Trapping of ions injected from an external source into a three-dimensional quadrupole trap

Nuclear Instruments and Methods 186 (1981) 219-230 North-Holland Pubhshmg Company

T R A P P I N G OF IONS I N J E C T E D F R O M AN E X T E R N A L SOURCE I N T O A THREEDIMENSIONAL QUADRUPOLE TRAP

Hans A. S C H U E S S L E R and Chun-sing O Department of Physics, Texas A & M University, College Station, Texas 77843, USA

The use of a quadrupole ion trap to catch ions in flight was investxgated numerically After briefly dxscussmgthe pnnoples of ion storage, the number of ions stored m equlhbnum and the storage time are presented for different injection conditions The results of the study show that 1on storage for a certain period of time is possible for ions injected into a quadrupole ion trap operated m the radio-frequency mode and also for a trap operated m the combined mode However, a quadrupole ion trap operated m the Penning mode is not suitable for trapping externally generated ions without an additional decelerating field gradient

1. Introduction

During the past few years, laser spectroscopy on-line with accelerators [1] has contributed a wealth of new knowledge on nuclear structure in regions off /3 -stability. Hereby already established methods were either adapted from the spectroscopy of stable isotopes or were specifically developed for on-line use. Examples of the first group are laser induced Doppler limited fluorescence spectroscopy [2], which was used by the M a i n z - I S O L D E group, where one of the authors collaborated during the past several summers. In these experiments, Doppler limited fluorescence spectroscopy was applied to study the neutron deficient mercury isotopes and isomers. Other techniques in this category are the quantum beat technique, used by us for the spin measurements of the very neutron deficient mercury isomers [3], and the laser optical pumping magnetic state selection technique [4], employed successfully by the Orsay group for the various long chains of the alkali isotopes. An example of the second group is collinear laser spectroscopy [5] of radioactive atoms in fast beams, developed by the Mainz-CERN-G/Stheb u r g - A a r h u s group at I S O L D E . This general method was tailored to on-line investigations and has already yielded results for a chain of barium nuclei [6] and also for some ytterbium nuclei [7]. In these experiments the beam intensity of the short-lived isotopes was in some cases as low as

105 atoms per second and the spectral resolution was a few MHz. Future methods will have to improve on these already remarkable numbers. To this end initial theoretical studies have been made which investigate the possible use of ion storage techniques for on-line spectroscopy. It is known that ions created externally cannot be stored for indefinite periods of time without energy extraction. However, it may still be possible to trap even hot ions long enough to perform an experiment. Clearly the ultimate in sensitivity and resolution of an on-line experiment would be obtained if it were possible to catch the radioactive ions after deceleration as they emerge from the mass separator and to accumulate them in a small region of space, where they would also be refrigerated to eliminate Doppler broadening. While the high sensitivity and intrinsic accuracy of stored ion spectroscopy and laser cooling to less than I°K have already been demonstrated [8, 9], stored ion experiments have usually relied on ions created inside the quadrupole ion trap [10]. A numerical study of the various aspects of injecting externally produced ions into a three-dimensional quadrupole trap is underway. The experimental arrangement is similar to the one shown in fig. 1. The nucleus of interest is produced in a nuclear reaction. After deceleration, the mass-separated ions are focused into the ion trap. Some ions are caught and stored for their nuclear lifetime. When the frequency of the laser beam is tuned on resonance with an

0029-554X/81/0000-0000/$2.50 O North-Holland

IV ON-LINE SEPARATOR TECHNIQUES

H A Schuessler, Chun-Smg 0 / Trapping of i o n s

220

TUNABLE DYE-LASER

~ . _ _ ~ DOUBLING CRYSTAL

INTENSITY

m POLARIZER BEAM LINES

POLARIZER

MASS SEPARATING MAGNET -

ION SOURCE SIGNAL RADIOACTIVE

HELMHOLTZ COIL

/

DECELERATION

ION BEAM

SYSTEM ION TRAP

TARGET

STABLE G-G NUCLEI BEAM FROM ACCELERATOR •

V

REFERENCE ION TRAP

Fig. 1 Experimental arrangement for on-hne stored ion spectroscopy.

optical transition of the isotope of interest, resonance fluorescence is observed at right angles to the laser beam. By measuring the fluorescent intensity as a function of the laser frequency, the isotope shift, the isomer shift, and in suitable cases also the hfs splitting can be determined. Laser frequency calibration is ettected by Z e e m a n shifting the fluorescence lines of a stable reference ion isotope, stored in a second trap, into the region of interest. This procedure of laser frequency calibration is analogous to the scheme [11] used in the investigation of the long chain of neutral mercury isotopes. A small ion trap can also be considered a point source of nuclear radiation and is therefore also of interest for nuclear spectroscopy. A short description of a three-dimensional quadrupole ion trap follows. The trap structure consists of three electrodes, a ring electrode and two end cap electrodes, which are c o m p l e m e n tary hyperboloids of revolution. Fig. 2 shows the ring electrode which has a radius of 0.5 cm and also displays o n e of the two end cap electrodes, which are placed on either side of the ring electrode. The electrodes were machined from m o l y b d e n u m and positioned with a close tolerance of a few thousandths of a centimeter. The assembled trap is depicted in fig. 3. In order

Fig. 2 Photograph of the quadrupole electrodes which are complementary hyperboloids of revolution (a) Ring electrode (b) End cap electrode

H.A Schuessler, Chun-Sing 0 / Trapping of tons

221

time, the ion motion must be stable and have a maximum displacement from the trap center smaller than the corresponding characteristic dimension of the trap. Depending on the applied electric and magnetic fields, the quadrupole ion trap can be operated in three modes, namely, the radio-frequency mode [12], and Penning mode [13], and the combined mode. In section 2 the various modes of operation are briefly described. In section 3 we consider ion injection from an external ion source and derives the optimum injection conditions. Ion cooling of stored ions is presented in section 4. Finally, the results are summarized in section 5.

2. Modes of operation of the quadrupole ion trap Fig 3 Picture of the assembled ion trap A wave grade is bolted to the ring electrode for reducing magnetic dipole transiUons on stored Ions

to store ions a three-dimensional potential well has to be generated. This is achieved by applying a suitable combination of ac and dc driving voltages and an external magnetic field to the quadrupole arrangement. Because of the limited well depths e/Sz and eD, produced by the confining electromagnetic fields, the ion beam has to be decelerated either electrostatically or by passing it through a thin foil for energy reduction before injection. The electrodes of the quadrupole ion trap are positioned relative to one another so that the axial distance z0 from the apex of either of the end caps to the equatorial plane and the equatorial radius r0 of the ring electrode satisfy the relation r~= 2z 2. Then the electric potential distribution inside the ion trap has the form

2.1. The radio frequency ion trap arrangement For the operation of the quadrupole ion trap in the radio-frequency mode no external magnetic field is used. The potential difference U(t) between the trap electrodes consists of a dc bias U0 and an ac oscillating voltage with amplitude V0 and angular frequency l-l, i.e. U ( t ) = U0+ V0cosl)t. The application of the various operational voltages to manipulate stored ions is shown in fig. 4. Ion detection is carried out by

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/

/,

~b~A(~S ~ z2)

CThalr°gne

......

_U(t)( x2+ ) V(x, y, z) - r--~-o Z2 y2 2 ' where U(t) is the time dependent potential difference maintained between the ring and end cap electrodes. With the addition of a homogeneous magnetic field H, the equation of motion for an ion of charge-to-mass ratio e/m is

m R = - e V V + e(R x H). For an ion to be trapped for indefinite periods of

Operating Voltages of Ion Trap

Fig 4 Electncal potentml distnbution assooated with the trapping voltage U0+ V0cos ~ t Side-band excitation at the frequency of the 1on m o h o n Is used in the emission method The voltage reduced by the coherent ion motion m the high Q resistive o r c m t at cos toot allows ion detection IV O N - L I N E S E P A R A T O R T E C H N I Q U E S

222

HA

Schuessler, C h u n - S m g 0 / Trapping of tons

the emission method. Hereby the stored ion cloud is driven by externally exciting one of the ion oscillation frequencies and by subsequently observing the voltage induced by the coherent ion motion in a high O circuit connected between the end cap electrodes. The equation of motion in each direction for an ion inside the radio-frequency trap can be written as the Mathieu equation, after an appropriate change in variables [14]. The stable ion motion is then the superposition of two main oscillations at different frequencies, which according to the direction of motion are labelled oJz and (or. In simple terms the principle of operation of the rf electric quadrupole ion trap is as follows. Consider a sequence of snapshots of the time varying potential distribution. The ac operation is depicted by a sequence of static quadrupole potential distributions increasing and decreasing in strength. A static quadrupole is focusing in one direction, while defocusing in the perpendicular direction, i.e. each snapshot shows a potential saddle point. In the sequence of snapshots the saddle points are time varying. If the potential changes from a defocusing to a focusing direction before an ion had the chance to move through an appreciable fraction of the trap dimension, the ion is trapped. Fig. 5 illustrates [15] the origin of the trapping force in a quadrupole. It should be noted that the rf fields in a quadrupole trap are similar to those of a suitably bent plate capacitor. Consider an ion of mass rn and charge + e being harmonically bound to a guiding center in the middle of the capacitor. First consider the case of parallel capacitor plates. The solid line shows the time evolution of the electric force Fz. It is apparent that the time average Fz vanishes. This is no longer the case when the capacitor is bent to produce an inhomogeneous rf field (dashed line). Now the electric force is stronger in the lower than in the upper half of the bent capacitor, and the time average force Fz is finite and points towards the region of the weaker field (solid line). The weaker field is for a quadrupole in the center of the electrode structure. This average force is the focusing force responsible for strong focusing and ion trapping. It should also be noted that the motion of a stored ion is chargeto-mass ratio selective. This situation is depicted in a stability diagram in fig. 6. Only ions with

~_

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~

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0 (b)

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trapping parameters az = - 2 a t and qz = - 2 q r within the enclosed area are trapped. The trapping parameters in the stability region are chosen for a particular ion of interest by selecting the proper combination of ac and dc operating voltages.

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Schuessler, Chun-Smg 0 / Trappmg of tons

2.2, The Penning ion trap arrangement The same electrode structure as before is used. However, for the operation of the quadrupole ion trap in the Penning mode, a strong homogeneous magnetic field H is applied along the symmetry axis of the trap and a constant potential difference U0 is maintained between the trap electrodes. The resultant motion of the charged particle is then a superposition of the harmonic oscillation toz in the axial z-direction, and the magnetron oscillation tom, as well as the spiraling cyclotron oscillation to', in the radial direction. For optimum operation the magnitudes of the three characteristic ion motional frequencies are chosen to fulfill the relation to~ >> toz ~" tom-

2.3. The combined mode ion trap arrangement Ion trapping studies using the combined mode for the operation of the quadrupole ion trap have recently been developed and carried out by our group. In the combined mode both a magnetic field H along the symmetry axis and a potential difference U(t) = Uo + Vo cos l-It between the trap electrodes are required. The

Rodfo-Frequency Mode q r : -O 25 a t : 0 0156

Penning Mode H =15 kGouss eDz ; 2 35 eV

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Combined Mode H= 7 kGuuss

(c)

Combined Mode H=15 kGauss

(d)

Fig 7 Projecnon of the ~on trajectories on the xy-plane for a 0 026 eV ~on created mstde an ~on trap m different modes (a) radio-frequency mode, (b) the Penning mode, (c) and (d) combined mode

223

motion in the z-direction is still governed by the Mathieu equation. However, the motions in the other two directions are coupled by the magnetic field. With a suitable change in variables the radial motions can still be represented in terms of the Mathieu equation having the new stability parameter a'r given by a~= ar+(tOc/~'~) 2. The radial motion of the ion consists of complicated patterns which can be regarded qualitatively as oscillations superimposed on the smooth cyclotron and magnetron orbits. Figure 7 shows the projection of the partial trajectories on the xy-plane for an ion with 0.026 eV energy created inside the trap operated in different modes. The radial oscillation motion at to, in the rf quadrupole trap is indicated in (a). For the Penning trap (b) displays the slow magnetron motion at tom, on which the fast cyclotron motion at to' is superimposed. Finally (c) and (d) exhibit the complicated patterns of the ion motion in the combined trap.

3. Trapping of injected ions The present calculation was performed to determine the storage time of a well collimated ion beam injected from an external source and to estimate the number of ions trapped when equilibrium is reached. Effects due to collisions between ions and background gas particles are neglected. Numerical integration of the equations of motion is carried out for a singly charged ion of mass number 100 injected into a quadrupole ion trap until the ion hits any electrode surface or up to a cutoff time. The trap dimensions are r0 = 0.54 cm and z0 = 0.38 cm. A seemingly natural way to inject an ion is through the gap between the trap electrodes, as shown in fig. 8. However, the storage time is found to be extremely short for ion injection into the quadrupole ion trap for any of the three operation modes. The short storage time is due mainly to the rather high electric field in the narrow gap between the trap electrodes. Low energy ions are deflected almost immediately and hit one of the electrodes while ions with higher energy go through the gap and hit the other side. Since gap injection is not possible, other injection locations were found. The cases conIV O N - L I N E S E P A R A T O R T E C H N I Q U E S

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are then applied to the other electrode. However, for simplicity of calculation, the rf driving voltage is assumed to be always applied to the end caps. The ion injection depends on the initial injection phase so0, which is measured with respect to the driving voltage at frequency ~ . All values of the initial phase s% referred to later should be replaced by s% = ~r-s% when U(t) is applied to the ring electrode. 3.1. Ion injection into the radio-frequency trap

sidered in detail are illustrated in fig. 9. These are ion injection through an aperture on either the midpoint of the ring electrode or the apex of one of the end cap electrodes and will be called ring injection and end cap injection, respectively. The injection aperture is assumed to be infinitesimally small so as not to disturb the electric field distribution. In fig. 10 the incidence direction of the b e a m is given in terms of 0 and ~b, where 0 is the cone angle of the cone surface on which the b e a m lies, and ~b is the azimuth angle measured on a plane perpendicular to the cone axis. End cap injection of the ion b e a m is independent of th because of the axial symmetry of the trap. On the other hand, the value of ~b is critical in the ring injection case. In both cases magnetic shielding up to the injection aperture is necessary. In addition, the electrode through which the ions are injected and the magnetic shield should be maintained at the same electric potential as the external ion source. The dc bias of appropriate polarity and the rf driving voltage

[161 In the present example, the radio-frequency trap operation p a r a m e t e r s were selected to be U0 = - 4.7 V, V0 = 150 V, ~/2¢r = 1 MI-Iz so that qz = 0.5, az = - 0.0313, and /Sx =/Sy = 16.8 eV

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H.A. Schuessler, Chun-Smg 0 / Trapping of t o n s

A value of 20 000 rf cycles, corresponding to 20 ms, is used as the cutoff of the storage time calculation. A typical storage time curve and the trajectory projections on the xy-plane for two values of ¢0 are depicted in fig. 11 for the ring injection case. The major graph displays the calculated storage time versus initial phase. The storage time depends critically on the initial injection phase ¢0 and exhibits a narrow spike at ¢0,ma~ depending on the energy and the incidence direction of the injected beam. The inserts show two particular trajectories. An unstable ion orbit (upper frame) and the partial trajectory of a stable orbit (lower frame) are drawn. If an ion beam of constant current I is injected into the trap, an equilibrium is reached when trapping and loss rates are equal. The equilibrium number no of stored ions obtained for a particular ~:0 is proportional to the storage time measured in units of rf cycles. The area A under the storage time curve is then a measure of the number of ions confined in the trap at any time after equilibrium has been reached. Quantitatively it holds for no = A I / ( t l / 2 r r ) .

Table 1 Maximum storage time in rf cycles for 1on beams injected through the midpoint of the ring electrode of an 1on trap operated m the combined mode The first entry in each case is for a rf quadrupole trap with azimuth angle 4~ = 45 ° The others are for the cases where a magnetic field is apphed parallel to the symmetry axis of the 1on trap The magnetic field strengths are 7 k G and 15 k G for the second and third entries, respectively" E(eV)\O(deg)

0

10

30

60

80

0 026

T T T

T T T

T T T

T T T

T T T

01

T T T

T T T

T T T

T T T

T T T

0.2

91 T T

173 T T

T T T

T T T

T T T

32 79 86

41 158 109

265

T

T

1

T

T

T

T

T

T

23 79 50

23 79 86

41 T T

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T T T

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10

9 39 13

9 158 109

196 T T

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20

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5 9 10

9 109 13

6 T 575

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225

10

E =2eV

The letter " T " m the table means that the calculated storage ¢ = 45*

tlme exceeds 20 000 rf cycles However, the rejected ion is trapped only for certain values of the azimuth angle ~b

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F~g. 11 Display of the storage time versus injection phase for nng injection of ions into a rf ion trap. The insert shows an unstable (upper frame) and a stable (lower frame) 1on orbit

respectively, for the ring injection case and 4~ = 45 ° . The second and third entries are for operation of the quadrupole ion trap in the combined mode and will be discussed in section 3.3. The trapping of externally injected ions is more efficient as the value of 4~ increases up to 4~ = 90 ° . The end cap injection case leads to similar but slightly better results. The major difference is that ~:0,maxis near rr/2 instead of being close to rr as in the ring injection case. For both cases trapping is more favorable for ions of low energy and large incidence angle 0. IV O N - L I N E S E P A R A T O R T E C H N I Q U E S

H A . Schuessler, Chun-Smg 0 / Trapping of ~ons

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Table 2 Area under the storage t~me versus m~tlal phase curve for xons injected through the midpoint of the n n g electrode of an ion trap operated m the combined mode. Only the largest area for five dflIerent values 0 °, 45 °, 90 °, 135 ° and 180 ° of the azimuth angle 4, Is hsted The first entry m each case Is for a rI quadrupole trap The others are for the cases where a magnetic field is apphed parallel to the symmetry axis of the ~on trap The magnetxc field strengths are 7 kG and 15 kG for the second and third entries, respectively ~

E(eV)\0(deg)

0

10

(122) (938)

(238) (938)

(2%) (938)

(476) (939)

(503) (940)

(585)

(585)

(355)

(584)

(586)

0.1

(122) (937) (586)

(122) (938) (354)

(238) (931) (576)

(470) (1054) (702)

(470) (1054) (703)

02

6.2 (938) (354)

66 (939) (356)

(124) (1054) (588)

(413) (1286) (705)

(458) (1401) (935)

1

53 97 59

54 13 74

66 (1059) (589)

(227) (1633) (940)

(414) (1757) (945)

2

50 96 4 1

52 11 65

55 (714) (698)

(130) (1636) (964)

(387) (1989) (1175)

10

53 57 40

53 7.8 55

52 18 13

94 (1656) (962)

(278) (2002) (1998)

20

61 60 4.4

5.8 8.2 66

54 15 82

38 (1435) 47

29 (1783) (2121)

50

4.9 49 43

5 1 56 50

45 60 84

25 28 9 1

20 20 (221)

0 026

30

60

80

very short, typically only a few /Ls. Ion trajectories of a 10 eV ion and ring electrode injection are shown in fig. 12 for a fixed incidence angle of 0 = 80 ° and for various azimuth angles ~b. The location where the ion hits the electrode surface is marked by a solid circle. The storage times for ions injected into the trap operated at larger H and eD: are, in general, even shorter except in some cases where 0 is large. Without the addition of a decelerating field gradient and/or energy changing collisions with the background gas molecules, this mode is the least suitable for trapping externally produced ions.

3.3. Ion injection into the combined trap [18] The operation parameters U0, V0, and D/2zr for the combined trap are the same as those for the radio-frequency trap. In addition, magnetic fields of strengths H = 7 and 15 kG, respectively, are applied along the symmetry axis of the trap. The cutoff of the calculation at 20 000 rf cycles is also followed. Fig. 13 depicts projections of ion trajectories on the xy-plane for a 2 e V ion injected through the ring electrode. The incident

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3.2. Ion injection into the Penning trap [17] Two different sets of operation conditions are used for the calculation of ion injection into the Penning trap, namely H = 1 5 k G and e/Sz = 2.35 eV, as well as H = 60 k G and e/Sz = 16.8 eV. Because of the static nature of the confining fields, the storage time is not dependent on the initial phase and the equilibrium ion number is simply the product of the constant injection beam current and the storage time. Integration of the equations of motion reveals that for ion injection into a Penning trap the storage time is

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12. Projections of trajectories on the xy-plane for a 10 eV ~on rejected through the nng electrode into a Penning trap The incidence angle 0 ls 80 ° The azimuth angle and the storage time are- (a) 0 °, 0 1 kts and 45 °, 0 3/zs, (b) 90 °, 34 ,tts, (c) shows the projection of the partial trajectory m the first f e w / ~ s for an Ion with azimuth angle 4, = 135 ° and a storage ttme of lust under 200 #s, (d) 180 °, 5/zs

Fig

H A . Schuessler, Chun-Smg 0 / Trapping of ions H=O

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Fig 13 Projecnons of the trajectories, or partial trajectories, on the xy-plane of a 2 eV ion using ring electrode rejection m an ion trap operated m the combined mode with H = 7 kG The incidence angle /9 is 60 ° and the mtial phase is ~0 = 0 972zr. The location where the ion hits the electrode surface is marked by a sohd orcle The inodence azimuth angle and the storage time are ~b = 0 °, 4 rf cycles, represented by the solid hne, and ~b = 45 °, 9 rf cycles, represented by the dashed hne, m (a) The storage rimes all exceed 20 000 rf cycles for the azimuth angles ~b = 90 °, 135 °, and 180 ° m (b), (c), and (d), respectwely

azimuthal angle ~b is varied. This figure shows that an initially non-trapped ion orbit becomes a trapped orbit for large values of ~b. Fig. 14 illustrates several storage time versus initial phase curves, showing the dependence on the magnetic field strength for ring electrode injection at two ion energies. The general feature of the storage versus initial phase curve still consists of a narrow spike and the equilibrium ion number is also given by the same expression no = AI/(t~/2zr). The dependence of the storage time on the azimuthal angle ~b is shown in fig. 15 for three values of the magnetic field. It shows that in this particular case the best azimuthal angle is ~b = 130 ° and the best suited magnetic field is 7 kG. Tables 1 and 2 provide results for the maximum storage time and the maximum area under the storage time curve for the combined mode as the second and third entries in each square, respectively, for the ring injection case. It is pointed out that the operation of the combined trap with H = 1 5 k G corresponds to a weakly unstable

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Fig 14 Sections of the storage time versus minal phase curves showing the dependence on the magnenc field strength for an ion rejected through the midpoint of the n n g electrode of an ion trap operated in the combined mode The upper row is for an ion beam with E = 2eV, 0 = 30 °, and 4' = 135 ° and the lower row is for E = 20eV, 0 = 60 °, and 4' = 135°

radial motion. However, the ion is still trapped up to the cutoff time of 2 0 0 0 0 r f cycles. In general, with the trap operated in the combined mode, higher energy ions can be trapped. For the same energy, ion beams incident at smaller incidence angles 0 are trappable. In situations

I 100 r f cycles

&

E = 20eV

e =60* ~*= o 9331I

90

180

(degrees) Fig 15 Dependence of the storage time on the azimuth angle ~b for an ion of energy E = 20 eV rejected through the midpomt of the ring electrode of an ion trap operated m the combined mode The m o d e n c e angle and initial phase are 0 = 60 ° and so0= 0 933zr, respecnvely The applied magnetic field strength is zero (dotted line), 7 k G (dashed hne), and 15 kG (sohd hne) IV O N - L I N E S E P A R A T O R T E C H N I Q U E S

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HA

Schuessler, Chun-Smg 0 / Trapping of zons

where ions can be confined already in the rf m o d e alone, the addition of a magnetic field greatly increases the area under the storage time curve. Contrary to the ring electrode injection case the operation of the quadrupole ion trap with end cap injection in the combined m o d e does not improve, but instead degrades, its trapping capacity for external ions.

4. Side-band cooling of stored ions T h e trapping of only a few ions is sufficient for laser spectroscopy experiments. We have shown that the m i n i m u m detectable 1on number, using the emission m e t h o d and observing the induced image currents, is about 1000 ions in the trap. For optical detection the observation of a single ion has already been demonstrated [19]. After the ions have been trapped the ion energy can still be further reduced by optical side-band cooling [20]. In fig. 16 a low energy b e a m of radioactive ions is incident through a hole cut in the end cap electrode. For fluorescence spectroscopy a laser b e a m is focused through the gap between one end cap and the

ring electrodes. The fluorescence is observed through slots cut into the ring electrode. A microwave field to induce magnetic dipole transitions is also indicated. The laser b e a m can also be used for side-band cooling of stored ions. A side-band spectrum of stored ions [21], observed for the first time, is shown in fig. 17. For this m e a s u r e m e n t 3He + ions were created inside the ion trap by electron b o m b a r d m e n t of the background 3He gas. The spectrum was obtained in the microwave region and was observed at the hfs splitting in the 1 s2S1/2 ground state for the field dependent (1, 1)~-+(0,0) transition at 8.655 662 G H z in a magnetic field of 7.13 G A similar spectrum will also occur at optical frequencies, but has not been observed yet, since a laser with less than 100 k H z band width is required for the m e a s u r e m e n t in a typical ion trap operation. The side-band spectrum is due to the binding of the ions to the three-dimensional potential well. T h e periodic ion motion at the characteristic ion oscillation frequencies OJwleads to a frequency and amplitude modulation of the absorbed radiation and thereby to side bands. The spectrum of a coherently excited ion consists then of the signal at the resonance frequency w0 and the side bands

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Fig 16 Diagram of a quadrupole ion trap The 1on mlectlon is along the z-direction The laser Is focused through the gap and resonance fluorescence is observed through slots cut mto the ring electrode The standing rmcrowavefield is used to mduce magnetic dipole transmons

H A . Schuessler, C-hun-Sing 0 / Trapping of ions

229

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t~

oO FREQUENCY

(MHZ)

Fig 17 S i d e - b a n d s p e c t r u m of s t o r e d SHe* ions at t h e (1, 1) ~ (0, 0) hfs t r a n s i t i o n In t h e 1 s 2Sm g r o u n d state.

IV. O N - L I N E S E P A R A T O R

TECHNIQUES

230

H.A Schuessler, Chun-Smg 0 / Trapping of

symmetrically located on both sides at integer multiples of the frequencies tOw of the ion oscillation in the w-direction. If laser light used to excite the ions is detuned from the resonance frequency and tuned to one of the side bands on the lower energy side of the resonance line cooling will occur, since ions excited by this radiation will reradiate symmetrically at all side-band frequencies. The average energy of the reradiated light is then larger than the average absorbed energy. This excess of energy between the emitted and absorbed radiation can only come from the oscillatory motion of the ions. As a result of this process the average kinetic energy of the ion motion is reduced.

5. Conclusion Numerical studies have been carried out for the trapping of ions injected into a quadrupole ion trap operated in three different operational modes: the radio-frequency mode, the Penning mode, and the combined mode. It is found that the Penning trap is least suitable for confining externally injected ions. On the other hand, confinement of externally injected ions is possible for the radio-frequency trap and the combined trap. It is expected that an ion which is trapped for 20 000 rf cycles will be trapped even longer, particularly if it loses energy in a suitable collision with the background gas by viscous drag cooling. We have also observed motional sideband spectra of stored ions which are of importance in connection with laser side-band cooling. The authors wish to thank H.S. Lakkaraju for his involvement in the side-band work and for fruitful discussions. This research is supported by the US National Science Foundation under Grant # PHY.79-09099, by the US Department of Energy under Contract # DE-AS0580ER10578, and by the Center for Energy and Mineral Resources of Texas A&M University.

sons

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