- Email: [email protected]
Lifetimes of relativistic heavy-ion beams in the High Energy Storage Ring of FAIR
Nuclear Inst, and Methods in Physics Research B 421 (2018) 45–49
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Lifetimes of relativistic heavy-ion beams in the High Energy Storage Ring of FAIR
T
⁎
V.P. Shevelkoa, , Yu. A. Litvinovb, Th. Stöhlkerb,c,d, I. Yu. Tolstikhinaa a
P.N. Lebedev Physical Institute, Leninskii prospect 53, 119991 Moscow, Russia GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany c Helmholtz-Institute Jena, 07743 Jena, Germany d Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, 07743 Jena, Germany b
A R T I C L E I N F O
A B S T R A C T
Keywords: Facility for Antiproton and Ion Research (FAIR) High Energy Storage Ring (HESR) Ion-beam lifetimes Charge-changing cross sections Vacuum conditions
The High Energy Storage Ring, HESR, will be constructed at the Facility for Antiproton and Ion Research, FAIR, Darmstadt. For the first time, it will be possible to perform experiments with cooled high-intensity stable and radioactive heavy ions at highly relativistic energies. To design experiments at the HESR, realistic estimations of beam lifetimes are indispensable. Here we report calculated cross sections and lifetimes for typical U88 + , U 90 +, U 92 + , Sn49 + and Sn50 + ions in the energy range E = 400 MeV/u–5 GeV/u, relevant for the HESR. Interactions with the residual gas and with internal gas-jet targets are also considered.
1. Introduction The Facility for Antiproton and Ion Research, FAIR, is under construction in Darmstadt, Germany [1]. One of the unique features of FAIR is the planned complex of various storage rings and traps covering about 10 orders of magnitude in kinetic energies of stored particles [2,3]. Available now are the HITRAP [4] for storing highly charged ions basically at rest, the just commissioned CRYRING [5,6] for storing ion beams in the energy range from a few hundred keV/u to 10−15 MeV/u, and the Experimental Storage Ring [7], ESR, covering energies from 4 MeV/u to about 400 MeV/u. Owing to the large magnetic rigidity Bρ = 50 Tm, the High Energy Storage Ring HESR, will enable storing and cooling beams of highly charged ions in the wide energy range starting from the ESR energies of 400 MeV/u up to high relativistic energies of ≈5 GeV/u. The HESR has originally been designed for experiments with stored and cooled antiproton beams, which is pursued by the PANDA collaboration of FAIR [8]. The consequence of the FAIR Modularized Start Version, MSV, [9] is that the experiments with stored highly charged ions are transferred also to the HESR. The feasibility of running the HESR with heavy ions has been thoroughly checked [10,11]. The envisioned research program at the HESR is rich and includes experiments in realm of atomic physics, astrophysics as well as tests of fundamental problems of symmetries and particle interactions. These experiments are being prepared within the SPARC collaboration of FAIR [12,13], and some of the physics cases are
⁎
already described in [14–20]. Since the HESR was not primarily aimed at storing highly charged ions, its vacuum system is not foreseen to be bakeable. In this work, we use the realistic composition of residual-gas components expected in the HESR to calculate the storage times of several highly charged heavy ions of interest. Furthermore, it is essential to consider particle losses due to interactions with internal gas-jet targets. The main aim of this work is to provide a reliable data basis for the design of physics experiments at HESR such as charge-changing cross sections (loss and capture) of highly charged uranium and tin ions, colliding with residual-gas components and gas-jet targets, and corresponding ion-beam lifetimes in the energy range of E = 400 MeV/ u − 5 GeV/u. These results can also be helpful for radiation safety and civil construction optimization of the FAIR facility. Calculated electronloss and electron capture cross sections can be applied for other storage rings or synchrotrons having the same projectile ion beams but different residual-gas compositions. In general, a contribution of recombination processes of ions with electron-cooling electrons plays also a significant role in storage rings (see, e.g., [21–23]). The beam losses due to these processes depend dramatically on the specific parameters of the electron cooler device. However, within the MSV of FAIR the HESR will be equipped with the 2 MeV electron cooler which will not allow for beam cooling up to the highest energies [24]. It is thus assumed that the beams in the energy range from 740 MeV/u to 5 GeV/u will be cooled by stochastic cooling [25]. Therefore, in this work we omit the discussion of the losses due to
Corresponding author. E-mail address: [email protected] (V.P. Shevelko).
https://doi.org/10.1016/j.nimb.2018.02.012 Received 20 November 2017; Received in revised form 8 February 2018; Accepted 12 February 2018 0168-583X/ © 2018 Elsevier B.V. All rights reserved.
Nuclear Inst, and Methods in Physics Research B 421 (2018) 45–49
V.P. Shevelko et al.
electron cooling. 2. Calculations of electron-loss and electron-capture cross sections Calculations of electron-loss (EL) and electron-capture (EC) cross sections are presented for U88 +, U 90 +, U 92 +, Sn49 +, and Sn50 + ions, colliding with H, He, C, N, O, Ar, Kr and Xe atoms at relativistic energies of E = 400 MeV/u–5 GeV/u. These data are required for estimation of the ion-beam lifetimes due to interactions of ions with residual-gas atoms and molecules and with internal gas-jet targets (see next sections). For collision systems considered, theoretical predictions for both chargechanging processes are studied in detail [26–29] and are benchmarked by experimental data [26,30,31]. The contribution of multi-electron loss and capture processes to the total cross sections at relativistic energies is very small (see, e.g., [27]), therefore, in calculations in the present paper only single-electron processes are considered. Single-electron loss cross-section data σEL are obtained using the RICODE-M program described in [32]. The code is based on the relativistic Born approximation using relativistic (magnetic) interaction between colliding particles and relativistic wave functions for the active projectile electron in discrete and continuum spectra. In the RICODE-M program, the relativistic radial wave functions are found by solving the Schrödinger equation in the effective field of atomic core, calculated with relativistic Dirac wave functions. At relativistic energies considered, single-electron capture cross sections σEC are calculated as a sum of non-radiative (NRC) and radiative (REC) capture cross sections:
σEC = σNRC + σREC ,
Fig. 2. Calculated single-electron capture cross sections for Sn ions, Eq. (1), colliding with H, He, C, N, O, F, Ar, Kr and Xe atoms as a function of ion energy, present work.
be estimated to be about 30%. In case of NRC it may exceed even a factor of 3 but for relativistic energies and low-Z targets (Z > 36) its role is basically negligible. Calculated EL and EC cross sections are presented in Figs. 1–3. EL cross sections for H-like tin, Be- and He-like uranium ions are presented in Fig. 1. In the energy range considered, EL cross sections increase as the target atomic number ZT increases approximately as σEL ∼ ZT2 + ZT in accordance to the Bohr scaling low. Due to the relativistic effect, in the case of atomic targets EL cross sections exhibit a quasi- constant behavior because of the screened Coulomb field created by the target atom, and EL cross sections increase with energy increasing in the case of ionic targets, e.g., protons (see [35,36] for more details). Ion-energy dependence of calculated EC cross sections, Eq. (1), is represented in Figs. 2 and 3. Calculations show that a contribution of tot σNRC to the total cross section σEC is different for different target atoms: for an H target it is practically negligible, for C, N and O targets it is about 10% and is the largest for Ar and Xe targets reaching up to 100%. A contribution of NRC cross sections at high energies can be very significant and should be accounted for together with REC cross sections (see, e.g., [40–42]).
(1)
where σNRC are calculated by the CAPTURE code [33], and σREC are rigorous relativistic photo-recombination cross-sections for bare ions treated within the impulse-approximation [34]. The CAPTURE code is intended for calculating probabilities and cross sections of one-electron capture processes and is based on the Brinkman-Kramers approximation. The code calculates normalized single-electron capture probabilities P (b,υ ), which are less than unity for all impact parameters b and ion velocities υ, and corresponding capture cross sections. The accuracy of the calculated charge-changing cross sections can in general
Fig. 1. Single-electron loss cross sections of Sn49 + , U88 + , and U 90 + ions by H, He, C, N, O, F, Ar, Kr and Xe atoms as a function of ion energy - calculations by the RICODE-M code, present work.
46
Nuclear Inst, and Methods in Physics Research B 421 (2018) 45–49
V.P. Shevelko et al.
Fig. 3. Calculated single-electron EC cross sections, Eq. (1), for uranium ions, colliding with H, He, C, N, O, F, Ar, Kr and Xe atoms as a function of ion energy, present work.
∑
3. Ion-beam lifetimes due to interaction with accelerator residual gas
Z =
The total ion-beam lifetime in accelerator τtot due to atomic interactions of the beam with a residual gas, a gaseous target and cooling electrons, is usually expressed in the form:
where N is the total number of atoms in the molecule. Then σmol per molecule can be found from the formula:
τtot =
(τec−1
+
τrg−1
+
τgt−1)−1,
σmol = Nσ (Z ),
(2)
∑ T
YT = 1,
(5)
(6)
where σ (Z ) is the cross section for an atom with an atomic number Zi = Z . The additivity rule (6) was examined experimentally in [38] for 6 MeV/u-Xe18 + ions colliding with noble-gas atoms and molecular targets, and it was found that under experimental conditions, the additivity rule works very well for the measured total and multiple-electron EL cross sections. In the present work, the lifetimes of U88 +, U 90 +, U 92 +, Sn49 + , and Sn50 + ion beams are calculated using Eq. (3) and the results are shown in Fig. 4 as a function of ion energy at a residual-gas pressure of 6.9 × 10−10 mbar. The fractions YT of the gas components are according to
where τec, τrg and τgt denotes lifetimes responsible for interaction of the ion beam with electrons in the electron cooler, residual- or target-gas atoms and molecules and with a gas target, respectively. Since electron cooling is not considered in this work, the quantity τec is set to zero. For an estimation of the ion-beam lifetimes τrg and τgt the following formula is accepted:
τrg,gt = [ρβc ∑T YT (σEC + σEL)]−1 ,
Zi ni / N ,
i
(3)
where ρ denotes the residual-gas density in part /cm3, β = υ / c the relativistic factor, υ the ion velocity, c the speed of light, c ≈ 3.0 × 1010 cm/s, YT the fraction of the gas components, σEC and σEL the total EC and EL cross sections in cm2, respectively, i.e., summed over all multiple-electron processes. The summation on T in Eq. (3) is made over all gas components. The formula (3) gives reasonable results for estimating and predicting the ion-beam lifetimes in accelerators and storage rings (see, e.g., [35–37]). For molecular targets, the Bragg’s additivity rule for charge-changing cross sections is used, i.e., cross section for a molecule σmol is represented as a sum of those for atoms composing the molecule
σmol =
∑ i
ni σ (Zi ),
(4)
where ni is the number of atoms in the molecule with atomic number Zi . For example, for the CO2 molecule target, EL and EC cross sections are calculated as σ (CO2) = σ (C) + 2σ (O), where σ (C) and σ (O) denote cross sections for atomic carbon and oxygen. Another form of the additivity rule to estimate EL cross sections for molecular targets is suggested in [38] by introducing the target average atomic number Z in the form:
Fig. 4. Calculated ion-beam lifetimes for U88 + , U 90 + , , Sn49 + , and Sn50 + ions as a function of ion energy using Eq. (3) at a residual-gas pressure of 6.9 × 10−10 mbar, present work. Concentrations of residual components are given in Table 1. The charge-changing cross sections are given in Figs. 1–3.
47
Nuclear Inst, and Methods in Physics Research B 421 (2018) 45–49
V.P. Shevelko et al.
Table 1 Residual atomic and molecular gas components used for calculating the ion/beam lifetimes, Eq. (3), for HESR conditions. Atom, molecule
Fraction
Atom, molecule
Fraction
H H2 HO H2O C N O
0.223 0.188 0.0437 0.0833 0.0385 0.0219 0.216
O2 CO CO2 CO/N2 F Ar Xe
0.0773 0.00208 0.0229 0.0583 0.0229 0.00106 0.00106
Fig. 5. Calculated ion-beam lifetimes (in s) for Sn49 + and Sn50 + ions in gaseous targets as a function of ion energy, Eq. (3), at a gas pressure of P = 6.44 × 10−8 mbar and a circumference of L = 575 m, present work. The charge-changing cross sections are given in Figs. Figs. 1–3.
HESR vacuum tests [39] and are presented in Table 1. As seen from Fig. 4, at given vacuum conditions and energies E ≳1 GeV/u, the predicted lifetimes for bare projectile ions, Sn50 + and U 92 +, are rather long and increase as ion energy increases because for bare ions EC is the only charge-changing mechanism which occurs with small cross sections and leads to increasing the beam lifetime with the ion energy increasing. For the projectile few-electron ions, Sn49 + , U88 + and U 90 +, the beam
Fig. 6. Estimated ion-beam lifetimes (in s) for U88 +, U 90 + and ions in gaseous targets as a function of ion energy, Eq. (3), at a gas pressure of P = 6.44 × 10−8 mbar and a circumference of L = 575 m, present woprk. The charge-changing cross sections are given in Figs. 1–3.
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Nuclear Inst, and Methods in Physics Research B 421 (2018) 45–49
V.P. Shevelko et al.
Acknowledgements
lifetimes at relativistic energies are mainly defined by EL processes, i.e., projectile ionization, which is characterized by quasi-constant cross sections due to the influence of the relativistic effects, and, as a consequence, lead to a quasi-constant behavior of the beam lifetimes.
The authors would like to thank the colleagues from the SPARC collaboration for their enthusiasm concerning the physics program at the HESR, which motivated us for this work. We thank Rudolf Maier, Dieter Prasuhn, Rolf Stassen, and Raimund Tölle for enlightening discussions on experimental capabilities at the HESR. We also thank Filip Zahariev for providing us the data on the expected rest-gas composition in the HESR.
4. Ion-beam lifetimes due to interaction with gaseous targets Using cross-section data, calculated above, ion-beam lifetimes of relativistic uranium and tin ions are also predicted for collisions with gaseous H2, He, N2, Ar, Kr and Xe targets at a gas areal density ρ = 1014 part/cm2 or a gas pressure P = 6.44 × 10−8 mbar, and a circumference of the HESR ring L = 575 m. The results are shown in Figs. 5 and 6. As is seen from Figs. 5 and 6, the lifetimes of relativistic ions show a different behavior: they are nearly constant for dressed ions and increase with energy increases for bare ions because of different behavior of the electron-loss cross sections. Unfortunately, it is difficult to predict the ion-beam lifetimes for arbitrary ions at high energies. However, in some cases it is possible to estimate the required lifetimes. In work [36], using the properties of the EL cross sections and numerical results, a semi-empirical formula was devised for single-electron loss cross sections of heavy ions colliding with neutral atoms, covering also the relativistic energy range. Using this formula together with the Schlachter semi-empirical formula [43] for single-electron capture cross sections, a reasonable estimate for the ion-beam lifetime over a wide energy range can be achieved (see, e.g., Fig. 14 in [27]).
References [1] W.F. Henning (Ed.), International Accelerator Facility for Beams of Ions and Antiprotons, GSI-Darmstadt, November 2001,http://www.fair-center.de/ fileadmin/fair/publicationsFAIR/FAIRCDR.pdf. [2] Th. Stöhlker, et al., Hyperfine Interact. 227 (2014) 45. [3] Th. Stöhlker, et al., Nucl. Instrum. Methods B 365 (2015) 680. [4] F. Herfurth, et al., Phys. Scr. T 166 (2015) 014065. [5] M. Lestinsky, et al., Phys. Scr. T 166 (2015) 014075. [6] M. Lestinsky, et al., Eur. Phys. J. Spec. Top. 225 (2016) 797. [7] B. Franzke, Nucl. Instrum. Methods B 24 (25) (1987) 18. [8] K. Peters, et al., Nucl. Phys. News. 27 (2017) 24. [9] FAIR Green Paper: The Modularized Start Version, Oktober 2009,http://www.gsi. de/documents/DOC-2009-Nov-124-1.pdf. [10] Th. Stöhlker, et al., SPARC Experiments at the HESR: A Feasibility Study, Report, GSI, Darmstadt, 2012 https://www.gsi.de/fileadmin/SPARC/documents/ SPARC%40HESRFSV26.pdf. [11] O. Kovalenko et al., in: Proc. Int. Part. Acc. Conf. (IPAC2014), Dresden, Germany, pp. 1117–1119 (July 2014). [12] SPARC Technical Proposal,http://www.gsi.de/forschung/fairexperiments/sparc/ documents.html, 2005. [13] Th. Stöhlker, et al., AIP Conf. Proc. 1336 (2011) 132. [14] P.M. Walker, et al., Int. J. Mass Spectrom. 349–350 (2013) 247. [15] Yu.A. Litvinov, et al., Nucl. Instrum. Methods B 317 (2013) 603. [16] S. Tashenov, et al., Phys. Scr. T 166 (2015) 014027. [17] P.-M. Hillenbrand, et al., Phys. Scr. T 166 (2015) 014026. [18] Th. Stöhlker, et al., Phys. Scr. T 166 (2015) 014025. [19] A. Gumberidze, et al., Phys. Scr. T 166 (2015) 014076. [20] Th. Stöhlker, et al., Phys. Scr. T 156 (2013) 014085. [21] H. Poth, Phys. Rep. 196 (1990) 135. [22] O. Boine-Frankenheim, R. Hasse, F. Hinterberger, et al., Nucl. Instrum. Methods A 560 (2006) 245. [23] R.D. DuBois, O. de Lucio, M. Thomason, et al., Nucl. Instrum. Methods B 261 (2007) 230. [24] M. Steck et al., in Proc. Int. Part. Acc. Conf. IPAC2012, New Orleans, Louisiana, USA, 2012, pp. THPPP002,http://www.jacow.org. [25] H. Stockhorst et al., in Proc. Int. Part. Acc. Conf. IPAC2012, New Orleans, Louisiana, USA, 2012, pp. MOPPD009,http://www.jacow.org. [26] T. Stöhlker, et al., Phys. Rev. A 58 (1998) 2043. [27] I. Yu Tolstikhina, V.P. Shevelko, Phys. Usp. 56 (2013) 213. [28] I. Yu. Tolstikhina, V.P. Shevelko, Phys. Usp. (2018), in press, doi: 10.3367/UFNe. 2017.02.038071. [29] I.Yu. Tolstikhina, M. Imai, N. Winckler, V.P. Shevelko, Basic Atomic Interactions of Accelerated Heavy Ions in Matter, Springer, Heidelberg, 2018 (in press). [30] T. Stöhlker, et al., Nucl. Instrum. Methods B 124 (1997) 160. [31] G. Baur, et al., Phys. Rev. A 80 (2009) 012713. [32] I.Yu. Tolstikhina, I.I. Tupitsyn, S.N. Andreev, V.P. Shevelko, J. Exp. Theoret. Phys. 119 (2014) 1. [33] V.P. Shevelko, O. Rosmej, H. Tawara, I.Yu. Tolstikhina, J. Phys. B 37 (2004) 201. [34] A. Ichihara, J. Eichler, Atomic Data Nucl. Data Tables 74 (2000) 1. [35] I.Yu. Tolstikhina, V.P. Shevelko, JETP Letters, 94 (2011) 152 Pisma v Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, 94 (2011) 157. [36] V.P. Shevelko, I.L. Beigman, M.S. Litsarev, et al., Nucl. Instrum. Methods B 269 (2011) 1455. [37] L. Bozyk, F. Chill, M.S. Litsarev, et al., Nucl. Instrum. Methods B 372 (2016) 102. [38] R.L. Watson, Y. Peng, V. Horvat, et al., Phys. Rev. A 67 (2003) 022706. [39] Filip Zahariev, private communications (2016–2017). [40] J. Eichler, Phys. Rep. 193 (1990) 165. [41] J. Eichler, W.E. Meyerhof, Relativistic Atomic Collisions, Academic Press, San Diego, 1995. [42] C. Scheidenberger, et al., Nucl. Instrum. Methods B 142 (1998) 441. [43] A.S. Schlachter, et al., Phys. Rev. A 27 (1983) 3372.
5. Summary Electron-loss and electron-capture cross sections were calculated for U88 +, U 90 +, U 92 +, Sn49 +, and Sn50 + ions colliding with H, He, C, N, O, Ar, Kr, and Xe atoms in the energy range of E = 400 MeV/u − 5 GeV/u. The ions and the energy range were selected to match the future experiments with highly charged heavy ions in the HESR. As expected, the bare ions have much longer lifetimes than fewelectron ions. The shortest lifetime is achieved for U 92 + colliding with dense Xe target. At 400 MeV/u it is about 1.6 s and it increases rapidly with energy reaching about 830 s at 5 GeV/u. All the other calculated lifetimes are considerably longer. Without internal gas targets, all lifetimes exceed one hour, which means that the particle losses of the beams during the acceleration in the HESR can be neglected. Thus the first preliminary conclusion is that the planned experiments on fullystripped ions have no severe constraints in terms of storage lifetimes. Considering the few-electron ions, the losses are dominated by electron-stripping processes. Without internal targets, the shortest lifetime is obtained for Be-like U88 + of about 103 s at 400 MeV/u. The lifetimes are about constant at all considered energies up to 5 GeV/u. These results confirm the fact that the slow acceleration in the HESR of few-electron ions is possible with the present residual gas composition. Using of dense internal targets, especially the Xe jet, dramatically decreases the lifetimes of U88 + to about 0.1 s, which makes the accomplishment of such experiments difficult and requires optimization of the duty cycle. However, if using light jet targets like H2 or He, the lifetimes are longer than about 100 s. According to experience at the ESR, we can conclude that the latter lifetimes are in the comfortable range for performing in-ring experiments.
49
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Lifetimes of relativistic heavy-ion beams in the High Energy Storage Ring of FAIR
T
⁎
V.P. Shevelkoa, , Yu. A. Litvinovb, Th. Stöhlkerb,c,d, I. Yu. Tolstikhinaa a
P.N. Lebedev Physical Institute, Leninskii prospect 53, 119991 Moscow, Russia GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany c Helmholtz-Institute Jena, 07743 Jena, Germany d Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, 07743 Jena, Germany b
A R T I C L E I N F O
A B S T R A C T
Keywords: Facility for Antiproton and Ion Research (FAIR) High Energy Storage Ring (HESR) Ion-beam lifetimes Charge-changing cross sections Vacuum conditions
The High Energy Storage Ring, HESR, will be constructed at the Facility for Antiproton and Ion Research, FAIR, Darmstadt. For the first time, it will be possible to perform experiments with cooled high-intensity stable and radioactive heavy ions at highly relativistic energies. To design experiments at the HESR, realistic estimations of beam lifetimes are indispensable. Here we report calculated cross sections and lifetimes for typical U88 + , U 90 +, U 92 + , Sn49 + and Sn50 + ions in the energy range E = 400 MeV/u–5 GeV/u, relevant for the HESR. Interactions with the residual gas and with internal gas-jet targets are also considered.
1. Introduction The Facility for Antiproton and Ion Research, FAIR, is under construction in Darmstadt, Germany [1]. One of the unique features of FAIR is the planned complex of various storage rings and traps covering about 10 orders of magnitude in kinetic energies of stored particles [2,3]. Available now are the HITRAP [4] for storing highly charged ions basically at rest, the just commissioned CRYRING [5,6] for storing ion beams in the energy range from a few hundred keV/u to 10−15 MeV/u, and the Experimental Storage Ring [7], ESR, covering energies from 4 MeV/u to about 400 MeV/u. Owing to the large magnetic rigidity Bρ = 50 Tm, the High Energy Storage Ring HESR, will enable storing and cooling beams of highly charged ions in the wide energy range starting from the ESR energies of 400 MeV/u up to high relativistic energies of ≈5 GeV/u. The HESR has originally been designed for experiments with stored and cooled antiproton beams, which is pursued by the PANDA collaboration of FAIR [8]. The consequence of the FAIR Modularized Start Version, MSV, [9] is that the experiments with stored highly charged ions are transferred also to the HESR. The feasibility of running the HESR with heavy ions has been thoroughly checked [10,11]. The envisioned research program at the HESR is rich and includes experiments in realm of atomic physics, astrophysics as well as tests of fundamental problems of symmetries and particle interactions. These experiments are being prepared within the SPARC collaboration of FAIR [12,13], and some of the physics cases are
⁎
already described in [14–20]. Since the HESR was not primarily aimed at storing highly charged ions, its vacuum system is not foreseen to be bakeable. In this work, we use the realistic composition of residual-gas components expected in the HESR to calculate the storage times of several highly charged heavy ions of interest. Furthermore, it is essential to consider particle losses due to interactions with internal gas-jet targets. The main aim of this work is to provide a reliable data basis for the design of physics experiments at HESR such as charge-changing cross sections (loss and capture) of highly charged uranium and tin ions, colliding with residual-gas components and gas-jet targets, and corresponding ion-beam lifetimes in the energy range of E = 400 MeV/ u − 5 GeV/u. These results can also be helpful for radiation safety and civil construction optimization of the FAIR facility. Calculated electronloss and electron capture cross sections can be applied for other storage rings or synchrotrons having the same projectile ion beams but different residual-gas compositions. In general, a contribution of recombination processes of ions with electron-cooling electrons plays also a significant role in storage rings (see, e.g., [21–23]). The beam losses due to these processes depend dramatically on the specific parameters of the electron cooler device. However, within the MSV of FAIR the HESR will be equipped with the 2 MeV electron cooler which will not allow for beam cooling up to the highest energies [24]. It is thus assumed that the beams in the energy range from 740 MeV/u to 5 GeV/u will be cooled by stochastic cooling [25]. Therefore, in this work we omit the discussion of the losses due to
Corresponding author. E-mail address: [email protected] (V.P. Shevelko).
https://doi.org/10.1016/j.nimb.2018.02.012 Received 20 November 2017; Received in revised form 8 February 2018; Accepted 12 February 2018 0168-583X/ © 2018 Elsevier B.V. All rights reserved.
Nuclear Inst, and Methods in Physics Research B 421 (2018) 45–49
V.P. Shevelko et al.
electron cooling. 2. Calculations of electron-loss and electron-capture cross sections Calculations of electron-loss (EL) and electron-capture (EC) cross sections are presented for U88 +, U 90 +, U 92 +, Sn49 +, and Sn50 + ions, colliding with H, He, C, N, O, Ar, Kr and Xe atoms at relativistic energies of E = 400 MeV/u–5 GeV/u. These data are required for estimation of the ion-beam lifetimes due to interactions of ions with residual-gas atoms and molecules and with internal gas-jet targets (see next sections). For collision systems considered, theoretical predictions for both chargechanging processes are studied in detail [26–29] and are benchmarked by experimental data [26,30,31]. The contribution of multi-electron loss and capture processes to the total cross sections at relativistic energies is very small (see, e.g., [27]), therefore, in calculations in the present paper only single-electron processes are considered. Single-electron loss cross-section data σEL are obtained using the RICODE-M program described in [32]. The code is based on the relativistic Born approximation using relativistic (magnetic) interaction between colliding particles and relativistic wave functions for the active projectile electron in discrete and continuum spectra. In the RICODE-M program, the relativistic radial wave functions are found by solving the Schrödinger equation in the effective field of atomic core, calculated with relativistic Dirac wave functions. At relativistic energies considered, single-electron capture cross sections σEC are calculated as a sum of non-radiative (NRC) and radiative (REC) capture cross sections:
σEC = σNRC + σREC ,
Fig. 2. Calculated single-electron capture cross sections for Sn ions, Eq. (1), colliding with H, He, C, N, O, F, Ar, Kr and Xe atoms as a function of ion energy, present work.
be estimated to be about 30%. In case of NRC it may exceed even a factor of 3 but for relativistic energies and low-Z targets (Z > 36) its role is basically negligible. Calculated EL and EC cross sections are presented in Figs. 1–3. EL cross sections for H-like tin, Be- and He-like uranium ions are presented in Fig. 1. In the energy range considered, EL cross sections increase as the target atomic number ZT increases approximately as σEL ∼ ZT2 + ZT in accordance to the Bohr scaling low. Due to the relativistic effect, in the case of atomic targets EL cross sections exhibit a quasi- constant behavior because of the screened Coulomb field created by the target atom, and EL cross sections increase with energy increasing in the case of ionic targets, e.g., protons (see [35,36] for more details). Ion-energy dependence of calculated EC cross sections, Eq. (1), is represented in Figs. 2 and 3. Calculations show that a contribution of tot σNRC to the total cross section σEC is different for different target atoms: for an H target it is practically negligible, for C, N and O targets it is about 10% and is the largest for Ar and Xe targets reaching up to 100%. A contribution of NRC cross sections at high energies can be very significant and should be accounted for together with REC cross sections (see, e.g., [40–42]).
(1)
where σNRC are calculated by the CAPTURE code [33], and σREC are rigorous relativistic photo-recombination cross-sections for bare ions treated within the impulse-approximation [34]. The CAPTURE code is intended for calculating probabilities and cross sections of one-electron capture processes and is based on the Brinkman-Kramers approximation. The code calculates normalized single-electron capture probabilities P (b,υ ), which are less than unity for all impact parameters b and ion velocities υ, and corresponding capture cross sections. The accuracy of the calculated charge-changing cross sections can in general
Fig. 1. Single-electron loss cross sections of Sn49 + , U88 + , and U 90 + ions by H, He, C, N, O, F, Ar, Kr and Xe atoms as a function of ion energy - calculations by the RICODE-M code, present work.
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Fig. 3. Calculated single-electron EC cross sections, Eq. (1), for uranium ions, colliding with H, He, C, N, O, F, Ar, Kr and Xe atoms as a function of ion energy, present work.
∑
3. Ion-beam lifetimes due to interaction with accelerator residual gas
Z =
The total ion-beam lifetime in accelerator τtot due to atomic interactions of the beam with a residual gas, a gaseous target and cooling electrons, is usually expressed in the form:
where N is the total number of atoms in the molecule. Then σmol per molecule can be found from the formula:
τtot =
(τec−1
+
τrg−1
+
τgt−1)−1,
σmol = Nσ (Z ),
(2)
∑ T
YT = 1,
(5)
(6)
where σ (Z ) is the cross section for an atom with an atomic number Zi = Z . The additivity rule (6) was examined experimentally in [38] for 6 MeV/u-Xe18 + ions colliding with noble-gas atoms and molecular targets, and it was found that under experimental conditions, the additivity rule works very well for the measured total and multiple-electron EL cross sections. In the present work, the lifetimes of U88 +, U 90 +, U 92 +, Sn49 + , and Sn50 + ion beams are calculated using Eq. (3) and the results are shown in Fig. 4 as a function of ion energy at a residual-gas pressure of 6.9 × 10−10 mbar. The fractions YT of the gas components are according to
where τec, τrg and τgt denotes lifetimes responsible for interaction of the ion beam with electrons in the electron cooler, residual- or target-gas atoms and molecules and with a gas target, respectively. Since electron cooling is not considered in this work, the quantity τec is set to zero. For an estimation of the ion-beam lifetimes τrg and τgt the following formula is accepted:
τrg,gt = [ρβc ∑T YT (σEC + σEL)]−1 ,
Zi ni / N ,
i
(3)
where ρ denotes the residual-gas density in part /cm3, β = υ / c the relativistic factor, υ the ion velocity, c the speed of light, c ≈ 3.0 × 1010 cm/s, YT the fraction of the gas components, σEC and σEL the total EC and EL cross sections in cm2, respectively, i.e., summed over all multiple-electron processes. The summation on T in Eq. (3) is made over all gas components. The formula (3) gives reasonable results for estimating and predicting the ion-beam lifetimes in accelerators and storage rings (see, e.g., [35–37]). For molecular targets, the Bragg’s additivity rule for charge-changing cross sections is used, i.e., cross section for a molecule σmol is represented as a sum of those for atoms composing the molecule
σmol =
∑ i
ni σ (Zi ),
(4)
where ni is the number of atoms in the molecule with atomic number Zi . For example, for the CO2 molecule target, EL and EC cross sections are calculated as σ (CO2) = σ (C) + 2σ (O), where σ (C) and σ (O) denote cross sections for atomic carbon and oxygen. Another form of the additivity rule to estimate EL cross sections for molecular targets is suggested in [38] by introducing the target average atomic number Z in the form:
Fig. 4. Calculated ion-beam lifetimes for U88 + , U 90 + , , Sn49 + , and Sn50 + ions as a function of ion energy using Eq. (3) at a residual-gas pressure of 6.9 × 10−10 mbar, present work. Concentrations of residual components are given in Table 1. The charge-changing cross sections are given in Figs. 1–3.
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Table 1 Residual atomic and molecular gas components used for calculating the ion/beam lifetimes, Eq. (3), for HESR conditions. Atom, molecule
Fraction
Atom, molecule
Fraction
H H2 HO H2O C N O
0.223 0.188 0.0437 0.0833 0.0385 0.0219 0.216
O2 CO CO2 CO/N2 F Ar Xe
0.0773 0.00208 0.0229 0.0583 0.0229 0.00106 0.00106
Fig. 5. Calculated ion-beam lifetimes (in s) for Sn49 + and Sn50 + ions in gaseous targets as a function of ion energy, Eq. (3), at a gas pressure of P = 6.44 × 10−8 mbar and a circumference of L = 575 m, present work. The charge-changing cross sections are given in Figs. Figs. 1–3.
HESR vacuum tests [39] and are presented in Table 1. As seen from Fig. 4, at given vacuum conditions and energies E ≳1 GeV/u, the predicted lifetimes for bare projectile ions, Sn50 + and U 92 +, are rather long and increase as ion energy increases because for bare ions EC is the only charge-changing mechanism which occurs with small cross sections and leads to increasing the beam lifetime with the ion energy increasing. For the projectile few-electron ions, Sn49 + , U88 + and U 90 +, the beam
Fig. 6. Estimated ion-beam lifetimes (in s) for U88 +, U 90 + and ions in gaseous targets as a function of ion energy, Eq. (3), at a gas pressure of P = 6.44 × 10−8 mbar and a circumference of L = 575 m, present woprk. The charge-changing cross sections are given in Figs. 1–3.
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Acknowledgements
lifetimes at relativistic energies are mainly defined by EL processes, i.e., projectile ionization, which is characterized by quasi-constant cross sections due to the influence of the relativistic effects, and, as a consequence, lead to a quasi-constant behavior of the beam lifetimes.
The authors would like to thank the colleagues from the SPARC collaboration for their enthusiasm concerning the physics program at the HESR, which motivated us for this work. We thank Rudolf Maier, Dieter Prasuhn, Rolf Stassen, and Raimund Tölle for enlightening discussions on experimental capabilities at the HESR. We also thank Filip Zahariev for providing us the data on the expected rest-gas composition in the HESR.
4. Ion-beam lifetimes due to interaction with gaseous targets Using cross-section data, calculated above, ion-beam lifetimes of relativistic uranium and tin ions are also predicted for collisions with gaseous H2, He, N2, Ar, Kr and Xe targets at a gas areal density ρ = 1014 part/cm2 or a gas pressure P = 6.44 × 10−8 mbar, and a circumference of the HESR ring L = 575 m. The results are shown in Figs. 5 and 6. As is seen from Figs. 5 and 6, the lifetimes of relativistic ions show a different behavior: they are nearly constant for dressed ions and increase with energy increases for bare ions because of different behavior of the electron-loss cross sections. Unfortunately, it is difficult to predict the ion-beam lifetimes for arbitrary ions at high energies. However, in some cases it is possible to estimate the required lifetimes. In work [36], using the properties of the EL cross sections and numerical results, a semi-empirical formula was devised for single-electron loss cross sections of heavy ions colliding with neutral atoms, covering also the relativistic energy range. Using this formula together with the Schlachter semi-empirical formula [43] for single-electron capture cross sections, a reasonable estimate for the ion-beam lifetime over a wide energy range can be achieved (see, e.g., Fig. 14 in [27]).
References [1] W.F. Henning (Ed.), International Accelerator Facility for Beams of Ions and Antiprotons, GSI-Darmstadt, November 2001,http://www.fair-center.de/ fileadmin/fair/publicationsFAIR/FAIRCDR.pdf. [2] Th. Stöhlker, et al., Hyperfine Interact. 227 (2014) 45. [3] Th. Stöhlker, et al., Nucl. Instrum. Methods B 365 (2015) 680. [4] F. Herfurth, et al., Phys. Scr. T 166 (2015) 014065. [5] M. Lestinsky, et al., Phys. Scr. T 166 (2015) 014075. [6] M. Lestinsky, et al., Eur. Phys. J. Spec. Top. 225 (2016) 797. [7] B. Franzke, Nucl. Instrum. Methods B 24 (25) (1987) 18. [8] K. Peters, et al., Nucl. Phys. News. 27 (2017) 24. [9] FAIR Green Paper: The Modularized Start Version, Oktober 2009,http://www.gsi. de/documents/DOC-2009-Nov-124-1.pdf. [10] Th. Stöhlker, et al., SPARC Experiments at the HESR: A Feasibility Study, Report, GSI, Darmstadt, 2012 https://www.gsi.de/fileadmin/SPARC/documents/ SPARC%40HESRFSV26.pdf. [11] O. Kovalenko et al., in: Proc. Int. Part. Acc. Conf. (IPAC2014), Dresden, Germany, pp. 1117–1119 (July 2014). [12] SPARC Technical Proposal,http://www.gsi.de/forschung/fairexperiments/sparc/ documents.html, 2005. [13] Th. Stöhlker, et al., AIP Conf. Proc. 1336 (2011) 132. [14] P.M. Walker, et al., Int. J. Mass Spectrom. 349–350 (2013) 247. [15] Yu.A. Litvinov, et al., Nucl. Instrum. Methods B 317 (2013) 603. [16] S. Tashenov, et al., Phys. Scr. T 166 (2015) 014027. [17] P.-M. Hillenbrand, et al., Phys. Scr. T 166 (2015) 014026. [18] Th. Stöhlker, et al., Phys. Scr. T 166 (2015) 014025. [19] A. Gumberidze, et al., Phys. Scr. T 166 (2015) 014076. [20] Th. Stöhlker, et al., Phys. Scr. T 156 (2013) 014085. [21] H. Poth, Phys. Rep. 196 (1990) 135. [22] O. Boine-Frankenheim, R. Hasse, F. Hinterberger, et al., Nucl. Instrum. Methods A 560 (2006) 245. [23] R.D. DuBois, O. de Lucio, M. Thomason, et al., Nucl. Instrum. Methods B 261 (2007) 230. [24] M. Steck et al., in Proc. Int. Part. Acc. Conf. IPAC2012, New Orleans, Louisiana, USA, 2012, pp. THPPP002,http://www.jacow.org. [25] H. Stockhorst et al., in Proc. Int. Part. Acc. Conf. IPAC2012, New Orleans, Louisiana, USA, 2012, pp. MOPPD009,http://www.jacow.org. [26] T. Stöhlker, et al., Phys. Rev. A 58 (1998) 2043. [27] I. Yu Tolstikhina, V.P. Shevelko, Phys. Usp. 56 (2013) 213. [28] I. Yu. Tolstikhina, V.P. Shevelko, Phys. Usp. (2018), in press, doi: 10.3367/UFNe. 2017.02.038071. [29] I.Yu. Tolstikhina, M. Imai, N. Winckler, V.P. Shevelko, Basic Atomic Interactions of Accelerated Heavy Ions in Matter, Springer, Heidelberg, 2018 (in press). [30] T. Stöhlker, et al., Nucl. Instrum. Methods B 124 (1997) 160. [31] G. Baur, et al., Phys. Rev. A 80 (2009) 012713. [32] I.Yu. Tolstikhina, I.I. Tupitsyn, S.N. Andreev, V.P. Shevelko, J. Exp. Theoret. Phys. 119 (2014) 1. [33] V.P. Shevelko, O. Rosmej, H. Tawara, I.Yu. Tolstikhina, J. Phys. B 37 (2004) 201. [34] A. Ichihara, J. Eichler, Atomic Data Nucl. Data Tables 74 (2000) 1. [35] I.Yu. Tolstikhina, V.P. Shevelko, JETP Letters, 94 (2011) 152 Pisma v Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, 94 (2011) 157. [36] V.P. Shevelko, I.L. Beigman, M.S. Litsarev, et al., Nucl. Instrum. Methods B 269 (2011) 1455. [37] L. Bozyk, F. Chill, M.S. Litsarev, et al., Nucl. Instrum. Methods B 372 (2016) 102. [38] R.L. Watson, Y. Peng, V. Horvat, et al., Phys. Rev. A 67 (2003) 022706. [39] Filip Zahariev, private communications (2016–2017). [40] J. Eichler, Phys. Rep. 193 (1990) 165. [41] J. Eichler, W.E. Meyerhof, Relativistic Atomic Collisions, Academic Press, San Diego, 1995. [42] C. Scheidenberger, et al., Nucl. Instrum. Methods B 142 (1998) 441. [43] A.S. Schlachter, et al., Phys. Rev. A 27 (1983) 3372.
5. Summary Electron-loss and electron-capture cross sections were calculated for U88 +, U 90 +, U 92 +, Sn49 +, and Sn50 + ions colliding with H, He, C, N, O, Ar, Kr, and Xe atoms in the energy range of E = 400 MeV/u − 5 GeV/u. The ions and the energy range were selected to match the future experiments with highly charged heavy ions in the HESR. As expected, the bare ions have much longer lifetimes than fewelectron ions. The shortest lifetime is achieved for U 92 + colliding with dense Xe target. At 400 MeV/u it is about 1.6 s and it increases rapidly with energy reaching about 830 s at 5 GeV/u. All the other calculated lifetimes are considerably longer. Without internal gas targets, all lifetimes exceed one hour, which means that the particle losses of the beams during the acceleration in the HESR can be neglected. Thus the first preliminary conclusion is that the planned experiments on fullystripped ions have no severe constraints in terms of storage lifetimes. Considering the few-electron ions, the losses are dominated by electron-stripping processes. Without internal targets, the shortest lifetime is obtained for Be-like U88 + of about 103 s at 400 MeV/u. The lifetimes are about constant at all considered energies up to 5 GeV/u. These results confirm the fact that the slow acceleration in the HESR of few-electron ions is possible with the present residual gas composition. Using of dense internal targets, especially the Xe jet, dramatically decreases the lifetimes of U88 + to about 0.1 s, which makes the accomplishment of such experiments difficult and requires optimization of the duty cycle. However, if using light jet targets like H2 or He, the lifetimes are longer than about 100 s. According to experience at the ESR, we can conclude that the latter lifetimes are in the comfortable range for performing in-ring experiments.
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