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Improving isotope separator performance by beam cooling
Nuclear Instruments and Methods in Physics Research B 204 (2003) 557–562 www.elsevier.com/locate/nimb
Improving isotope separator performance by beam cooling R.B. Moore *, O. Gianfrancesco Physics Department, McGill University, Rutherford Physics Building, 3600 University St., Montreal, Canada PQ H3A 2T8
Abstract Cooling of 60 keV radioactive ion beams in radiofrequency quadrupole (RFQ) ion guides has recently been demonstrated. Such cooling has potentially great implications for isotope separators in that it could greatly reduce the emittance of a beam, entering the separator. However, to achieve the least possible emittance, and to overcome space– charge effects of the higher-current beams, the confining RF fields would have to be greatly increased over those used in present systems. Studies of the feasibility of using much higher electric fields have shown that indeed DC potential differences of up to 35 kV can be achieved across an electrode gap of only 150 lm in the presence of up about 50 Pa of helium, much higher than would be needed for buffer gas cooling. The power required to achieve these potentials at RF is therefore a practical concern. For a representative RFQ electrode geometry, RF amplitudes of 20 kV at 5 MHz have been achieved using a resonant circuit that absorbed about 100 W of RF power. The fields arising from these potentials were about 100 times those of present systems. Extrapolation from the present beam cooling results indicate that with such fields it should be possible to cool beams of 1 lA to emittances of less than 1 p-mm-mrad at 60 keV. For a typical highperformance on-line isotope separator (ISOL) this could lead to resolutions of several tens of thousands. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Beam cooling; RFQ confinement; Mass separators; Emittance improvement
1. Introduction Cooling of 60 keV radioactive ion beams by electrostatic deceleration to almost thermal energies followed by buffer gas collisions while under radiofrequency quadrupole (RFQ) radial confinement has recently been demonstrated at the ISOLTRAP facility [1]. Practically all of a beam cooled in this way is collected in an RFQ trap and extracted as a pulse that is delivered to a Penning trap for very high resolution mass spectrometry. *
Corresponding author. Tel.: +1-514-398-7028; fax: +1-514398-7022. E-mail address: [email protected] (R.B. Moore).
Such beam cooling has potentially great implications for isotope separators. If the incoming beam of an isotope separator can be similarly cooled it would greatly reduce the emittance of the beam, leading to greatly enhanced resolution of the separator without any changes to the separator itself. However, to make such cooling feasible for typical isotope separator beams the confining RF fields would have to be greatly increased over those presently used for cooling at ISOLTRAP, where the RF fields used for beam containment are created by electrodes that are separated by about 10 mm and at potential differences of about 300 V. At these modest fields the number of ions that can be cooled and contained in the RFQ trap is only
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(02)02132-8
558
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
about 1000. While this is of no consequence for the trace beams of short-lived radioisotopes under investigation until now with ISOLTRAP, which requires that there be no more than 10 ions in the measurement trap at any one time if the accuracy of the mass measurements is to be preserved, much stronger confinement would be required to overcome the space–charge effects of the more intense beams that would have to be accommodated for a typical isotope separator. This paper reports on studies of the feasibility of using high RF potentials for RFQ confinement of ions while they are being cooled by buffer gas and presents estimates of what can be expected for typical mass separator beams.
V
2 ro y z
2. The principles of RFQ confinement for buffer gas cooling Fig. 1. Schematic of the cooler system.
1.0 x - cm
Some sort of radial confinement is necessary during buffer gas cooling of an ion collection in order to prevent diffusion of the ions and to limit their radial excursions so as to achieve small emittances in the extracted beams. The basic principle of RFQ confinement is that a driving oscillatory field that has an amplitude that has a spatial variation and against which the primary reactance of a particle is inertial will, over a full cycle of the driven oscillation, have a net impulse on the particle in the direction of reduced field amplitude. The simplest such field is an oscillating electric quadrupole, which in the cylindrical configuration is produced by an electrode configuration as shown in Fig. 1. Such a field has a uniform electric field gradient and therefore results in a net ion impulse per cycle that is proportional to the distance of the ion from the quadrupole center, where the field is zero. The impulses therefore result in simple harmonic motion, upon which the driven oscillations are superimposed. A typical motion is shown in Fig. 2. The frequency of the simple harmonic motion, as well as the ratio of its amplitude to the amplitude of the driven oscillations, is determined by the dimensionless parameter q introduced by Mathieu in his mid-19th century investigation of such mo-
x
0 -1.0
0
5 Time - driven cycles
10
Fig. 2. Typical motion of an ion under RFQ confinement.
tion and which, for the motion of an ion in a quadrupole electric field is defined as q¼
2eV ; mx2 ro2
ð1Þ
where e is the charge and m is the mass of the ion, and x is the angular frequency of the quadrupole oscillation. For values of q less than about 0.3 the relationships between frequency and amplitudes are, to accuracies better than 1%, simply q xSHM ¼ pffiffiffi x; 2 2
ADrivenmax q ¼ ; 2 ASHM
ð2Þ
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
where ADrivenmax is the amplitude of the driven oscillation at the maximum displacement of the simple harmonic motion. For the motion shown in Fig. 2 q is 0.3. For a collection of ions, such as in a beam, the motions are best displayed in momentum–displacement action diagrams. For the simple harmonic motion of RFQ confinement these are particularly simple, the point representing any one ion just orbiting in a right ellipse (Fig. 3). The ellipse for each ion will have the same shape and the same orbit period, the only difference being their amplitudes and phases. The full action diagram for the ion collection is therefore simply the ellipse of the most energetic particle of the collection, the interior of this ellipse being filled to a density distribution determined by the original momentum–displacement distribution of the ions entering the confinement and any subsequent interactions they may have with each other or with background gas molecules. At thermal equilibrium the particle density in the action diagram of the simple harmonic motion will have a gaussian distribution both in the displacement and momentum coordinates, with the standard deviation parameter having the forms rffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi 1 kT rx ¼ ð3Þ ; rpx ¼ mkT : xSHM m For such a distribution about 95% of thepions will be within an ellipse that extends out to 6r, making that ellipse a useful measure of the effective action area of the collection. This is
270 ˚
0˚
90˚
px m ωA max x
O
180˚
SHM
A max q = 0.2
Fig. 3. Action diagrams for ions under RFQ confinement. The diagram on the left is for the simple harmonic motion. Diagram on the right show the full action, including driven oscillations, at representative phases of the oscillating field. (Zero phase is when the field is zero going positive.)
Sx ¼ 6p
kT : xSHM
559
ð4Þ
The emittance of a beam formed by extracting such a collection will be this action area divided by the momentum to which the ions are accelerated. However, the effective action area of a thermalized collection of ions will be considerably larger than that of the SHM action ellipse. This is because the driven oscillation distorts the action ellipse of the SHM, as shown for a representative case in Fig. 3. While this distortion preserves the area of the ellipse, its elongation at certain phases of the motion, particularly in the momentum coordinate, effectively increases its action area, typically by about a factor of two. The action area of an ion collection cooled under RFQ confinement in a buffer gas is therefore expected to be of the order of 10 pkT =xSHM . This increase in the effective beam emittance by the distortion from the driven oscillation, together with the difficulties of accommodating an incoming beam to the distortion (see below), limits the q that can be used for RFQ confinement in a beam cooler to about 0.3. In any case, the emittance of the extracted beam is proportional to the effective action area of the confined thermalized ions and so for a given ion temperature after cooling the lowest possible emittance is achieved by having the higher possible SHM frequency. In turn, for a given limit on q and for a given cooler aperture 2r, this is achieved by having the highest possible RF potential. Recent work [2] has shown that 20 kV of RF amplitude can be generated across adjacent quadrupole electrodes with ro ¼ 5 mm in the presence of adequate helium for beam cooling. At a q of 0.3 such potentials would generate xSHM for 100 amu ions of about 6 ls1 . The action area of a cooled beam could therefore be made as small as about pkT . For intense ion beams, strong RF confinement is also needed to overcome space–charge effects, which were neglected in the first-order development given above. Essentially, space charge forces tend to neutralize the confinement forces, leading to lower oscillation frequencies than given by (2) and to larger beam cross-sections than given by (3).
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R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
The presence of buffer gas while ions are under RFQ confinement adds a viscous drag force to the inertial reactance of the ions. At the gas pressures used for ion cooling the amplitude of the drag force is considerably less than the amplitude of the inertial force and so its effect is to cause an exponential decay in the SHM. If the SHM were pure the average energy of the SHM would approach the thermal energy of the gas molecules. However, due to friction with the buffer gas the velocity associated with the driven oscillation can cause the ions to be continually heated (a process often referred to as ‘‘RF heating’’) and the equilibrium temperature of the ions will be elevated above the gas temperature. Measurements have shown it will be typically twice the gas temperature [3,4]. The action area of an ion beam cooled by room temperature gas is therefore expected to be of the order of 0.05 p-eV-ls. As a representative case, if 100 amu ions were cooled in room temperature buffer gas while under RFQ confinement at xSHM ¼ 6 ls1 and reaccelerated to 60 keV the emittance of the beam could be expected to be as low as 0.15 pmm-mrad.
3. Injection, capture and extraction Beam cooling by buffer gas involves bringing the ions to a stop in the gas so that they can be cooled and then extracting so as to reform into a beam. A schematic of how this is accomplished in the ISOLTRAP beam cooler is shown in Fig. 4. Here the cooling system is mounted on a DC potential so that the ions are decelerating as they are brought to the cooler and then reaccelerated by the same DC potential upon extraction. By using a multiple electrode configuration such as shown in
Fig. 4. The beam cooler of the ISOTRAP facility.
−1133V −60,000V
−133V
−67V
Fig. 5. The deceleration system used for beam cooling at the ISOTRAP installation.
Fig. 5 the ions are brought to about 100 eV at delivery to the RFQ confinement region. Such a deceleration system must be designed to provide a beam transverse action that matches the action diagram of the RFQ confinement. As shown above, this action diagram has a rotating shape distortion, which is not feasible to induce in the incoming beam. The decelerated beam emittance is therefore aimed to approximate the stable ellipse of the SHM. The beam action diagram that results from the mismatch at various RF phases of entrance causes the beam profile after capture to be as shown in Fig. 6. Once the ions are under RFQ radial confinement most of their remaining kinetic energy can be removed by an axial DC electric field, such as produced by the DC potentials on successive
Fig. 6. The beam cross-section after entry into RFQ confinement. The various curves are for ions entering at various RF phases.
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
4. Vacuum considerations To stop and cool the incoming beam requires of the order of 700 Pa mm (for 100 amu ions). Depending on the compromises taken in balancing gas stopping power, cooling times and injection aperture, this can be provided in RFQ confinement lengths of from 300 to 1000 mm. However, because of gas scattering of high-velocity ions, deceleration and reacceleration must be carried out in regions where helium is present only to the order of 10 mPa. For RFQ lengths of up to 1000 mm and for helium injected at the mid-point it is expected that achieving this pressure will require about 1000 l/s of pumping at each of the deceleration and reacceleration ends of the structure.
5. Electrical considerations To determine the feasibility of using high electric potentials for RFQ confinement, a system was set up to test the electrical breakdown of small symmetrical stainless steel electrodes separated by 150 lm in various pressures of helium. The DC
Breakdown Threshhold 100
Voltage (kV)
quadrupole segments shown in Fig. 6. Retaining about 10 eV of average ion energy, so as to accommodate any original energy spread in the incoming beam, this remaining energy can be removed by the buffer gas itself. Once the ions are stopped and cooled within the buffer gas they must be dragged through the remaining gas in the path to the exit. This is accomplished by a gentle axial electric field, again provided by DC potentials applied to the successive RFQ segments. The ISOLTRAP cooler shown ion Fig. 4 includes a set of quadrupole segments forming a trap, so as to form an ion bunch. For continuous beams such a trap need not be provided, or could be simply turned off. Extraction of the ion beam from the RFQ region would then just require an extraction electrode to pull the ions into the region where they can be reaccelerated to ground potential.
561
10
3mm electrodes 9mm electrodes
1 0.1
1
10
100
Pressure (Pa)
Fig. 7. The breakdown potentials for small stainless steel electrodes separated by 150 lm in helium at various pressures. The threshold for the smaller electrodes was consistently higher than for the larger, presumably because of the fewer microprotrusions available for breakdown.
breakdown potentials for two sets of electrodes are shown in Fig. 7. From these studies it was concluded that it was safe to apply up to 20 kV of RF amplitude across adjacent electrodes in a RFQ confinement device. Such a device was constructed in the form of a small trap and, indeed, 20 kV of RF amplitude at 5 MHz could be applied using a simple resonant circuit that absorbed about 100 W of RF power. As with the DC tests, breakdown at this RF amplitude occurred at a helium pressure of about 50 Pa. One of the great technical difficulties in the sort of buffer gas beam coolers described here is that of providing the DC potentials that must be superimposed on the RF of the confinement electrodes. Presently this is done by using inductors and capacitors with many leads entering the vacuum. To reduce the exposure of these leads to the high RF fields produced by high RF potentials, it is suggested that they be protected by being introduced into the confinement system through the interior of the conductor providing the RF.
6. Space charge effects The emittance of 0.15 p-mm-mrad that was estimated to be achievable by such high RF
562
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
potentials is only for ions that experience no space–charge effects. Measurements by Kim [4] of beam temperature after buffer gas cooling as a function of beam current show a linear increase of 0.01 eV/na for currents of Csþ up to 1 nA. Assuming that space charge effects at higher currents still result in phase space distributions that approximate those of thermal equilibrium, extrapolating these results gives an estimated emittance of 1 p-mm-mrad at about 25 nA. However, this study of space charge effects was with a very gentle axial drift after ion cooling. By increasing the drift field so as to reduce the ion density it should be possible to increase the beam current, for the same emittance, by perhaps 10fold, i.e. to 250 nA. Finally, one of the features of RFQ confinement is that it holds negative ions just as effectively as positive ones. However, because of the antiphase of their driven oscillations compared to the positive ions they do not have the same phase space coordinates as the positive ions and so do not annihilate them. It is, in fact, well known that negative ions can be a contamination in any RFQ confinement device. Because they occupy the same physical space such positive and negative ions can neutralize their space charges. In the case of the beam cooler system described here the axial electric potentials actually provide an axial confinement for negative ions throughout the whole of the RFQ confinement region so that any ions entering the system will stay. It is expected therefore that the deliberate provision of a small current of negative ions could allow a considerably greater positive ion current
before space charge effects become important. One microampere of cooled beam seems conservative.
7. Conclusions The basic principles of buffer gas ion beam cooling using RFQ confinement are well understood, so that it is possible to engineer a system for emittance improvement of an ion beam leading into a mass separator. By using the highest RF voltages possible it is expected that a 60 keV beam of ions of mass 100 amu could be delivered at emittances of less than 1 p-mm-mrad at currents up to about 1 lA.
Acknowledgement The support of NSERC for this work is gratefully acknowledged.
References [1] G. Bollen, S. Becker, H.-J. Kluge, M. Konig, R.B. Moore, T. Otto, H. Raimbault-Hartmann, G. Savard, L. Schweikhard, H. Stolzenberg, Nucl. Instr. and Meth. A 368 (1996) 675. [2] O. Gianfrancesco, Design Principles of a High Field RFQ Device for Ion Confinement and Cooling, M.Sc. Thesis, McGill University, 2002. [3] M.D.M. Lunney, The Phase Space Volume of Ion Clouds in Paul Traps, Ph.D. Thesis, McGill University, 1992. [4] T. Kim, Buffer Gas Cooling of Ions in a Radio Frequency Quadrupole Ion Guide, Ph.D. Thesis, McGill University, 1997.
Improving isotope separator performance by beam cooling R.B. Moore *, O. Gianfrancesco Physics Department, McGill University, Rutherford Physics Building, 3600 University St., Montreal, Canada PQ H3A 2T8
Abstract Cooling of 60 keV radioactive ion beams in radiofrequency quadrupole (RFQ) ion guides has recently been demonstrated. Such cooling has potentially great implications for isotope separators in that it could greatly reduce the emittance of a beam, entering the separator. However, to achieve the least possible emittance, and to overcome space– charge effects of the higher-current beams, the confining RF fields would have to be greatly increased over those used in present systems. Studies of the feasibility of using much higher electric fields have shown that indeed DC potential differences of up to 35 kV can be achieved across an electrode gap of only 150 lm in the presence of up about 50 Pa of helium, much higher than would be needed for buffer gas cooling. The power required to achieve these potentials at RF is therefore a practical concern. For a representative RFQ electrode geometry, RF amplitudes of 20 kV at 5 MHz have been achieved using a resonant circuit that absorbed about 100 W of RF power. The fields arising from these potentials were about 100 times those of present systems. Extrapolation from the present beam cooling results indicate that with such fields it should be possible to cool beams of 1 lA to emittances of less than 1 p-mm-mrad at 60 keV. For a typical highperformance on-line isotope separator (ISOL) this could lead to resolutions of several tens of thousands. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Beam cooling; RFQ confinement; Mass separators; Emittance improvement
1. Introduction Cooling of 60 keV radioactive ion beams by electrostatic deceleration to almost thermal energies followed by buffer gas collisions while under radiofrequency quadrupole (RFQ) radial confinement has recently been demonstrated at the ISOLTRAP facility [1]. Practically all of a beam cooled in this way is collected in an RFQ trap and extracted as a pulse that is delivered to a Penning trap for very high resolution mass spectrometry. *
Corresponding author. Tel.: +1-514-398-7028; fax: +1-514398-7022. E-mail address: [email protected] (R.B. Moore).
Such beam cooling has potentially great implications for isotope separators. If the incoming beam of an isotope separator can be similarly cooled it would greatly reduce the emittance of the beam, leading to greatly enhanced resolution of the separator without any changes to the separator itself. However, to make such cooling feasible for typical isotope separator beams the confining RF fields would have to be greatly increased over those presently used for cooling at ISOLTRAP, where the RF fields used for beam containment are created by electrodes that are separated by about 10 mm and at potential differences of about 300 V. At these modest fields the number of ions that can be cooled and contained in the RFQ trap is only
0168-583X/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(02)02132-8
558
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
about 1000. While this is of no consequence for the trace beams of short-lived radioisotopes under investigation until now with ISOLTRAP, which requires that there be no more than 10 ions in the measurement trap at any one time if the accuracy of the mass measurements is to be preserved, much stronger confinement would be required to overcome the space–charge effects of the more intense beams that would have to be accommodated for a typical isotope separator. This paper reports on studies of the feasibility of using high RF potentials for RFQ confinement of ions while they are being cooled by buffer gas and presents estimates of what can be expected for typical mass separator beams.
V
2 ro y z
2. The principles of RFQ confinement for buffer gas cooling Fig. 1. Schematic of the cooler system.
1.0 x - cm
Some sort of radial confinement is necessary during buffer gas cooling of an ion collection in order to prevent diffusion of the ions and to limit their radial excursions so as to achieve small emittances in the extracted beams. The basic principle of RFQ confinement is that a driving oscillatory field that has an amplitude that has a spatial variation and against which the primary reactance of a particle is inertial will, over a full cycle of the driven oscillation, have a net impulse on the particle in the direction of reduced field amplitude. The simplest such field is an oscillating electric quadrupole, which in the cylindrical configuration is produced by an electrode configuration as shown in Fig. 1. Such a field has a uniform electric field gradient and therefore results in a net ion impulse per cycle that is proportional to the distance of the ion from the quadrupole center, where the field is zero. The impulses therefore result in simple harmonic motion, upon which the driven oscillations are superimposed. A typical motion is shown in Fig. 2. The frequency of the simple harmonic motion, as well as the ratio of its amplitude to the amplitude of the driven oscillations, is determined by the dimensionless parameter q introduced by Mathieu in his mid-19th century investigation of such mo-
x
0 -1.0
0
5 Time - driven cycles
10
Fig. 2. Typical motion of an ion under RFQ confinement.
tion and which, for the motion of an ion in a quadrupole electric field is defined as q¼
2eV ; mx2 ro2
ð1Þ
where e is the charge and m is the mass of the ion, and x is the angular frequency of the quadrupole oscillation. For values of q less than about 0.3 the relationships between frequency and amplitudes are, to accuracies better than 1%, simply q xSHM ¼ pffiffiffi x; 2 2
ADrivenmax q ¼ ; 2 ASHM
ð2Þ
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
where ADrivenmax is the amplitude of the driven oscillation at the maximum displacement of the simple harmonic motion. For the motion shown in Fig. 2 q is 0.3. For a collection of ions, such as in a beam, the motions are best displayed in momentum–displacement action diagrams. For the simple harmonic motion of RFQ confinement these are particularly simple, the point representing any one ion just orbiting in a right ellipse (Fig. 3). The ellipse for each ion will have the same shape and the same orbit period, the only difference being their amplitudes and phases. The full action diagram for the ion collection is therefore simply the ellipse of the most energetic particle of the collection, the interior of this ellipse being filled to a density distribution determined by the original momentum–displacement distribution of the ions entering the confinement and any subsequent interactions they may have with each other or with background gas molecules. At thermal equilibrium the particle density in the action diagram of the simple harmonic motion will have a gaussian distribution both in the displacement and momentum coordinates, with the standard deviation parameter having the forms rffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi 1 kT rx ¼ ð3Þ ; rpx ¼ mkT : xSHM m For such a distribution about 95% of thepions will be within an ellipse that extends out to 6r, making that ellipse a useful measure of the effective action area of the collection. This is
270 ˚
0˚
90˚
px m ωA max x
O
180˚
SHM
A max q = 0.2
Fig. 3. Action diagrams for ions under RFQ confinement. The diagram on the left is for the simple harmonic motion. Diagram on the right show the full action, including driven oscillations, at representative phases of the oscillating field. (Zero phase is when the field is zero going positive.)
Sx ¼ 6p
kT : xSHM
559
ð4Þ
The emittance of a beam formed by extracting such a collection will be this action area divided by the momentum to which the ions are accelerated. However, the effective action area of a thermalized collection of ions will be considerably larger than that of the SHM action ellipse. This is because the driven oscillation distorts the action ellipse of the SHM, as shown for a representative case in Fig. 3. While this distortion preserves the area of the ellipse, its elongation at certain phases of the motion, particularly in the momentum coordinate, effectively increases its action area, typically by about a factor of two. The action area of an ion collection cooled under RFQ confinement in a buffer gas is therefore expected to be of the order of 10 pkT =xSHM . This increase in the effective beam emittance by the distortion from the driven oscillation, together with the difficulties of accommodating an incoming beam to the distortion (see below), limits the q that can be used for RFQ confinement in a beam cooler to about 0.3. In any case, the emittance of the extracted beam is proportional to the effective action area of the confined thermalized ions and so for a given ion temperature after cooling the lowest possible emittance is achieved by having the higher possible SHM frequency. In turn, for a given limit on q and for a given cooler aperture 2r, this is achieved by having the highest possible RF potential. Recent work [2] has shown that 20 kV of RF amplitude can be generated across adjacent quadrupole electrodes with ro ¼ 5 mm in the presence of adequate helium for beam cooling. At a q of 0.3 such potentials would generate xSHM for 100 amu ions of about 6 ls1 . The action area of a cooled beam could therefore be made as small as about pkT . For intense ion beams, strong RF confinement is also needed to overcome space–charge effects, which were neglected in the first-order development given above. Essentially, space charge forces tend to neutralize the confinement forces, leading to lower oscillation frequencies than given by (2) and to larger beam cross-sections than given by (3).
560
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
The presence of buffer gas while ions are under RFQ confinement adds a viscous drag force to the inertial reactance of the ions. At the gas pressures used for ion cooling the amplitude of the drag force is considerably less than the amplitude of the inertial force and so its effect is to cause an exponential decay in the SHM. If the SHM were pure the average energy of the SHM would approach the thermal energy of the gas molecules. However, due to friction with the buffer gas the velocity associated with the driven oscillation can cause the ions to be continually heated (a process often referred to as ‘‘RF heating’’) and the equilibrium temperature of the ions will be elevated above the gas temperature. Measurements have shown it will be typically twice the gas temperature [3,4]. The action area of an ion beam cooled by room temperature gas is therefore expected to be of the order of 0.05 p-eV-ls. As a representative case, if 100 amu ions were cooled in room temperature buffer gas while under RFQ confinement at xSHM ¼ 6 ls1 and reaccelerated to 60 keV the emittance of the beam could be expected to be as low as 0.15 pmm-mrad.
3. Injection, capture and extraction Beam cooling by buffer gas involves bringing the ions to a stop in the gas so that they can be cooled and then extracting so as to reform into a beam. A schematic of how this is accomplished in the ISOLTRAP beam cooler is shown in Fig. 4. Here the cooling system is mounted on a DC potential so that the ions are decelerating as they are brought to the cooler and then reaccelerated by the same DC potential upon extraction. By using a multiple electrode configuration such as shown in
Fig. 4. The beam cooler of the ISOTRAP facility.
−1133V −60,000V
−133V
−67V
Fig. 5. The deceleration system used for beam cooling at the ISOTRAP installation.
Fig. 5 the ions are brought to about 100 eV at delivery to the RFQ confinement region. Such a deceleration system must be designed to provide a beam transverse action that matches the action diagram of the RFQ confinement. As shown above, this action diagram has a rotating shape distortion, which is not feasible to induce in the incoming beam. The decelerated beam emittance is therefore aimed to approximate the stable ellipse of the SHM. The beam action diagram that results from the mismatch at various RF phases of entrance causes the beam profile after capture to be as shown in Fig. 6. Once the ions are under RFQ radial confinement most of their remaining kinetic energy can be removed by an axial DC electric field, such as produced by the DC potentials on successive
Fig. 6. The beam cross-section after entry into RFQ confinement. The various curves are for ions entering at various RF phases.
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
4. Vacuum considerations To stop and cool the incoming beam requires of the order of 700 Pa mm (for 100 amu ions). Depending on the compromises taken in balancing gas stopping power, cooling times and injection aperture, this can be provided in RFQ confinement lengths of from 300 to 1000 mm. However, because of gas scattering of high-velocity ions, deceleration and reacceleration must be carried out in regions where helium is present only to the order of 10 mPa. For RFQ lengths of up to 1000 mm and for helium injected at the mid-point it is expected that achieving this pressure will require about 1000 l/s of pumping at each of the deceleration and reacceleration ends of the structure.
5. Electrical considerations To determine the feasibility of using high electric potentials for RFQ confinement, a system was set up to test the electrical breakdown of small symmetrical stainless steel electrodes separated by 150 lm in various pressures of helium. The DC
Breakdown Threshhold 100
Voltage (kV)
quadrupole segments shown in Fig. 6. Retaining about 10 eV of average ion energy, so as to accommodate any original energy spread in the incoming beam, this remaining energy can be removed by the buffer gas itself. Once the ions are stopped and cooled within the buffer gas they must be dragged through the remaining gas in the path to the exit. This is accomplished by a gentle axial electric field, again provided by DC potentials applied to the successive RFQ segments. The ISOLTRAP cooler shown ion Fig. 4 includes a set of quadrupole segments forming a trap, so as to form an ion bunch. For continuous beams such a trap need not be provided, or could be simply turned off. Extraction of the ion beam from the RFQ region would then just require an extraction electrode to pull the ions into the region where they can be reaccelerated to ground potential.
561
10
3mm electrodes 9mm electrodes
1 0.1
1
10
100
Pressure (Pa)
Fig. 7. The breakdown potentials for small stainless steel electrodes separated by 150 lm in helium at various pressures. The threshold for the smaller electrodes was consistently higher than for the larger, presumably because of the fewer microprotrusions available for breakdown.
breakdown potentials for two sets of electrodes are shown in Fig. 7. From these studies it was concluded that it was safe to apply up to 20 kV of RF amplitude across adjacent electrodes in a RFQ confinement device. Such a device was constructed in the form of a small trap and, indeed, 20 kV of RF amplitude at 5 MHz could be applied using a simple resonant circuit that absorbed about 100 W of RF power. As with the DC tests, breakdown at this RF amplitude occurred at a helium pressure of about 50 Pa. One of the great technical difficulties in the sort of buffer gas beam coolers described here is that of providing the DC potentials that must be superimposed on the RF of the confinement electrodes. Presently this is done by using inductors and capacitors with many leads entering the vacuum. To reduce the exposure of these leads to the high RF fields produced by high RF potentials, it is suggested that they be protected by being introduced into the confinement system through the interior of the conductor providing the RF.
6. Space charge effects The emittance of 0.15 p-mm-mrad that was estimated to be achievable by such high RF
562
R.B. Moore, O. Gianfrancesco / Nucl. Instr. and Meth. in Phys. Res. B 204 (2003) 557–562
potentials is only for ions that experience no space–charge effects. Measurements by Kim [4] of beam temperature after buffer gas cooling as a function of beam current show a linear increase of 0.01 eV/na for currents of Csþ up to 1 nA. Assuming that space charge effects at higher currents still result in phase space distributions that approximate those of thermal equilibrium, extrapolating these results gives an estimated emittance of 1 p-mm-mrad at about 25 nA. However, this study of space charge effects was with a very gentle axial drift after ion cooling. By increasing the drift field so as to reduce the ion density it should be possible to increase the beam current, for the same emittance, by perhaps 10fold, i.e. to 250 nA. Finally, one of the features of RFQ confinement is that it holds negative ions just as effectively as positive ones. However, because of the antiphase of their driven oscillations compared to the positive ions they do not have the same phase space coordinates as the positive ions and so do not annihilate them. It is, in fact, well known that negative ions can be a contamination in any RFQ confinement device. Because they occupy the same physical space such positive and negative ions can neutralize their space charges. In the case of the beam cooler system described here the axial electric potentials actually provide an axial confinement for negative ions throughout the whole of the RFQ confinement region so that any ions entering the system will stay. It is expected therefore that the deliberate provision of a small current of negative ions could allow a considerably greater positive ion current
before space charge effects become important. One microampere of cooled beam seems conservative.
7. Conclusions The basic principles of buffer gas ion beam cooling using RFQ confinement are well understood, so that it is possible to engineer a system for emittance improvement of an ion beam leading into a mass separator. By using the highest RF voltages possible it is expected that a 60 keV beam of ions of mass 100 amu could be delivered at emittances of less than 1 p-mm-mrad at currents up to about 1 lA.
Acknowledgement The support of NSERC for this work is gratefully acknowledged.
References [1] G. Bollen, S. Becker, H.-J. Kluge, M. Konig, R.B. Moore, T. Otto, H. Raimbault-Hartmann, G. Savard, L. Schweikhard, H. Stolzenberg, Nucl. Instr. and Meth. A 368 (1996) 675. [2] O. Gianfrancesco, Design Principles of a High Field RFQ Device for Ion Confinement and Cooling, M.Sc. Thesis, McGill University, 2002. [3] M.D.M. Lunney, The Phase Space Volume of Ion Clouds in Paul Traps, Ph.D. Thesis, McGill University, 1992. [4] T. Kim, Buffer Gas Cooling of Ions in a Radio Frequency Quadrupole Ion Guide, Ph.D. Thesis, McGill University, 1997.