magnets must be tuned to obtain the transition energy ctr equal the Lorentz factor c (g = 0). That means the different optics of the CR can be done by a different focusing strength of the ring quadrupoles. 12 independent power supplies for quadrupole magnets are foreseen in order to have flexibility in the optics variation. For the isochronous condition a very large dispersion value of Dh max is needed (up to 23 m), which leads to a decrease in ring acceptance. In Fig. 2 the calculated betatron bh,v and dispersion Dh functions for a quarter of the ring are shown in the isochronous mode.
Fig. 2. Twiss and dispersion functions over one quarter of the CR lattice.
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4579–4582
3. Time-of-Flight measurements in a ring The principle of the TOF detector is that the ions passing through a thin foil emit secondary electrons, which are detected to determine the revolution time in the ring. The mass of different nuclides is calculated from the revolution time (or frequency). Having the frequencies of unknown and known nuclides one can define the unknown mass by the formula Df 1 Dðm=qÞ c2 Dm df ð1Þ ¼ 2 þ 1 2 þ ctr m f ctr m=q f error In the ideal case in the isochronous condition (ctr = c and ctr = const) the ions with different mass-to-charge ratio (m/q) are recognized in frequency if their mean relative frequency shift Df/f is larger than the full relative frequency width of the beam signal (df/f)error. Therefore, an accurate determination of the m/q ratio depends on how low the relative spread (df/ferror of the frequency signal can be achieved. In practice the parameter ctr has a dependence on the momentum deviation of the particle from the reference orbit (ctr = ctr(Bq)) that results in a low resolving power. This effect arises because of the chromatic aberrations of the magnetic elements in the CR lattice and therefore must be minimized by means of the sextupole correction. In Fig. 3 one can see the ctr variation over the momentum acceptance of 1% before and after correction. One needs at least two independently powered sextupole families in order to reduce the ctr variation from 3.6% up to 0.1% as shown in Fig. 3. After sextupole correction the resolving power of more than 106 can be reached if the relative frequency spread of a signal (df/f)error is better than 5 107. An additional aspect that should be considered is that the ideal isochronous condition in the ring can be fulfilled only for one species with one mass-to-charge ratio. Ions with other m/q will become less isochronous. During more than hundred turns in the ring the stored ions lose energy
Fig. 3. Variation of the ctr over full momentum acceptance in the ring due to the chromatic aberration of the quadrupole magnets.
4581
in the foil of the TOF detector, which leads to non-isochronous conditions and, as consequence, to a reduction of accuracy of measurements. For evaluations of non-isochronous particles one needs to measure their velocity deviation from the reference particle by means of the second TOF detector, which will be placed downstream by 30 m distance from the first TOF detector. The measurement of the velocity with about Dv/v = 104 accuracy allows to determine the time and consequently the mass of an isotope with an accuracy of better than 106, when ions fulfil the isochronous condition.
4. Nonlinear effects Nonlinear effects are an essential part of the study in the isochronous mode because of its influence the width of the beam signal (df/f)error in formula (1) and as consequence the resolving power of the TOF measurements. The momentum dependence of the dipole curvature and of the quadrupole focusing strength produces a variation of the orbit dispersion and betatron functions. The control of the orbit dispersion and therefore adjustment of the orbit length imposes an extra condition with respect to the chromaticity correction. In [7] the detailed analysis of the frequency spread depending on the ring acceptance, magnet misalignments, nonlinear field errors in the CR are given. It was shown in [7] that six independently powered sextupole families are required in order to correct the chromatic effect and simultaneously to minimize the influence of the nonlinear field effect on the width of the beam signal (df/f)error. Another effect, which was investigated for the CR ring, is the fringe field influence on the parameter ctr. Because of the exceptionally large emittance associated with hot ion beams, which will be injected in the ring, unprecedented apertures are required for the quadrupole magnets. In the CR it is planned that the normal conducting arc quadrupoles will have an aperture of 40 cm, which leads to strong
Fig. 4. Dependence of ctr on a momentum deviation Dp/p.
4582
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4579–4582
extended fringe field proportional to the pole field. In Fig. 4 the result of calculations showing the influence of the fringe field of quadrupoles on the parameter ctr is plotted. Fortunately the fringe field acts in the opposite direction compared to the influence of the nonlinear field errors of the magnets. To control the parameter ctr over the full momentum acceptance against fringe fields one needs two families of octupole correctors. From Fig. 4 we can deduce that octupole corrections can considerably reduce the influence of the fringe field on the variation of the parameter ctr over the full momentum acceptance. 5. Conclusion The CR, which is designed for a fast cooling of ions, is considered also to be used as an isochronous ring for the mass measurements of short-lived nuclei. Numerous simulations show that in this storage ring the accuracy of mea-
surements can be reached better that 106. A strong impact on the resolving power is arisen by fringe field of the wide aperture quadrupole magnets. The correction scheme of the CR requires six independently powered sextupole and two octupole corrector families in order to minimize the chromatic, geometrical and fringe field effects. References [1] [2] [3] [4]
H. Wollnik, Nucl. Instr. and Meth. A 258 (1987) 289. T. Radon et al., Nucl. Phys. A 677 (2000) 75. M. Hausmann et al., Nucl. Instr. and Meth. A 446 (2000) 569. W. Henning, in: Proceedings of the EPAC2004, Lucerne, Switzerland, p. 50. [5] H. Geissel et al., Nucl. Instr. and Meth. B 204 (2003) 71. [6] A. Dolinskii, P. Beller, K. Beckert, B. Franzke, F. Nolden, M. Steck, Nucl. Instr. and Meth. A 532 (2004) 483. [7] A. Dolinskii, S. Litvinov, M. Steck, H. Weick, Nucl. Instr. and Meth. A 574 (2007) 207.
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 266 (2008) 4579–4582 www.elsevier.com/locate/nimb
The CR storage ring in an isochronous mode operation with nonlinear optics characteristics A. Dolinskii *, H. Geissel, S. Litvinov, F. Nolden, M. Steck, H. Weick GSI, Planckstrasse 1, 64291 Darmstadt, Germany Available online 6 June 2008
Abstract In the Facility for Antiproton and Ion Research (FAIR), which is presently designed at GSI (Darmstadt, Germany) a variety of new short-lived nuclides will be generated with the Super-FRS by using projectile fragmentation or uranium fission. The storage rings for the CR-RESR complex have been designed for efficient cooling and accumulation of antiprotons and cooling and deceleration of rare isotopes beams. A new Collector Ring (CR) is planned to be constructed, where one of the functions is devoted also to mass measurements of very short-lived nuclei when it is tuned to an isochronous mode. The structure of the ring lattice and its ion-optical properties in the isochronous mode are described. Nonlinear ion-optical characteristics and their influence on an achievable mass resolving power in an isochronous mode operation of the CR are discussed. Ó 2008 Elsevier B.V. All rights reserved. PACS: 29.20.Dh; 29.27.Fh; 41.85.p Keywords: CR; Storage ring; Isochronous optic; Mass measurements
1. Introduction Mass measurements of very exotic nuclei up to the limits of nuclear existence are essential for studies of nuclear structure allowing to discover new shell effects, nuclear shapes, decay properties, creation of the elements in stars. Mass measurements of exotic nuclei are a challenge because of the low production cross sections, the large transverse emittance and longitudinal momentum spread of radioactive ion beams separated in flight. A further challenge arises due to the limit in preparation and observation times because of the short life time of the secondary ions. Storage rings can be used as instruments for mass measurements of nuclei [1]. At GSI two methods have been developed for precise mass measurements of exotic nuclei at relativistic energies using the ESR storage ring: ‘Schottky Mass Spectometry (SMS)’ for longer-lived isotopes *
Corresponding author. Tel.: +49 06159 711511; fax: +49 06159 712044. E-mail address: [email protected] (A. Dolinskii). 0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.05.082
[2], and ‘Isochronous Mass Spectrometry (IMS)’ for short-lived isotopes [3]. Both methods are based on accurate measurements of the revolution frequency which characterizes the mass-to-charge ratio of the circulating ions. In SMS the velocity spread of the relativistic hot fragment beams is reduced by electron cooling. For IMS the ring optics is tuned to an isochronous mode such that the differences in velocities are compensated by different path lengths. The planned FAIR facility [4] will open unique opportunities for the production, accumulation and mass measurements of radioactive nuclides, which are very far from stability. The Super-FRS [5] – CR (Collector Ring) [6] will be a powerful tool to provide short-lived exotic nuclides for precise measurements at relativistic energies. Experiments involving nuclei with very short half-lives, down to the ls range will be performed in the CR operated in the isochronous mode. The experimental equipment in the CR will include two time-of-flight detectors, which enable precise revolution frequency measurements in a very short time. The goal for the mass resolving power is more than 105
4580
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4579–4582
with a mass accuracy better then 106. In this article the isochronous mode of the CR operation is discussed. 2. The CR characteristics in the first order design The general layout of the CR is shown in Fig. 1. The CR is dedicated to efficient cooling of rare isotope beams (RIB mode) as well as antiproton beams (PBAR mode). Tuning the CR to an isochronous mode (IMS) it will be used as a time-of-flight (TOF) mass spectrometer. The CR will accept the hot beams coming from the Super-FRS (in RIB and IMS modes) or antiproton separator (in PBAR mode) with acceptances given in Table 1. The lattice is designed as a racetrack-shaped storage ring, consisting of two 180o arc sections connected by two long straight sections. One straight section will be occupied by the injection/extraction system devices and three pick-up tanks for stochastic cooling. The other straight section will host five RF-cavities for bunch rotation and three kicker tanks for stochastic cooling. Pick-
Fig. 1. Layout of the CR lattice. SCP – stochastic cooling pick-ups; SCK – stochastic cooling kickers; dipol – dipole magnet, quad – quadrupole magnet; RF – cavities – rf-cavities for bunch rotations; ink-n – injection kicker; exk-n – extraction kicker; TOF – time-of-flight detector; sx-n – sextupole magnets (n-number of family).
Table 1 The CR parameters Mode operation
RIB
PBAR
IMS
Ion energy (MeV/u) Hor. acceptance (mm mrad) Ver. acceptance (mm mrad) Momentum acceptance (%)
740 200 200 3
3000 240 240 6
790 100 100 1
Betatron tunes Hor. Qx Ver. Qy Transition energy, ctr
3.18 3.17 3.52
4.45 4.43 2.91
3.56 4.41 1.84
up and kicker tanks for stochastic cooling are located close to one of the arcs. Special requirements for the lattice are the following: (a) dispersion-free straight sections; (b) certain betatron phase advances between pick-ups and kickers for stochastic cooling (Dlh,v = (2n + 1)p/2); (c) the ctr (transition energies) given in Table 1 must be provided. All CR (RIB, PBAR ans IMS) modes will be operated at constant magnetic field level close to the maximum bending power of Bq = 13 Tm. Hence the velocity of the ions in each operation mode is different. To achieve efficient stochastic cooling only in RIB and PBAR modes one has to optimize the frequency slip factor g = |1/c2 1/ctr2| for each beam velocity. In IMS mode one has to achieve the condition when the circulation time of a particle is independent of their velocity. In this case the quadrupole magnets must be tuned to obtain the transition energy ctr equal the Lorentz factor c (g = 0). That means the different optics of the CR can be done by a different focusing strength of the ring quadrupoles. 12 independent power supplies for quadrupole magnets are foreseen in order to have flexibility in the optics variation. For the isochronous condition a very large dispersion value of Dh max is needed (up to 23 m), which leads to a decrease in ring acceptance. In Fig. 2 the calculated betatron bh,v and dispersion Dh functions for a quarter of the ring are shown in the isochronous mode.
Fig. 2. Twiss and dispersion functions over one quarter of the CR lattice.
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4579–4582
3. Time-of-Flight measurements in a ring The principle of the TOF detector is that the ions passing through a thin foil emit secondary electrons, which are detected to determine the revolution time in the ring. The mass of different nuclides is calculated from the revolution time (or frequency). Having the frequencies of unknown and known nuclides one can define the unknown mass by the formula Df 1 Dðm=qÞ c2 Dm df ð1Þ ¼ 2 þ 1 2 þ ctr m f ctr m=q f error In the ideal case in the isochronous condition (ctr = c and ctr = const) the ions with different mass-to-charge ratio (m/q) are recognized in frequency if their mean relative frequency shift Df/f is larger than the full relative frequency width of the beam signal (df/f)error. Therefore, an accurate determination of the m/q ratio depends on how low the relative spread (df/ferror of the frequency signal can be achieved. In practice the parameter ctr has a dependence on the momentum deviation of the particle from the reference orbit (ctr = ctr(Bq)) that results in a low resolving power. This effect arises because of the chromatic aberrations of the magnetic elements in the CR lattice and therefore must be minimized by means of the sextupole correction. In Fig. 3 one can see the ctr variation over the momentum acceptance of 1% before and after correction. One needs at least two independently powered sextupole families in order to reduce the ctr variation from 3.6% up to 0.1% as shown in Fig. 3. After sextupole correction the resolving power of more than 106 can be reached if the relative frequency spread of a signal (df/f)error is better than 5 107. An additional aspect that should be considered is that the ideal isochronous condition in the ring can be fulfilled only for one species with one mass-to-charge ratio. Ions with other m/q will become less isochronous. During more than hundred turns in the ring the stored ions lose energy
Fig. 3. Variation of the ctr over full momentum acceptance in the ring due to the chromatic aberration of the quadrupole magnets.
4581
in the foil of the TOF detector, which leads to non-isochronous conditions and, as consequence, to a reduction of accuracy of measurements. For evaluations of non-isochronous particles one needs to measure their velocity deviation from the reference particle by means of the second TOF detector, which will be placed downstream by 30 m distance from the first TOF detector. The measurement of the velocity with about Dv/v = 104 accuracy allows to determine the time and consequently the mass of an isotope with an accuracy of better than 106, when ions fulfil the isochronous condition.
4. Nonlinear effects Nonlinear effects are an essential part of the study in the isochronous mode because of its influence the width of the beam signal (df/f)error in formula (1) and as consequence the resolving power of the TOF measurements. The momentum dependence of the dipole curvature and of the quadrupole focusing strength produces a variation of the orbit dispersion and betatron functions. The control of the orbit dispersion and therefore adjustment of the orbit length imposes an extra condition with respect to the chromaticity correction. In [7] the detailed analysis of the frequency spread depending on the ring acceptance, magnet misalignments, nonlinear field errors in the CR are given. It was shown in [7] that six independently powered sextupole families are required in order to correct the chromatic effect and simultaneously to minimize the influence of the nonlinear field effect on the width of the beam signal (df/f)error. Another effect, which was investigated for the CR ring, is the fringe field influence on the parameter ctr. Because of the exceptionally large emittance associated with hot ion beams, which will be injected in the ring, unprecedented apertures are required for the quadrupole magnets. In the CR it is planned that the normal conducting arc quadrupoles will have an aperture of 40 cm, which leads to strong
Fig. 4. Dependence of ctr on a momentum deviation Dp/p.
4582
A. Dolinskii et al. / Nucl. Instr. and Meth. in Phys. Res. B 266 (2008) 4579–4582
extended fringe field proportional to the pole field. In Fig. 4 the result of calculations showing the influence of the fringe field of quadrupoles on the parameter ctr is plotted. Fortunately the fringe field acts in the opposite direction compared to the influence of the nonlinear field errors of the magnets. To control the parameter ctr over the full momentum acceptance against fringe fields one needs two families of octupole correctors. From Fig. 4 we can deduce that octupole corrections can considerably reduce the influence of the fringe field on the variation of the parameter ctr over the full momentum acceptance. 5. Conclusion The CR, which is designed for a fast cooling of ions, is considered also to be used as an isochronous ring for the mass measurements of short-lived nuclei. Numerous simulations show that in this storage ring the accuracy of mea-
surements can be reached better that 106. A strong impact on the resolving power is arisen by fringe field of the wide aperture quadrupole magnets. The correction scheme of the CR requires six independently powered sextupole and two octupole corrector families in order to minimize the chromatic, geometrical and fringe field effects. References [1] [2] [3] [4]
H. Wollnik, Nucl. Instr. and Meth. A 258 (1987) 289. T. Radon et al., Nucl. Phys. A 677 (2000) 75. M. Hausmann et al., Nucl. Instr. and Meth. A 446 (2000) 569. W. Henning, in: Proceedings of the EPAC2004, Lucerne, Switzerland, p. 50. [5] H. Geissel et al., Nucl. Instr. and Meth. B 204 (2003) 71. [6] A. Dolinskii, P. Beller, K. Beckert, B. Franzke, F. Nolden, M. Steck, Nucl. Instr. and Meth. A 532 (2004) 483. [7] A. Dolinskii, S. Litvinov, M. Steck, H. Weick, Nucl. Instr. and Meth. A 574 (2007) 207.