paul-Nobel prize lecture 1989 (1248333)
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ELECTROMAGNETIC TRAPS FOR CHARGEDAND NEUTRAL PARTICLESNobel Lecture, December 8, 1989byWO L F G A N G P A U LPhysikalisches Institut der Universität Bonn, Nussallee 12, D-5300 Bonn,F.R.G.Experimental physics is the art of observing the structure of matter and ofdetecting the dynamic processes within it. But in order to understand theextremely complicated behaviour of natural processes as an interplay of afew constituents governed by as few as possible fundamental forces andlaws, one has to measure the properties of the relevant constituents andtheir interaction as precisely as possible.
And as all processes in nature areinterwoven one must separate and study them individually. It is the skill ofthe experimentalist to carry out clear experiments in order to get answers tohis questions undisturbed by undesired effects and it is his ingenuity toimprove the art of measuring to ever higher precision. There are manyexamples in physics showing that higher precision revealed new phenomena, inspired new ideas or confirmed or dethroned well established theories.
On the other hand new experimental techniques conceived to answerspecial questions in one field of physics became very fruitful in other fieldstoo, be it in chemistry, biology or engineering. In awarding the Nobel prizeto my colleagues Norman Ramsey, Hans Dehmelt and me for new experimental methods the Swedish Academy indicates her appreciation for theaphorism the Göttingen physicist Georg Christoph Lichtenberg wrote twohundred years ago in his notebook “one has to do something new in orderto see something new”. On the same page Lichtenberg said: “I think it is asad situation in all our chemistry that we are unable to suspend the constituents of matter free”.Today the subject of my lecture will be the suspension of such constituents of matter or in other words, about traps for free charged and neutralparticles without material walls. Such traps permit the observation of isolated particles, even of a single one, over a long period of time and thereforeaccording to Heisenberg’s uncertainty principle enable us to measure theirproperties with extremely high accuracy.In particular, the possibility to observe individual trapped particles opensup a new dimension in atomic measurements.
Until few years ago allmeasurements were performed on an ensemble of particles. Therefore, themeasured value - for example, the transition probability between twoeigenstates of an atom - is a value averaged over many particles. Tacitly602Physics 1989one assumes that all atoms show exactly the same statistical behaviour if oneattributes the result to the single atom. On a trapped single atom, however,one can observe its interaction with a radiation field and its own statisticalbehaviour alone.The idea of building traps grew out of molecular beam physics, massspectrometry and particle accelerator physics I was involved in during thefirst decade of my career as a physicist more than 30 years ago. In theseyears (1950 - 55) we had learned that plane electric and magnetic multipolefields are able to focus particles in two dimensions acting on the magnetic orelectric dipole moment of the particles.
Lenses for atomic and molecularbeams [1,2,3] were conceived and realized improving considerably themolecular beam method for spectroscopy or for state selection. The lensesfound application as well to the ammonia as to the hydrogen maser [4].The question “What happens if one injects charged particles, ions orelectrons, in such multipole fields” led to the development of the linearquadrupole mass spectrometer. It employs not only the focusing and defocusing forces of a high frequency electric quadrupole field acting on ionsbut also exploits the stability properties of their equations of motion inanalogy to the principle of strong focusing for accelerators which had justbeen conceived.If one extends the rules of two-dimensional focusing to three dimensionsone posseses all ingredients for particle traps.As already mentioned the physics or the particle dynamics in such focusing devices is very closely related to that of accelerators or storage rings fornuclear or particle physics.
In fact, multipole fields were used in molecularbeam physics first. But the two fields have complementary goals: the storageof particles, even of a single one, of extremely low energy down to the microelectron volt region on the one side, and of as many as possible of extremely high energy on the other.
Today we will deal with the low energy part. Atfirst I will talk about the physics of dynamic stabilization of ions in two- andthree-dimensional radio frequency quadrupole fields, the quadrupole massspectrometer and the ion trap. In a second part I shall report on trapping ofneutral particles with emphasis on an experiment with magnetically storedneutrons.As in most cases in physics, especially in experimental physics, theachievements are not the achievements of a single person, even if hecontributed in posing the problems and the basic ideas in solving them.
Allthe experiments I am awarded for were done together with research students or young colleagues in mutual inspiration. In particular, I have tomention H. Friedburg and H. G. Bennewitz, C.H. Schlier and P. Toschek inthe field of molecular beam physics, and in conceiving and realizing thelinear quadrupole spectrometer and the r.f.
ion trap H. Steinwedel, O.Osberghaus and especially the late Erhard Fischer. Later H.P. Reinhard, U.v. Zahn and F. v. Busch played an important role in developing this field.W.Paul603Focusing and Trapping of particlesWhat are the principles of focusing and trapping particles? Particles areelastically bound to an axis or a coordinate in space if a binding force actson them which increases linearly with their distance rIn other words if they move in a parabolic potentialThe tools appropriate to generate such fields of force to bind chargedparticles or neutrals with a dipole moment are electric or magnetic multipole fields. In such configurations the field strength, or the potentialrespectively increases according to a power law and shows the desiredsymmetry. Generally if m is the number of “poles” or the order of symmetrythe potential is given byFor a quadrupole m = 4 it gives @ ~ r2 cos 2ϕ, and for a sextupole m = 6 onegets CD ~ r cos 3~ corresponding to a field strength increasing with r and r2respectively.3Trapping of charged particles in 2- and J-dimensional quadrupole fieldsIn the electric quadrupole field the potential is quadratic in the Cartesiancoordinates.The Laplace condition A@ = 0 imposes the condition α + β + γ = 0There are two simple ways to satisfy this condition.a) a = 1 = −γ, β=0 results in the two-dimensional field(2)b) a = β = 1 , γ = -2 generates the three-dimensional configuration, incylindrical coordinatesThe two-dimensional quadrapole or the mass filter [5,6]Configuration a) is generated by 4 hyperbolically shaped electrodes linearlyextended in the y-direction as is shown in Fig.
1. The potential on theelectrodes is ±Φ0/2 if one applies the voltage a0 between the electrodepairs. The field strength is given by604Physics 1989Figure I. a) Equipotential lines for a plane quadrupole fild, b) the electrodes Structure for themass filter.If one injects ions in the y-direction it is obvious that for a constant voltage<Do the ions will perform harmonic oscillations in the the x-y-plane but dueto the opposite sign in the field E their amplitude in the z-direction willincrease exponentially. The particles are defocused and will be lost byhitting the electrodes.This behaviour can be avoided if the applied voltage is periodic.
Due tothe periodic change of the sign of the electric force one gets focusing anddefocusing in both the x- and z-directions alternating in time. If the appliedvoltage is given by a dc voltage U plus an r.f. voltage V with the drivingfrequency ωzthe equations of motion areAt first sight one expects that the time-dependent term of the forcecancels out in the time average. But this would be true only in a homogenous field. In a periodic inhomogenous field, like the quadrupole field thereis a small average force left, which is always in the direction of the lowerfield, in our case toward the center.
Therefore, certain conditions exist thatenable the ions to traverse the quadrupole field without hitting the electrodes, i.e. their motion around the y-axis is stable with limited amplitudesin x- and z-directions. We learned these rules from the theory of the Mathieuequations, as this type of differential equation is called.In dimensionless parameters these equations are written(5)W.Paul605By comparison with equation (4) one gets63)The Mathieu equation has two types of solution.1.
stable motion: the particles oscillate in the x-z-plane with limited amplitudes.They pass the quadrupole field in y-direction without hitting the electrodes.Figure 2. The overall stability diagram for the two-dimensional quadrupole field.0.30.230.2ta0.1Figure 3. The lowest region for simultaneous stability in x-and z-direction.
All ion masses lie on theoperation line, m1 > m1.606Physics 19892. unstable motion: the amplitudes grow exponentialy in x, z or in bothdirections. The particles will be lost.Whether stability exists depends only on the parameters a and q and noton the initial parameters of the ion motion, e.g. their velocity. Therefore, inan a-q-map there are regions of stability and instability (Fig.2). Only theoverlapping region for x and z stability is of interest for our problem.
Themost relevant region 0 < a, q < 1 is plotted in Fig. 3. The motion is stable inx and z only within the triangle.For fixed values r0 ω, U and V all ions with the same m/e have the sameoperating point in the stability diagram. Since a/q is equal to 2U/V anddoes not depend on m, all masses lie along the operating line a/q = const.On the q axis (a = 0, no d.c.
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