paul-Nobel prize lecture 1989 (1248333), страница 2
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voltage) one has stability from 0 < q < q =0.92 with the consequence that all masses between ∞ > m > m havestable orbits. In this case the quadrupole field works as a high pass massfilter. The mass range ∆m becomes narrower with increasing dc voltage Ui.e. with a steeper operating line and approaches ∆m = 0, if the line goesthrough the tip of the stability region. The bandwidth in this case is givenonly by the fluctuation of the field parameters. If one changes U and Vsimultaneously and proportionally in such a way that a/q remains sonstant,one brings the ions of the various masses successively in the stability regionscanning through the mass spectrum in this way.
Thus the quadrupoleworks as a mass spectrometer.A schematic view of such a mass spectrometer is given in Fig. 4. In Figs.5a,b. the first mass spectra obtained in 1954 are shown [6]. Clearly one seesthe influence of the d.c. voltage U on the resolving power.In quite a number of theses the performance and application of suchmaxminW.Paul607Figure 5.
a) Very first mass spectrum of Rubidium. Mass scanning was achieved by periodicvariation of the driving frequency v. Parameter: u = $, at u = 0.164 85 Rb and 87 Rb are fullyresolved. b) Mass doublet 83Kr - C 6H 11. . Resolving power m/∆m = 6500 [9].608Physics 1989instruments was investigated at Bonn University [7,8,9]. We studied theinfluence of geometrical and electrical imperfections giving rise to highermultipole terms in the field. A very long instrument (l = 6 m) for highprecision mass measurements was built achieving an accuracy of 2 * 10-7 indetermining mass ratios at a resolving power 2 = 16 000. Very small oneswere used in rockets to measure atomic abundances in the high atmosphere.In another experiment we succeeded in separating isotopes in amounts ofmilligrams using a resonance method to shake single masses out of anintense ion beam guided in the quadrupole.In recent decades the r.f.
quadrupole whether as mass spectrometer orbeam guide due to its versatility and technical simplicity has found broadapplications in many fields of science and technology. It became a kind ofstandard instrument and its properties were. treated extensively in theliterature [10].The Ion TrapAlready at the very beginning of our thinking about dynamic stabilization ofions we were aware of the possibility using it for trapping ions in a threedimensional field. We called such a device “Ionenkäfig”[11,12,13].
Nowadays the word “ion trap” is preferred.The potential configuration in the ion trap has been given in eq. (3).This configuration is generated by an hyperbolically shaped ring and twohyperbolic rotationally symmetric caps as it is shown schematically in Fig.6a. Fig. 6b gives the view of the first realized trap in 1954.Figure 6.
a) Schematic view of the ion trap. b) Cross section of the first trap (1955).W. Paul609If one brings ions into the trap, which is easily achieved by ionizing insidea low pressure gas by electrons passing through the volume, they performthe same forced motions as in the two-dimensional case. The only differenceis that the field in z-direction is stronger by a factor 2. Again a periodic fieldis needed for the stabilization of the orbits.
If the voltage Q0 = U + Vcos mtis applied between the caps and the ring electrode the equations of motionare represented by the same Mathieu functions of eq.(5). The relevantparameters for the r motion correspond to those in the x-direction in theplane field case. Only the z parameters are changed by a factor 2.Accordingly, the region of stability in the a-q-map for the trap has adifferent shape as is shown in Fig. 7. Again the mass range of the storableions (i.e. ions in the stable region) can be chosen by the slope of theoperation line a/q = 2U/V.
Starting with operating parameters in the tip ofthe stable region one can trap ions of a single mass number. By lowering thed.c. voltage one brings the ions near the q-axis where their motions aremuch more stable.For many applications it is necessary to know the frequency spectrum ofthe oscillating ions. From mathematics we learn that the motion of the ionscan be described as a slow (secular) oscillation with the fundamental fre-Figure 7.
The lowest region for stability in the ion trap. On the lines inside the stability region /$and B, resp. are constant.610quencies o,,, = PI,L . ω/2 modulated with a micromotion, a much fasteroscillation of the driving frequency ω if one neglects higher harmonics. Thefrequency determining factor β is a function only of the Mathieu parameters a and q and therefore mass dependent. Its value varies between 0 and1; lines of equal β are drawn in Fig. 7.Due to the stronger field the frequency O, of the secular motion becomestwice 0,.
The ratio O/O, is a criterion for the stability. Ratios of 10: 1 areeasily achieved and therefore the displacement by the micromotion averagesout over a period of the secular motion.The dynamic stabilization in the trap can easily be demonstrated in amechanical analogue device. In the trap the equipotential lines form asaddle surface as is shown in Fig. 8. We have machined such a surface on around disc. If one puts a small steel ball on it, then it will roll down: itsposition is unstable. But if one let the disk rotate with the right frequencyFigure 8.
Mechanical analogue model for the ion trap with steelball as “particle”w. Paul611appropriate to the potential parameters and the mass of the ball (in our casea few turns/s) the ball becomes stable, makes small oscillations and can bekept in position over a long time. Even if one adds a second or a third ballthey stay near the center of the disc. The only condition is that the relatedMathieu parameter q be in the permitted range. I brought the device withme.
It is made out of Plexiglas which allows demonstration of the particlemotions with the overhead projector.This behaviour gives us a hint of the physics of the dynamic stabilization.The ions oscillating in the r- and z-directions to first approximation harmonically, behave as if they are moving in a pseudo potential well quadraticin the coordinates. From their frequencies O, and O, we can calculate thedepth of this well for both directions. It is related to the amplitude V of thedriving voltage and to the parameters a and q. Without any d.c.
voltage thedepth is given by Dz = (q/8) V, in the r-direction it is half of this. As inpractice V amounts to a few hundred volts the potential depth is of theorder of 10 Volts. The width of the well is given by the geometric dimensions. The resulting configuration of the pseudo potential [14] is thereforegiven byCooling processAs mentioned, the depth of the relevant pseudopotential in the trap is ofthe order of a few volts. Accordingly the permitted kinetic energy of thestored ions is of the same magnitude and the amplitude of the oscillationscan reach the geometrical dimensions of the trap. But for many applicationsone needs particles of much lower energy well concentrated in the center ofthe trap.
Especially for precise spectroscopic measurements it is desirableto have extremely low velocities to get rid of the Doppler effect and aneventual Stark effect, caused by the electric field. It becomes necessary tocool the ions. Relatively rough methods of cooling are the use of a coldbuffer gas or the damping of the oscillations by an external electric circuit.The most effective method is the laser induced sideband fluorescencedeveloped by Wineland and Dehmelt [15].In 1959 Wuerker et al. [16] performed an experiment trapping smallcharged Aluminium particles (φ ~ mm) in the quadrupole trap.
Thenecessary driving frequency was around 50 Hz accordingly. They studied allthe eigenfrequencies and took photographs of the particle orbits; see Figs.9a, b. After they have damped the motion with a buffer gas they observedthat the randomly moving particles arranged themselves in a regular pattern. They formed a crystal.In recent years one has succeeded in observing optically single trappedions by laser resonance fluorescence [17]. Walther et al., using a highresolution image intensifier observed the pseudo-crystallization of ions inthe trap after cooling the ions with laser light. The ions are moving to suchFigure 9. a) Photomicrograph of a Lissajous orbit in the r-z-plane of a single charged particle ofAluminium powder.
The micro motion is visible. b) Pattern of “ condensed” Al particles [16].positions where the repulsive Coulomb force is compensated by the focusing forces in the trap and the energy of the ensemble has a minimum. Figs.10a, b show such a pattern with 7 ions. Their distance is of the order of afew micrometers. These observations opened a new field of research [18].The Ion Trap as Muss SpectrometerAs mentioned the ions perform oscillations in the trap with frequencies O,and o, which at fixed field parameters are determined by the mass of theion.
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