- Email: [email protected]
Ion–ion charge exchange cross-sections for heavy ion fusion
Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
Ion–ion charge exchange cross-sections for heavy ion fusion R. Trassla, H. Br.auninga, K.v. Diemara, F. Melcherta, E. Salzborna,*, I. Hofmannb a
Institut fuer Kernphysik, University of Giessen, Leihgesterner Weg 217, 35392 Giessen, Germany b GSI Darmstadt, Planckstrasse 1, 64291 Darmstadt, Germany
Abstract In heavy ion fusion the compression of the DT-pellet requires adequate accelerators and storage rings for the driving projectile ions. The design of such storage rings crucially depends on the expected particle losses due to charge-changing collisions between the stored ions. Although the kinetic energy of driver ions in a heavy ion fusion scenario is in the order of several GeV, the relative kinetic energy of intrabeam ion–ion collisions is only in the keV region and therefore attainable in an ion–ion crossed-beams experiment. In this paper we report on the investigation of charge exchange in collisions between quadruply charged xenon and bismuth ions. With the knowledge of these cross-sections we were able to estimate the particle losses from a 100 Tm synchrotron which is one of the possible options for a future GSI upgrade. The relevance of such a synchrotron for plasma physics and HIF is given by the possible intensity of 1013 ions and approximately 40 kJ bunch energy. # 2001 Elsevier Science B.V. All rights reserved. PACS: 34.70.+e; 52.20. Hv
1. Introduction Crossed-beams experiments are a proven tool for the investigation of charge-changing processes in ion–ion collisions (see e.g. review articles by Gilbody [1], Dolder and Peart [2], and Salzborn [3]). In the past decades, the experimental effort was concentrated mainly on collisions involving singly or at most doubly charged ions (see bibliography by Tawara [4]). While the data base for collisions between singly charged heavy ions is still rather small, practically no data at all exist for collisions between multiply charged ions. Using the Giessen ion–ion crossed*Corresponding author. E-mail address: [email protected] (E. Salzborn).
beams facility, we measured for the first time absolute cross-sections for electron capture in collisions between quadruply charged ions X4þ þ X4þ ! X3þ þ X5þ
ð1:1Þ
where X4þ ¼ Xe4þ and Bi4þ , respectively.
2. Experimental methods and techniques The straightforward idea to investigate ion–ion collisions is the so-called crossed-beams technique where two ion beams are made to intersect. Although this technique, in principle, seems to be rather simple, inherent difficulties arise from the tenuous particle densities provided by typical ion beams.
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 0 1 1 - 0
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
Mutual Coulomb repulsion between the ions within their beams causes them to expand along their beam path. To ensure experimental resolution, the beam diameter and divergence have to be limited which, as a consequence, limits the ion beam currents. For example, a beam of singly charged Arþ ions (energy 5 keV, diameter 4 mm, max. divergence 18) cannot transport more than a few mA of ion beam current. This beam contains less than 107 ions per cm3 which is comparable to the particle density within ultrahigh vacuum (UHV). While two ion beams penetrate each other, ion–ion collision rates can be expected which are equal to the rates observed when an ion beam travels through UHV, and that is almost nothing. Depending on the particular cross-section, only 1010 –1014 of the incoming flux undergoes an ion–ion collision. Furthermore, the ion beams travel through UHV along their complete trajectory, while they overlap only in the interaction region which has typically mm dimensions for a crossed-beams arrangement. That is why the ion–ion reaction signal is masked by 102 –104 times more intense background contribu-
81
tions which arise from ionic collisions with the residual gas, even at prevailing UHV conditions of 1011 mbar. The experimental challenge of crossed-beams experiments is to single out the ion–ion events, which occur at absolute rates of 102 –101 /s, from background rates of ions in the same charge state in the order of 102 –104 /s, and from the incoming flux in the order of 1010 –1013 /s. For this purpose coincidence [5] techniques have to be applied. A schematic overview of the actual experimental setup is shown in Fig. 1. Here, only a short description of the experiment will be given; for more details see Ref. [6]. The whole apparatus consists of two ion beam lines and the interaction chamber. The beam lines are differentially pumped in order to achieve a pressure of about 1011 mbar in the interaction region. One of the ion beams is produced in a 5 GHz ECR ion source and accelerated with voltages of max. 20 kV. After the extraction the ions are focused with an electrostatic quadrupole triplet (Q1). The 908 analyzing magnet M3 selects the desired mass-tocharge ratio. Two pairs of slits (C4, C5) together
Fig. 1. Schematic setup of the Giessen ion–ion crossed-beams facility.
III. ATOMIC PHYSICS
82
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
with the quadrupole quadruplet Q2 collimate and focus the ion beam on the reaction region. Here two modes can be adjusted: a high-current mode with a beam focus at the interaction volume or a high-brilliance mode with a low current but a nearly parallel ion beam. Shortly before the intersection, the ion beam passes the electrostatic deflectors ES1 and ES2. Here the ion beam is cleaned from impurity ions, which were produced in collisions with residual gas molecules on its path through the beam line, and deflected to an interaction angle of 17.58. The second ion beam is produced on a highvoltage terminal where only limited space and electrical power are available. Therefore, the ions are produced here in an all-permanent magnet 10 GHz ECR ion source. In this ion source all magnetic fields for the confinement of the hot plasma electrons are produced with permanent magnets only. After the extraction, the ion beam is focused by an electrostatic Einzel lens (S1) and then further accelerated with voltages of up to 200 kV. An electrostatic quadrupole triplet (Q3) focuses the ion beam and the desired mass-tocharge ratio is selected in the 178 analyzing magnet M2. Two pairs of slits (C2, C3) collimate the beam which then passes the electrostatic deflector ES5 shortly before the intersection. After the reaction the product ions remain within the primary beams due to the low momentum transfer during the collision. They are then separated from the parent ion beams by the electrostatic analyzers AFB and ASB, respectively. The reaction products are counted in singleparticle detectors whereas the primary ion beams are measured in Faraday cups. If two ion beams cross at an angle a, the crosssection sC can be calculated from the equation sC ¼
v1 v2 sin a R q1 q2 F vrel I1 I2
Fig. 2. Coincidence spectrum for the charge exchange reaction Bi4þ þ Bi4þ ! Bi3þ þ Bi5þ . The Bi5þ product ions, recorded by a single-particle detector, start a time-to-amplitude-converter (TAC) which is stopped by the Bi3þ product ions.
Among all quantities in Eq. (2.1), the event rate R of ion–ion reactions is the most difficult to determine. Far more particles originating from interactions other than ion–ion collisions reach the detectors. If both collision partners alter their charge state, e.g. in an electron capture reaction (1.1), both reaction products can be detected in coincidence. Since they are generated simultaneously and since their flight times from the beam intersection to the detectors are fixed, the corresponding output pulses of single-particle detectors show a fixed time delay in the case of true ion–ion signals, whereas there is no time correlation between background events. Hence, time-to-amplitude-converter (TAC) spectra display a sharp peak produced by ion–ion collisions on top of a flat background due to random coincidences. A typical TAC spectrum is shown in Fig. 2 for the reaction Bi4þ +Bi4þ !Bi3þ +Bi5þ ; details of this technique are discussed in Ref. [5].
ð2:1Þ
where vi , qi and Ii are the velocities, charges and ion currents of both ion beams i ¼ 1; 2. The socalled formfactor F describes the spatial overlap of the ion beams and is determined by sliding a slotted shutter along the z-axis, which is perpendicular to the interaction plane, through the ion beams. vrel denotes the relative velocity of the ions.
3. Experimental results Measurements of absolute cross-sections require the correct measurement of beam intensities, beam energies, beam overlap and the complete detection of all reaction products by the single-particle detectors. Several tests performed in order to
83
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
After these tests charge exchange cross-sections were measured for quadruply-charged Xe- and Biions. Table 1 shows typical experimental parameters obtained during the measurements. The cross-sections are shown in Fig. 4 as a function of the center-of-mass energy. With the current experimental setup a center-of-mass energy range between 2.5 and 63 keV could be covered. The error bars represent the 90% confidence interval of the statistical error. For the collision system Xe4þ +Xe4þ we obtained a value of the crosssection of about 1.51016 cm2 . The cross-section remains rather constant over the whole investigated energy range. The cross-section for the collisions system Bi4þ + Bi4þ is a factor of 5 smaller and also shows no significant energy dependence.
ensure the proper function of the apparatus have been described in detail elsewhere [5,6]. Here, in particular, the complete detection of the X3þ reaction products in the high-energy beam line was ensured by using a position-sensitive channelplates detector. The left-hand side of Fig. 3 shows a Bi3þ scattering distribution for a center-of-mass energy of 28 keV. The comparison with the primary beam profile (right-hand side) shows only a small increase of the spatial distribution of the reaction products due to scattering processes in the ion–ion collision. This test makes sure that all reaction products in the high-energy beam line are completely detected. Simulations including the crossed-beams dynamics show that also in the low-energy beam line, where a channeltron detector is used, all products can be detected.
Fig. 3. Scattering distribution of the Bi3þ reaction products (left) for a center-of-mass energy of 28 keV measured by a positionsensitive channelplates detector. The comparison with the primary beam profile (right) shows only a small increase of the spatial distribution of the product ions due to scattering processes.
Table 1 Typical experimental parameters during the cross-section measurements at Ecm =12.6 keV. IFB , ISB , NFB , NSB denote the ion currents and detector counts rates in the ‘‘fast’’ (FB) and ‘‘slow’’ (SB) beam line. R is the the coincidence signal rate and t the actual measuring time Ion
EFB (keV)
ESB (keV)
IFB (nA)
ISB (nA)
NFB (kHz)
NSB (Hz)
R ðs1 )
t (s)
Xe4þ Bi4þ
99.2 114
30 40
28 60
30 70
8 4
40 50
0.08 0.09
2387 5000
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R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
Fig. 4. Measured cross-sections for the charge transfer reaction X4þ þ X4þ ! X3þ þ X5þ with X=Xe, Bi as a function of the centerof-mass energy. The error bars represent the 90% confidence interval of the statistical error.
4. Estimation of particle losses in a storage ring With the knowledge of these cross-sections we were able to estimate the expected particle losses in a 100 Tm synchrotron as discussed as one of the options for a future GSI upgrade. The total beam loss cross-section sL is given by sL ¼ 2ð2sC þ sI Þ
ð4:1Þ
where sC denotes the electron capture crosssection described above and sI the ionization cross-section X4þ +X4þ !X4þ +X5þ +e . The factors of 2 arise from the fact that in the capture reaction (1.1) both ions change their charge state and that furthermore both ions act simultaneously as projectile and target. In a crossed-beams experiment, however, one ion beam is treated as the projectile where the increased charge state is measured whereas in the target ion beam the corresponding decreased charge state is detected. In the experiment, the ionization cross-section could not be determined because in this reaction only one of the collision partners alters its charge state. For this measurement a beam pulsing technique [7] has to be applied but due to the large background in the investigated collision systems this would have resulted in unreasonably
long measuring times. Earlier experiments, e.g. for the collision system Bi1þ +Bi1þ [8], showed that in the observed energy range the ionization channel is weak compared to that of electron capture. In the following, the ionization cross-section has either been set to zero or equal to the capture crosssection in order to get a lower and an upper limit for the expected particle losses. The number of particles lost from the beam due to charge-changing ion–ion collisions dN ¼ R ðtÞ dt can be calculated from the reaction rate Z 1 RðtÞ ¼ n2 ðr; tÞhsL vi dV: ð4:2Þ 2 V Since the measured cross-sections show no significant energy dependence, the rate coefficient is sL hvi, where hvi is the expectation value of the relative velocities. It is dominated by the transverse velocity spread, whereas the momentum spread is negligible here. hvi has been evaluated numerically for a waterbag phase space distribution and increases during synchrotron acceleration due to the increase of the rms transverse velocity spread. Furthermore, the assumption is made that the particle density nðr; tÞ is constant throughout the whole storage ring. This approximation can be made because in a storage ring quadrupole
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85 Table 2 Parameters used for the estimation of the expected particle losses in a 100 Tm synchrotron [9] Final energy Ring radius, R Acceleration time, t Beam current from LINAC rms emittance Number of betatron oscillations per turn, Q Bunching factor, b Number of ions, N
127 MeV/u 127 m 1s 15 mA 60 p mm mrad 12 0.5 8 1012
magnets are used to focus the ion beam. Here focusing in one direction results in defocusing in the direction perpendicular and therefore the ion beam density remains constant within typically 20%, which can be ignored. This leads to an equation for the particle loss: 1 dN 1 NQ ¼ sL vrms 2 2 N dt 2 2p R erms b
ð4:3Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where vrms ¼ 12bgc eðQ=RÞ and the last term in Eq. (4.3) is the beam volume. For the estimation of the expected intensity losses the synchrotron parameters listed in Table 2 were used [9]. With these values the particle losses
85
for Xe4þ ions are 10.7% (sI =0) and 16% (sI ¼ sC ). For the storage of Bi4þ ions we expect a loss of 2.1% (sI =0) and 3.2% (sI ¼ sC ), respectively. As can be seen from our results, ion–ion collisions in stored heavy-ion beams can lead to substantial particle losses and hence have to be taken into consideration when designing a storage ring. This work was supported by BMBF under Contract No. 06Gi850(0).
References [1] H.B. Gilbody, in: Physics of Electronic and Atomic Collisions, S. Datz (Ed.), North-Holland, Amsterdam, 1982, p. 223. [2] K. Dolder, B. Peart, Rep. Prog. Phys. 48 (1985) 1283. [3] E. Salzborn, J. Phys. C 1 (1989) 207. [4] H. Tawara, Report IPP-AM-25, Institute of Plasma Physics, Nagoya University, Japan, 1983. [5] K. Rinn, F. Melchert, E. Salzborn, J. Phys. B 18 (1985) 3783. [6] S. Meuser, F. Melchert, S. Kruedener, A. Pfeiffer, K.v. Diemar, E. Salzborn, Rev. Sci. Instr. 67 (1996) 2752. [7] K. Rinn, F. Melchert, K. Rink, E. Salzborn, J. Phys. B 19 (1986) 3717. . [8] F. Melchert, E. Salzborn, I. Hofmann, R.W. Muller, V.P. Shevelko, Nucl. Instr. and Meth. A 278 (1989) 65. [9] I. Hofmann, private communication.
III. ATOMIC PHYSICS
Ion–ion charge exchange cross-sections for heavy ion fusion R. Trassla, H. Br.auninga, K.v. Diemara, F. Melcherta, E. Salzborna,*, I. Hofmannb a
Institut fuer Kernphysik, University of Giessen, Leihgesterner Weg 217, 35392 Giessen, Germany b GSI Darmstadt, Planckstrasse 1, 64291 Darmstadt, Germany
Abstract In heavy ion fusion the compression of the DT-pellet requires adequate accelerators and storage rings for the driving projectile ions. The design of such storage rings crucially depends on the expected particle losses due to charge-changing collisions between the stored ions. Although the kinetic energy of driver ions in a heavy ion fusion scenario is in the order of several GeV, the relative kinetic energy of intrabeam ion–ion collisions is only in the keV region and therefore attainable in an ion–ion crossed-beams experiment. In this paper we report on the investigation of charge exchange in collisions between quadruply charged xenon and bismuth ions. With the knowledge of these cross-sections we were able to estimate the particle losses from a 100 Tm synchrotron which is one of the possible options for a future GSI upgrade. The relevance of such a synchrotron for plasma physics and HIF is given by the possible intensity of 1013 ions and approximately 40 kJ bunch energy. # 2001 Elsevier Science B.V. All rights reserved. PACS: 34.70.+e; 52.20. Hv
1. Introduction Crossed-beams experiments are a proven tool for the investigation of charge-changing processes in ion–ion collisions (see e.g. review articles by Gilbody [1], Dolder and Peart [2], and Salzborn [3]). In the past decades, the experimental effort was concentrated mainly on collisions involving singly or at most doubly charged ions (see bibliography by Tawara [4]). While the data base for collisions between singly charged heavy ions is still rather small, practically no data at all exist for collisions between multiply charged ions. Using the Giessen ion–ion crossed*Corresponding author. E-mail address: [email protected] (E. Salzborn).
beams facility, we measured for the first time absolute cross-sections for electron capture in collisions between quadruply charged ions X4þ þ X4þ ! X3þ þ X5þ
ð1:1Þ
where X4þ ¼ Xe4þ and Bi4þ , respectively.
2. Experimental methods and techniques The straightforward idea to investigate ion–ion collisions is the so-called crossed-beams technique where two ion beams are made to intersect. Although this technique, in principle, seems to be rather simple, inherent difficulties arise from the tenuous particle densities provided by typical ion beams.
0168-9002/01/$ - see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 0 0 1 1 - 0
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
Mutual Coulomb repulsion between the ions within their beams causes them to expand along their beam path. To ensure experimental resolution, the beam diameter and divergence have to be limited which, as a consequence, limits the ion beam currents. For example, a beam of singly charged Arþ ions (energy 5 keV, diameter 4 mm, max. divergence 18) cannot transport more than a few mA of ion beam current. This beam contains less than 107 ions per cm3 which is comparable to the particle density within ultrahigh vacuum (UHV). While two ion beams penetrate each other, ion–ion collision rates can be expected which are equal to the rates observed when an ion beam travels through UHV, and that is almost nothing. Depending on the particular cross-section, only 1010 –1014 of the incoming flux undergoes an ion–ion collision. Furthermore, the ion beams travel through UHV along their complete trajectory, while they overlap only in the interaction region which has typically mm dimensions for a crossed-beams arrangement. That is why the ion–ion reaction signal is masked by 102 –104 times more intense background contribu-
81
tions which arise from ionic collisions with the residual gas, even at prevailing UHV conditions of 1011 mbar. The experimental challenge of crossed-beams experiments is to single out the ion–ion events, which occur at absolute rates of 102 –101 /s, from background rates of ions in the same charge state in the order of 102 –104 /s, and from the incoming flux in the order of 1010 –1013 /s. For this purpose coincidence [5] techniques have to be applied. A schematic overview of the actual experimental setup is shown in Fig. 1. Here, only a short description of the experiment will be given; for more details see Ref. [6]. The whole apparatus consists of two ion beam lines and the interaction chamber. The beam lines are differentially pumped in order to achieve a pressure of about 1011 mbar in the interaction region. One of the ion beams is produced in a 5 GHz ECR ion source and accelerated with voltages of max. 20 kV. After the extraction the ions are focused with an electrostatic quadrupole triplet (Q1). The 908 analyzing magnet M3 selects the desired mass-tocharge ratio. Two pairs of slits (C4, C5) together
Fig. 1. Schematic setup of the Giessen ion–ion crossed-beams facility.
III. ATOMIC PHYSICS
82
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
with the quadrupole quadruplet Q2 collimate and focus the ion beam on the reaction region. Here two modes can be adjusted: a high-current mode with a beam focus at the interaction volume or a high-brilliance mode with a low current but a nearly parallel ion beam. Shortly before the intersection, the ion beam passes the electrostatic deflectors ES1 and ES2. Here the ion beam is cleaned from impurity ions, which were produced in collisions with residual gas molecules on its path through the beam line, and deflected to an interaction angle of 17.58. The second ion beam is produced on a highvoltage terminal where only limited space and electrical power are available. Therefore, the ions are produced here in an all-permanent magnet 10 GHz ECR ion source. In this ion source all magnetic fields for the confinement of the hot plasma electrons are produced with permanent magnets only. After the extraction, the ion beam is focused by an electrostatic Einzel lens (S1) and then further accelerated with voltages of up to 200 kV. An electrostatic quadrupole triplet (Q3) focuses the ion beam and the desired mass-tocharge ratio is selected in the 178 analyzing magnet M2. Two pairs of slits (C2, C3) collimate the beam which then passes the electrostatic deflector ES5 shortly before the intersection. After the reaction the product ions remain within the primary beams due to the low momentum transfer during the collision. They are then separated from the parent ion beams by the electrostatic analyzers AFB and ASB, respectively. The reaction products are counted in singleparticle detectors whereas the primary ion beams are measured in Faraday cups. If two ion beams cross at an angle a, the crosssection sC can be calculated from the equation sC ¼
v1 v2 sin a R q1 q2 F vrel I1 I2
Fig. 2. Coincidence spectrum for the charge exchange reaction Bi4þ þ Bi4þ ! Bi3þ þ Bi5þ . The Bi5þ product ions, recorded by a single-particle detector, start a time-to-amplitude-converter (TAC) which is stopped by the Bi3þ product ions.
Among all quantities in Eq. (2.1), the event rate R of ion–ion reactions is the most difficult to determine. Far more particles originating from interactions other than ion–ion collisions reach the detectors. If both collision partners alter their charge state, e.g. in an electron capture reaction (1.1), both reaction products can be detected in coincidence. Since they are generated simultaneously and since their flight times from the beam intersection to the detectors are fixed, the corresponding output pulses of single-particle detectors show a fixed time delay in the case of true ion–ion signals, whereas there is no time correlation between background events. Hence, time-to-amplitude-converter (TAC) spectra display a sharp peak produced by ion–ion collisions on top of a flat background due to random coincidences. A typical TAC spectrum is shown in Fig. 2 for the reaction Bi4þ +Bi4þ !Bi3þ +Bi5þ ; details of this technique are discussed in Ref. [5].
ð2:1Þ
where vi , qi and Ii are the velocities, charges and ion currents of both ion beams i ¼ 1; 2. The socalled formfactor F describes the spatial overlap of the ion beams and is determined by sliding a slotted shutter along the z-axis, which is perpendicular to the interaction plane, through the ion beams. vrel denotes the relative velocity of the ions.
3. Experimental results Measurements of absolute cross-sections require the correct measurement of beam intensities, beam energies, beam overlap and the complete detection of all reaction products by the single-particle detectors. Several tests performed in order to
83
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
After these tests charge exchange cross-sections were measured for quadruply-charged Xe- and Biions. Table 1 shows typical experimental parameters obtained during the measurements. The cross-sections are shown in Fig. 4 as a function of the center-of-mass energy. With the current experimental setup a center-of-mass energy range between 2.5 and 63 keV could be covered. The error bars represent the 90% confidence interval of the statistical error. For the collision system Xe4þ +Xe4þ we obtained a value of the crosssection of about 1.51016 cm2 . The cross-section remains rather constant over the whole investigated energy range. The cross-section for the collisions system Bi4þ + Bi4þ is a factor of 5 smaller and also shows no significant energy dependence.
ensure the proper function of the apparatus have been described in detail elsewhere [5,6]. Here, in particular, the complete detection of the X3þ reaction products in the high-energy beam line was ensured by using a position-sensitive channelplates detector. The left-hand side of Fig. 3 shows a Bi3þ scattering distribution for a center-of-mass energy of 28 keV. The comparison with the primary beam profile (right-hand side) shows only a small increase of the spatial distribution of the reaction products due to scattering processes in the ion–ion collision. This test makes sure that all reaction products in the high-energy beam line are completely detected. Simulations including the crossed-beams dynamics show that also in the low-energy beam line, where a channeltron detector is used, all products can be detected.
Fig. 3. Scattering distribution of the Bi3þ reaction products (left) for a center-of-mass energy of 28 keV measured by a positionsensitive channelplates detector. The comparison with the primary beam profile (right) shows only a small increase of the spatial distribution of the product ions due to scattering processes.
Table 1 Typical experimental parameters during the cross-section measurements at Ecm =12.6 keV. IFB , ISB , NFB , NSB denote the ion currents and detector counts rates in the ‘‘fast’’ (FB) and ‘‘slow’’ (SB) beam line. R is the the coincidence signal rate and t the actual measuring time Ion
EFB (keV)
ESB (keV)
IFB (nA)
ISB (nA)
NFB (kHz)
NSB (Hz)
R ðs1 )
t (s)
Xe4þ Bi4þ
99.2 114
30 40
28 60
30 70
8 4
40 50
0.08 0.09
2387 5000
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84
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85
Fig. 4. Measured cross-sections for the charge transfer reaction X4þ þ X4þ ! X3þ þ X5þ with X=Xe, Bi as a function of the centerof-mass energy. The error bars represent the 90% confidence interval of the statistical error.
4. Estimation of particle losses in a storage ring With the knowledge of these cross-sections we were able to estimate the expected particle losses in a 100 Tm synchrotron as discussed as one of the options for a future GSI upgrade. The total beam loss cross-section sL is given by sL ¼ 2ð2sC þ sI Þ
ð4:1Þ
where sC denotes the electron capture crosssection described above and sI the ionization cross-section X4þ +X4þ !X4þ +X5þ +e . The factors of 2 arise from the fact that in the capture reaction (1.1) both ions change their charge state and that furthermore both ions act simultaneously as projectile and target. In a crossed-beams experiment, however, one ion beam is treated as the projectile where the increased charge state is measured whereas in the target ion beam the corresponding decreased charge state is detected. In the experiment, the ionization cross-section could not be determined because in this reaction only one of the collision partners alters its charge state. For this measurement a beam pulsing technique [7] has to be applied but due to the large background in the investigated collision systems this would have resulted in unreasonably
long measuring times. Earlier experiments, e.g. for the collision system Bi1þ +Bi1þ [8], showed that in the observed energy range the ionization channel is weak compared to that of electron capture. In the following, the ionization cross-section has either been set to zero or equal to the capture crosssection in order to get a lower and an upper limit for the expected particle losses. The number of particles lost from the beam due to charge-changing ion–ion collisions dN ¼ R ðtÞ dt can be calculated from the reaction rate Z 1 RðtÞ ¼ n2 ðr; tÞhsL vi dV: ð4:2Þ 2 V Since the measured cross-sections show no significant energy dependence, the rate coefficient is sL hvi, where hvi is the expectation value of the relative velocities. It is dominated by the transverse velocity spread, whereas the momentum spread is negligible here. hvi has been evaluated numerically for a waterbag phase space distribution and increases during synchrotron acceleration due to the increase of the rms transverse velocity spread. Furthermore, the assumption is made that the particle density nðr; tÞ is constant throughout the whole storage ring. This approximation can be made because in a storage ring quadrupole
R. Trassl et al. / Nuclear Instruments and Methods in Physics Research A 464 (2001) 80–85 Table 2 Parameters used for the estimation of the expected particle losses in a 100 Tm synchrotron [9] Final energy Ring radius, R Acceleration time, t Beam current from LINAC rms emittance Number of betatron oscillations per turn, Q Bunching factor, b Number of ions, N
127 MeV/u 127 m 1s 15 mA 60 p mm mrad 12 0.5 8 1012
magnets are used to focus the ion beam. Here focusing in one direction results in defocusing in the direction perpendicular and therefore the ion beam density remains constant within typically 20%, which can be ignored. This leads to an equation for the particle loss: 1 dN 1 NQ ¼ sL vrms 2 2 N dt 2 2p R erms b
ð4:3Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where vrms ¼ 12bgc eðQ=RÞ and the last term in Eq. (4.3) is the beam volume. For the estimation of the expected intensity losses the synchrotron parameters listed in Table 2 were used [9]. With these values the particle losses
85
for Xe4þ ions are 10.7% (sI =0) and 16% (sI ¼ sC ). For the storage of Bi4þ ions we expect a loss of 2.1% (sI =0) and 3.2% (sI ¼ sC ), respectively. As can be seen from our results, ion–ion collisions in stored heavy-ion beams can lead to substantial particle losses and hence have to be taken into consideration when designing a storage ring. This work was supported by BMBF under Contract No. 06Gi850(0).
References [1] H.B. Gilbody, in: Physics of Electronic and Atomic Collisions, S. Datz (Ed.), North-Holland, Amsterdam, 1982, p. 223. [2] K. Dolder, B. Peart, Rep. Prog. Phys. 48 (1985) 1283. [3] E. Salzborn, J. Phys. C 1 (1989) 207. [4] H. Tawara, Report IPP-AM-25, Institute of Plasma Physics, Nagoya University, Japan, 1983. [5] K. Rinn, F. Melchert, E. Salzborn, J. Phys. B 18 (1985) 3783. [6] S. Meuser, F. Melchert, S. Kruedener, A. Pfeiffer, K.v. Diemar, E. Salzborn, Rev. Sci. Instr. 67 (1996) 2752. [7] K. Rinn, F. Melchert, K. Rink, E. Salzborn, J. Phys. B 19 (1986) 3717. . [8] F. Melchert, E. Salzborn, I. Hofmann, R.W. Muller, V.P. Shevelko, Nucl. Instr. and Meth. A 278 (1989) 65. [9] I. Hofmann, private communication.
III. ATOMIC PHYSICS