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Ion confinement in a marginally stable penning trap
Nuclear Instruments and Methods in Physics Research A240 (1985) 457-460 North-Holland, Amsterdam
ION CONFINEMENT
IN A MARGINALLY
457
STABLE PENNING
TRAP
H.M. HOLZSCHEITER Department of Physics, Texas A&M University, College Station, TX 77843, USA
The behaviour of ions stored in a Penning trap operated near the stability boundary is investigated. It is found that a marginally stable region exists with width a B which appears to depend on the initial kinetic energy of the ions at time of production. It is pointed out how this property, presenting an inherent limitation to the stored ion collision method, can be utilized in the production of higher charge states using electron-impact ionization and to obtain information on the intermediate states in charge exchange reactions.
!. Introduction The process of charge exchange collisions between multiply charged ions and neutral molecules and atoms at relative energies of a few electronvolts is important in the interpretation of astrophysical processes [1] and the behaviour of magnetically confined plasmas [2]. It has been pointed out recently that data for charge exchange collisions between few times ionized oxygen, nitrogen and carbon impurities colliding with neutral hydrogen atoms at relative energy below 10 eV are needed to understand edge effects in magnetically confined plasmas [3]. Since energies in this range are not yet accessible to conventional beam experiments, and high charge states of interest to these questions are not easily obtainable by drift-tube, ECR or after-glow experi~ ments, we have developed a stored ion collision technique enabling us to study a variety of collisions between 1-3 times charged ions at electronvolt energy with neutral hydrogen, nitrogen and oxygen [4-6]. An extension to this method is provided by the use of recoil ions resulting from heavy ion impact on gaseous targets as a mechanism to produce highly charged ions inside the potential well of a Penning trap [7]. Even though the Penning trap provides stability for a range of masses and charges, the operating point of the trap for some of the higher mass-to-charge ratios might be near the stability boundary in some experiments due to the limitation in magnetic field strength available or the need for high axial well depth for initial confinement. On the other hand this property has been routinely used in the work on recoil ions to eliminate the lower charge states to avoid excessive space charge effects.
trode producing a three-dimensional hyperbolic potential (fig. 1). This potential will confine ions with kinetic energy less than the well depth D. = Vo/2 , where V0 is the dc voltage applied to the ring, in the z-direction but defocus the ions in the x - y plane. To overcome this defocusing a strong homogeneous magnetic field (usually in the order of 10 kG) is superimposed parallel to the z-axis. In this arrangement the ions move along closed trajectories having radii which are small compared to the trap dimensions and characteristic frequencies
[ qvo),j2
..•[
13ruing electronics [
. . . .,
I
,, zjF,-fl
i
/
F eamp.
v
2. Experimental methods Ions are created by electron impact inside a Penning trap consisting of two end-electrodes and one ring-elec0168-9002/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Fig. 1. Schematic diagram of the Penning trap configuration, showing the magnetic field and dc bias arrangement, and the measurement electronics.
458
H.M. Holzscheiter/ Ion confinementin a marginallystable Penning trap
and i
~°+=T t-4--
!
/ ~5c
-~ ul
where V0 is the dc voltage applied to the ring, z 0 is the trap dimension (see fig. 1) and q and m are the charge and mass of the ion under investigation. The condition for stable confinement is given by the requirement, that the defocusing effect of the electric potential is overcome by the Lorentz force due to the magnetic field. For an ideal Penning trap this yields a critical magnetic field Bc given by (2)
below which the ion motion in the trap becomes unstable. In fields only slightly larger than Bc confined ions are only marginally stable in the sense that other parameters such as ion mean energy, ion velocity, elastic scattering cross sections, or the presence of other ions in the trap may influence ion stability and lead to rapid ion loss. To characterize the strongest of these influences, ion storage near the stability boundary has been studied in detail. The number of ions confined after a fixed storage interval (~< 100 ms) has been measured as a function of magnetic field B at different axial well depths D~, with different numbers of stored ions, and with different proportions of the mass-tocharge ratios stored. In fig. 2 the results of all these different measurements are presented in one single graph showing the dependence of the critical magnetic field Bc u
1
'
I
I
I 30
* : Vo = ,50 VOLTS I
+ : V o : 30 VOLTS ~" : Vo : 20 VOLTS .,,
~
~
: THEORY
LL ~-
÷#+
.5
p-
a
J
I0
I
y-/
He+
i
I 20
(vo.%) '~ Fig. 2. Critical magnetic field for a variety of mass-to-charge ratios and well depths in comparison with the ideal trap theory.
# C +
0+#
,
/ ~r++
Z
0 .2
+"~'~"~ "---'~, . MAGNETIC
[ 2rnVo ] ]/2 Be= \ qz---~-o ] ,
g
i
_J
wc = --q B = cyclotron frequency, m
ua
j
,4
"4-
.5 FIELD
,G
,7
.8
[TESLA]
Fig. 3. Trapping efficiency with a fixed storage time of 100 ms before detection vs magnetic field for different ion species. on the mass-to-charge ratio and the axial well depth. The results are in excellent agreement with the predicted values from the ideal trap theory, for the parameters used. For fields slightly above the critical value, the storage time of the ions is reduced, however. Fig. 3 shows that with a constant pulsed electron current used to produce the ions, the detected ion number increases from 0 to an equilibrium value over a range of magnetic field values AB, rather than instantaneously, For an ideal Penning trap this should correspond to a voltage range for the dc potential V0 = (qzZo/m)Bo . It is found that the width of the marginally stable region is strongly different for different ion species. For ions produced via dissociative ionization where the products might have significant initial kinetic energy (i.e. C + and O + produced from CO 2) zaB is much larger than for those ions produced by direct ionization (He + and Ar2+). To investigate this property further we studied the storage time for different ions near their respective stability boundary. By changing the background gas pressure we adjusted the charge exchange rate to obtain storage times in the order of 100 s when the operating point was chosen far away from the stability boundary. Then the magnetic field was reduced and the number of ions remaining in the trap after a time delay T between the end of the electron pulse and the beginning of the detection sweep was measured using the resonant detection method described in detail elsewhere [4}. Fig. 4 shows a series of measurements obtained for helium ions. Unlike the pure exponential decay of the signal amplitude which is expected for storage times limited by charge exchange reactions the measurements exhibit the typical shape predicted for ion loss by radial diffusion with an initially flat ion population and subsequent loss from the detection volume when the ion cloud has
H.M. ttolzscheiter / Ion confinement in a marginally stable Penning trap
~.3GT
5(3
z ~9 t/1 z IO
.2G T
\
1
.32
T
i
STORAGE T,ME [SEC] Fig. 4. Storage times of helium ions for different magnetic field strengths near the critical field (Bc = 0.25 T). spread to the edge of the trap. This drift process can be understood from purely kinematic reasons. Ions colliding elastically with residual gas molecules may increase their drift motion radius r by as much as two cyclotron radii r+, depending on the relative mass of the collision partners and the impact angle. Near the critical magnetic field the cyclotron radius becomes independent of the mass-to-charge ratio and approaches the drift motion radius r_ and only a few collisions are needed for the ions to escape from the trapping volume. For ions with large initial kinetic energy this process can lead to a significant outward diffusion and rapid ion loss even before the ions are thermalized to their mean energy of approximately 1/10 of the well depth. The statistical properties of the collision process and the distribution of the initial kinetic energy among the different possible degrees of freedom lead to a spread A B in the detected ion number at a fixed time interval which depends on the initial kinetic energy rather than to a shift of the observed critical magnetic field B~.
3. Implementations of marginal stability 3.1. Intermediate state analysis In almost all measurements of charge transfer collisions using the stored ion collision technique the oper-
459
ation points of the Penning trap were carefully chosen to be far away from the stability boundary for the investigated ion species, thus ensuring that the dominating ion loss mechanism was due to charge exchange reactions. This was normally verified by repeating the measurements at different target gas densities and looking for a linear dependence of the loss time constant on the gas density. For the lower charge state product ions resulting from the charge exchange process under investigation it is not always possible to choose the operating point as easily far in the stable domain since higher dc potentials are required for the detection whereas higher magnetic fields are needed for confinement. Therefore the trap might be operating near the stability boundary for the high mass-to-charge ratio product ions and if the kinetic energy acquired by the products during the charge exchange reaction exceeds a certain value, the loss due to radial drift may be large enough to inhibit a detectable accumulation of product ions. In the case of the reaction Ar2++ N 2 the failure to observe N2+ or N + ions indicates that the process occurs via a double charge capture leading to N 2+ with subsequent dissociation into two N + ions sharing a kinetic energy of 13.6 eV [8]. On the other hand N + ions resulting from the reaction of N =+ with N 2 were observed in the same experimental setup [9]. A better understanding of marginal stability and its dependence on the initial kinetic energy will enable us eventually to obtain information on the intermediate states involved in these processes comparable to energy gain spectroscopy experiments
0o1. 3.2. Production of higher charge states A second potential application of the marginal stability is given in the production of multicharged ions with moderate charge states. So far we have produced charge states up to q = 3 using electron impact ionization but had to resort to more elaborate methods to obtain higher charge states. The main limitation with electron impact ionization has been the space charge produced by the lower charge states produced simultaneously with larger cross sections. Resonance excitation has enabled us to eliminate this problem to a certain extent but inhibited us at the same time from using stepwise ionization. If the operating point of the trap is chosen appropriately it seems feasible to limit the space charge buildup while still keeping the lower charge states in the trap long enough to allow a second electron impact ionization to increase the charge state and to stabilize the ion. If the dc potential or the magnetic field is programmed according to the time evolution of the population of the different charge states this should result in a detectable accumulation of higher charge states. With sufficient electron energy this might free the experiments from the necessity of access to high energy accelerators or synchrotron light sources.
460
H.M. Holzscheiter / Ion confinement in a marginally stable Penning trap
4. Summary Marginal stability, although a limiting property of Penning traps to many experiments, can be of potential use if controlled in an appropriate fashion. If the exact energy dependence of the time evolution of an ion ensemble stored near the stability boundary is known, detailed information on the intermediate states involved in a specific charge exchange process can be obtained. In many cases a discrimination between possible candidates for a reaction can even be obtained without a detailed study. This would open the field of energy gain spectroscopy to reaction partners which are not easily accessible to conventional methods. Programming of the operating point of a Penning trap during ion production might significantly enhance the production efficiency for higher charge states and allow experiments to be performed in university laboratories which so far have required access to larger facilities. Both these possible applications are currently under investigation. I thank Mrs. K. Holdschick for assistance in the experiment, and Prof. D.A. Church for critical discussions. This research is supported by the Robert A. Welch Foundation, by the National Science Founda-
tion, and by the Texas A & M Center for Energy and Mineral Resources.
References [1] A. Dalgarno and S.E. Butler, Comments At. Mol. Phys. 7 (1978) 129. [2] C.F. Barnet, Atomic Physics, vol. 5, eds., R. Marrus, M. Prior and H. Shugart (Plenum, New York, 1977) p. 375. [3] D. Crandall, private communication. [4] H.M. Holzscheiter and D.A. Church, Phys. Scripta T3 (1983) 173. [5] H.M. Holzscheiter and D.A. Church, Phys. Lett. 86A (1981) 25. [6] D.A. Church and H.M. Holzscheiter, Phys. Rev. Lett. 49 (1982) 643. [7] D.A. Church, R.A. Kenefick, W.S. Burns, C.S.O, R. Holmes, S. Huldt, S. Berry, M. Breinig, S. Elston, J.-P. Rozet, I.A. Sellin, D. Taylor and B. Thomas, Phys. Rev. Lett. 51 (1983) 1636. [8] H.M. Holzscheiter and D.A. Church, J. Chem. Phys. 74 (1981) 2313. [9] D.A. Church and H.M. Holzscheiter, Chem. Phys. Lett. 76 (1980) 1. [10] B.A. Huber and H.J. Kahlert, Z. Physik A317 (1984).
ION CONFINEMENT
IN A MARGINALLY
457
STABLE PENNING
TRAP
H.M. HOLZSCHEITER Department of Physics, Texas A&M University, College Station, TX 77843, USA
The behaviour of ions stored in a Penning trap operated near the stability boundary is investigated. It is found that a marginally stable region exists with width a B which appears to depend on the initial kinetic energy of the ions at time of production. It is pointed out how this property, presenting an inherent limitation to the stored ion collision method, can be utilized in the production of higher charge states using electron-impact ionization and to obtain information on the intermediate states in charge exchange reactions.
!. Introduction The process of charge exchange collisions between multiply charged ions and neutral molecules and atoms at relative energies of a few electronvolts is important in the interpretation of astrophysical processes [1] and the behaviour of magnetically confined plasmas [2]. It has been pointed out recently that data for charge exchange collisions between few times ionized oxygen, nitrogen and carbon impurities colliding with neutral hydrogen atoms at relative energy below 10 eV are needed to understand edge effects in magnetically confined plasmas [3]. Since energies in this range are not yet accessible to conventional beam experiments, and high charge states of interest to these questions are not easily obtainable by drift-tube, ECR or after-glow experi~ ments, we have developed a stored ion collision technique enabling us to study a variety of collisions between 1-3 times charged ions at electronvolt energy with neutral hydrogen, nitrogen and oxygen [4-6]. An extension to this method is provided by the use of recoil ions resulting from heavy ion impact on gaseous targets as a mechanism to produce highly charged ions inside the potential well of a Penning trap [7]. Even though the Penning trap provides stability for a range of masses and charges, the operating point of the trap for some of the higher mass-to-charge ratios might be near the stability boundary in some experiments due to the limitation in magnetic field strength available or the need for high axial well depth for initial confinement. On the other hand this property has been routinely used in the work on recoil ions to eliminate the lower charge states to avoid excessive space charge effects.
trode producing a three-dimensional hyperbolic potential (fig. 1). This potential will confine ions with kinetic energy less than the well depth D. = Vo/2 , where V0 is the dc voltage applied to the ring, in the z-direction but defocus the ions in the x - y plane. To overcome this defocusing a strong homogeneous magnetic field (usually in the order of 10 kG) is superimposed parallel to the z-axis. In this arrangement the ions move along closed trajectories having radii which are small compared to the trap dimensions and characteristic frequencies
[ qvo),j2
..•[
13ruing electronics [
. . . .,
I
,, zjF,-fl
i
/
F eamp.
v
2. Experimental methods Ions are created by electron impact inside a Penning trap consisting of two end-electrodes and one ring-elec0168-9002/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Fig. 1. Schematic diagram of the Penning trap configuration, showing the magnetic field and dc bias arrangement, and the measurement electronics.
458
H.M. Holzscheiter/ Ion confinementin a marginallystable Penning trap
and i
~°+=T t-4--
!
/ ~5c
-~ ul
where V0 is the dc voltage applied to the ring, z 0 is the trap dimension (see fig. 1) and q and m are the charge and mass of the ion under investigation. The condition for stable confinement is given by the requirement, that the defocusing effect of the electric potential is overcome by the Lorentz force due to the magnetic field. For an ideal Penning trap this yields a critical magnetic field Bc given by (2)
below which the ion motion in the trap becomes unstable. In fields only slightly larger than Bc confined ions are only marginally stable in the sense that other parameters such as ion mean energy, ion velocity, elastic scattering cross sections, or the presence of other ions in the trap may influence ion stability and lead to rapid ion loss. To characterize the strongest of these influences, ion storage near the stability boundary has been studied in detail. The number of ions confined after a fixed storage interval (~< 100 ms) has been measured as a function of magnetic field B at different axial well depths D~, with different numbers of stored ions, and with different proportions of the mass-tocharge ratios stored. In fig. 2 the results of all these different measurements are presented in one single graph showing the dependence of the critical magnetic field Bc u
1
'
I
I
I 30
* : Vo = ,50 VOLTS I
+ : V o : 30 VOLTS ~" : Vo : 20 VOLTS .,,
~
~
: THEORY
LL ~-
÷#+
.5
p-
a
J
I0
I
y-/
He+
i
I 20
(vo.%) '~ Fig. 2. Critical magnetic field for a variety of mass-to-charge ratios and well depths in comparison with the ideal trap theory.
# C +
0+#
,
/ ~r++
Z
0 .2
+"~'~"~ "---'~, . MAGNETIC
[ 2rnVo ] ]/2 Be= \ qz---~-o ] ,
g
i
_J
wc = --q B = cyclotron frequency, m
ua
j
,4
"4-
.5 FIELD
,G
,7
.8
[TESLA]
Fig. 3. Trapping efficiency with a fixed storage time of 100 ms before detection vs magnetic field for different ion species. on the mass-to-charge ratio and the axial well depth. The results are in excellent agreement with the predicted values from the ideal trap theory, for the parameters used. For fields slightly above the critical value, the storage time of the ions is reduced, however. Fig. 3 shows that with a constant pulsed electron current used to produce the ions, the detected ion number increases from 0 to an equilibrium value over a range of magnetic field values AB, rather than instantaneously, For an ideal Penning trap this should correspond to a voltage range for the dc potential V0 = (qzZo/m)Bo . It is found that the width of the marginally stable region is strongly different for different ion species. For ions produced via dissociative ionization where the products might have significant initial kinetic energy (i.e. C + and O + produced from CO 2) zaB is much larger than for those ions produced by direct ionization (He + and Ar2+). To investigate this property further we studied the storage time for different ions near their respective stability boundary. By changing the background gas pressure we adjusted the charge exchange rate to obtain storage times in the order of 100 s when the operating point was chosen far away from the stability boundary. Then the magnetic field was reduced and the number of ions remaining in the trap after a time delay T between the end of the electron pulse and the beginning of the detection sweep was measured using the resonant detection method described in detail elsewhere [4}. Fig. 4 shows a series of measurements obtained for helium ions. Unlike the pure exponential decay of the signal amplitude which is expected for storage times limited by charge exchange reactions the measurements exhibit the typical shape predicted for ion loss by radial diffusion with an initially flat ion population and subsequent loss from the detection volume when the ion cloud has
H.M. ttolzscheiter / Ion confinement in a marginally stable Penning trap
~.3GT
5(3
z ~9 t/1 z IO
.2G T
\
1
.32
T
i
STORAGE T,ME [SEC] Fig. 4. Storage times of helium ions for different magnetic field strengths near the critical field (Bc = 0.25 T). spread to the edge of the trap. This drift process can be understood from purely kinematic reasons. Ions colliding elastically with residual gas molecules may increase their drift motion radius r by as much as two cyclotron radii r+, depending on the relative mass of the collision partners and the impact angle. Near the critical magnetic field the cyclotron radius becomes independent of the mass-to-charge ratio and approaches the drift motion radius r_ and only a few collisions are needed for the ions to escape from the trapping volume. For ions with large initial kinetic energy this process can lead to a significant outward diffusion and rapid ion loss even before the ions are thermalized to their mean energy of approximately 1/10 of the well depth. The statistical properties of the collision process and the distribution of the initial kinetic energy among the different possible degrees of freedom lead to a spread A B in the detected ion number at a fixed time interval which depends on the initial kinetic energy rather than to a shift of the observed critical magnetic field B~.
3. Implementations of marginal stability 3.1. Intermediate state analysis In almost all measurements of charge transfer collisions using the stored ion collision technique the oper-
459
ation points of the Penning trap were carefully chosen to be far away from the stability boundary for the investigated ion species, thus ensuring that the dominating ion loss mechanism was due to charge exchange reactions. This was normally verified by repeating the measurements at different target gas densities and looking for a linear dependence of the loss time constant on the gas density. For the lower charge state product ions resulting from the charge exchange process under investigation it is not always possible to choose the operating point as easily far in the stable domain since higher dc potentials are required for the detection whereas higher magnetic fields are needed for confinement. Therefore the trap might be operating near the stability boundary for the high mass-to-charge ratio product ions and if the kinetic energy acquired by the products during the charge exchange reaction exceeds a certain value, the loss due to radial drift may be large enough to inhibit a detectable accumulation of product ions. In the case of the reaction Ar2++ N 2 the failure to observe N2+ or N + ions indicates that the process occurs via a double charge capture leading to N 2+ with subsequent dissociation into two N + ions sharing a kinetic energy of 13.6 eV [8]. On the other hand N + ions resulting from the reaction of N =+ with N 2 were observed in the same experimental setup [9]. A better understanding of marginal stability and its dependence on the initial kinetic energy will enable us eventually to obtain information on the intermediate states involved in these processes comparable to energy gain spectroscopy experiments
0o1. 3.2. Production of higher charge states A second potential application of the marginal stability is given in the production of multicharged ions with moderate charge states. So far we have produced charge states up to q = 3 using electron impact ionization but had to resort to more elaborate methods to obtain higher charge states. The main limitation with electron impact ionization has been the space charge produced by the lower charge states produced simultaneously with larger cross sections. Resonance excitation has enabled us to eliminate this problem to a certain extent but inhibited us at the same time from using stepwise ionization. If the operating point of the trap is chosen appropriately it seems feasible to limit the space charge buildup while still keeping the lower charge states in the trap long enough to allow a second electron impact ionization to increase the charge state and to stabilize the ion. If the dc potential or the magnetic field is programmed according to the time evolution of the population of the different charge states this should result in a detectable accumulation of higher charge states. With sufficient electron energy this might free the experiments from the necessity of access to high energy accelerators or synchrotron light sources.
460
H.M. Holzscheiter / Ion confinement in a marginally stable Penning trap
4. Summary Marginal stability, although a limiting property of Penning traps to many experiments, can be of potential use if controlled in an appropriate fashion. If the exact energy dependence of the time evolution of an ion ensemble stored near the stability boundary is known, detailed information on the intermediate states involved in a specific charge exchange process can be obtained. In many cases a discrimination between possible candidates for a reaction can even be obtained without a detailed study. This would open the field of energy gain spectroscopy to reaction partners which are not easily accessible to conventional methods. Programming of the operating point of a Penning trap during ion production might significantly enhance the production efficiency for higher charge states and allow experiments to be performed in university laboratories which so far have required access to larger facilities. Both these possible applications are currently under investigation. I thank Mrs. K. Holdschick for assistance in the experiment, and Prof. D.A. Church for critical discussions. This research is supported by the Robert A. Welch Foundation, by the National Science Founda-
tion, and by the Texas A & M Center for Energy and Mineral Resources.
References [1] A. Dalgarno and S.E. Butler, Comments At. Mol. Phys. 7 (1978) 129. [2] C.F. Barnet, Atomic Physics, vol. 5, eds., R. Marrus, M. Prior and H. Shugart (Plenum, New York, 1977) p. 375. [3] D. Crandall, private communication. [4] H.M. Holzscheiter and D.A. Church, Phys. Scripta T3 (1983) 173. [5] H.M. Holzscheiter and D.A. Church, Phys. Lett. 86A (1981) 25. [6] D.A. Church and H.M. Holzscheiter, Phys. Rev. Lett. 49 (1982) 643. [7] D.A. Church, R.A. Kenefick, W.S. Burns, C.S.O, R. Holmes, S. Huldt, S. Berry, M. Breinig, S. Elston, J.-P. Rozet, I.A. Sellin, D. Taylor and B. Thomas, Phys. Rev. Lett. 51 (1983) 1636. [8] H.M. Holzscheiter and D.A. Church, J. Chem. Phys. 74 (1981) 2313. [9] D.A. Church and H.M. Holzscheiter, Chem. Phys. Lett. 76 (1980) 1. [10] B.A. Huber and H.J. Kahlert, Z. Physik A317 (1984).