The invention relates to electrostatic Kingdon ion traps in which ions can oscillate harmonically in the longitudinal direction, decoupled from their motions in the transverse direction. Kingdon ion traps are electrostatic ion traps in which ions can orbit around one or more inner longitudinal electrodes or oscillate in the center plane between inner longitudinal electrodes, while an outer, enclosing housing is at a DC potential which the ions with a specified kinetic energy cannot reach. A very simple Kingdon ion trap consists of a rod (in the ideal case, an infinitely long rod) as the inner electrode and a surrounding tube as the housing or outer electrode (
In this document, the term “Kingdon ion traps” refers only to these special forms in which ions can oscillate harmonically in the longitudinal direction, decoupled from their motions in the transverse direction.
The document U.S. Pat. No. 5,886,346 (A. A. Makarov) elucidates the fundamentals of a special Kingdon ion trap which was introduced by Thermo-Fischer Scientific GmbH Bremen under the name Orbitrap®. This ion trap consists of a housing electrode which is split across the center and a single spindle-shaped coaxial inner electrode (
The cross-sections of the inner surface of the housing electrodes and the outer surfaces of the inner electrodes are both circular. The hyperlogarithmic potential between inner and outer electrodes is represented by
ΨOrbitrap(r, φ, z)=Ψ1z2/l12−Ψ1r2/2l12+2Ψ2ln(r/l2)+Ψ3.
In the document U.S. Pat. No. 7,994,473 B2 (C. Köster; correspondent to DE 10 2007 024 858 B4 and GB 2448413 B), which is incorporated herein by reference, other types of Kingdon ion trap are described which, in their basic form, have precisely two inner electrodes (
Ψ(r, φ, z)=Ψ1z2/l12−Ψ1{r2(1−k)sin2φ+kcos2φ)/l12}+Ψ2ln{(r4−2b2r2cos(2φ)+b4)/l24}+Ψ3.
With this potential distribution, the exact inner shapes of the housing electrodes and the outer shapes of the inner electrodes are described by two fixed values for Ψ(r,φ, z)=ΨOuter and Ψ(r, φ, z)=ΨInner because each of these must form equipotential surfaces of the desired field. These “bipolar Cassini ion traps” or “second-order Cassini ion traps” are characterized by the fact that the ions not only fly on complicated trajectories around the two inner electrodes, but can also oscillate in the center plane between the two inner electrodes. The ions orbiting around or oscillating between the electrodes in this way can then execute harmonic oscillations in the longitudinal direction.
Bipolar Cassini curves are curves in a plane, which can be defined like plane ellipses. While an ellipse is the quantity of all points whose distances al and a2 from two focal points result in a constant sum s (a1+a2=s), a Cassini curve is the quantity of all points whose distances al and a2 from two focal points (called “poles” here) result in a constant product p:a1×a2=p. In the same way as ellipses degenerate to circles if the two foci coincide to form one focus, Cassini curves also degenerate to circles if the two poles coincide to form one pole. Ellipses form a concentric family of curves with s as the family parameter. As shown in
The term Ψ2ln{(r4−2b2r2 cos(2φ)+b4)/ l24} contains, in the curly brackets, the equation for a family of Cassini curves; the term Ψ1z2/l2 represents the axial potential well, which is independent of r and φ. The term Ψ1{r2(1−k)sin2φ+k cos2φ)/l12}, which modifies the radial potential distribution, is included so that the Laplace condition ∇2Ψ=0 is fulfilled, which must apply to all potential distributions.
By superimposing the potentials of several bipolar Cassini ion traps with suitable twists and shifts, it is possible to design ion traps with three, four and more inner electrodes, as is stated in the document U.S. Pat. No. 7,994,473 B2. These still belong to the class of second-order Cassini ion traps, however.
In contrast to ellipses, the Cassini curves can be expanded to n-polar curves. These curves are the quantities of all points in a plane whose distances ai(i=1 . . . n) from the n poles result in constant products p:Πi=1i=n(ai)=p . These n-polar Cassini curves are also called Cassini curves of the nth order. These also include curves which surround all poles together, as well as n curves which each surround one pole.
In view of the above there is a need to find further electrostatic ion traps in which ions can oscillate harmonically in the longitudinal direction, decoupled from their motions in the transverse direction.
In accordance with the principles of the invention, a Kingdon ion trap comprises n inner electrodes and one outer electrode and the electrodes create a potential distribution of the form
Ψ(r, φ, z)=Ψ1z2/l12−Ψ1r2(1−k)sin2φ+kcos2φ)/l12+Ψ2ln{(r2n−2bnrncos(nφ)+b2n)/l22n}+Ψ3
with n≧3 and b≠0. The potential distribution can be split up into the form Ψ(r, φ, z)=Ψz+ΨLapl+ΨCass+Ψ3, where the term Ψz=Ψ1z2/l12 represents the harmonic potential well in the axial direction, and the term ΨCass=Ψ2ln{(r2n=2bnrncos(nφ)+b2n)/l22n} represents the determining part of the radial distributions of the potential; this contains the equation for a family of nth-order Cassini curves in the curly brackets. The term ΨLapl=−Ψ1r2(1−k) sin2φ+k cos2 φ)/l12 which is independent of z must be added so that the total potential fulfills the Laplace condition ∇2Ψ=0. With given values for the potential constants Ψ1, Ψ2 and Ψ3, for the numerical constants k and n (with n≧3), and for the length parameters b (with b≠0), l1 (a length parameter for a longitudinal elongation) and l2 (a length parameter for the transverse dimensions of inner and outer electrodes), it is possible, by suitable selection of two specific, fixed values for the potential Ψ(r, φ,z), to obtain the potential surfaces of the inner surface of the outer electrode and the outer surfaces of the inner electrodes, which must be equipotential surfaces, of course. Kingdon ion traps with a potential distribution of this form fulfill the condition that ions can oscillate harmonically in the axial z-direction independently of their motion in the radial direction.
More complex ion traps are obtained if further Cassini potential distributions of the first, second or higher order are superimposed in an appropriate way on higher-order potential distributions.
The trajectories of the ions within the ion trap in planes perpendicular to the z-axis can be extraordinarily complicated. In addition to trajectories which orbit around all the inner electrodes, more complex, cycloidal trajectories can also occur which orbit all or some of the inner electrodes in turn. Thus ion traps with three inner electrodes can bring about trajectories in the form of a three-leafed clover; in ion traps with four inner electrodes, the trajectories can even resemble double-bladed propellers (lemniscates) or a four-leafed clover. With even numbers of electrodes it is also possible for the ions to oscillate through one of the center planes.
In this illustration the ions execute oscillations (19) in the center plane between the two spindle-shaped inner electrodes.
The invention concerns Kingdon ion traps in which the ions can oscillate harmonically in the longitudinal z-direction as required, decoupled from any type of motion they may have in the transverse direction, but which have at least three inner longitudinal electrodes within an outer housing electrode, and whose radial potential distributions have components which follow Cassini families of curves of at least the third order.
The inner shape of the housing electrode and the outer shape of the inner electrodes must be chosen so that in the interior of the housing a potential distribution is created of the general form
Ψ(r, φ, z)=Ψ1z2/l12−Ψ1r2((1−k)sin2φ+kcos2φ)/l12+Ψ2ln{(r2n−2bnrncos(nφ)+b2n)/l22n}+Ψ3,
where b≠0 and n≧3. The number n of poles must naturally be an integer. The potential constants Ψ1, Ψ2 and Ψ3, the numerical constants k, n and the length constants b, l1 and l2 are freely selectable within their limitations. The length l1 is a stretching factor in the z-direction, the length l2 a radial dimensional factor for the Cassini curves. After all these parameters have been specified, the next step is, as any person skilled in the art knows, to select two suitable values for the constant potentials Ψ(r, φ,z)=Ψouter and Ψ(r, φ, z)=Ψinner and thereby to obtain the equations for the equipotential surfaces of the inner surface of the housing electrodes and the outer surfaces of the inner electrodes, since these must, of course, be equipotential surfaces.
The equations for the inner surface of the housing electrodes and for the outer surfaces of the inner electrodes can be used to manufacture the ion traps in modern machining centers. Kingdon ion traps with a potential distribution of this form fulfill the condition that ions can oscillate harmonically in the axial z-direction independently of their motion in the radial direction.
The potential distribution can be split up in the form Ψ(r, φ, z)=Ψz+ΨLapl+ΨCass+Ψ3, where the term Ψz=Ψ1z2/l12 represents the harmonic potential well in the axial direction, and the term ΨCass=Ψ2ln{(r2n−2bnrncos(nφ)+b2n)/l22n} represents the determining part of the radial distributions of the potential; this term contains the nth-order family of Cassini curves in the curly brackets. The term ΨLapl=−Ψ1r2(1−k)sin2φ+kcos2φ)/l12, which is independent of z, must be added so that the total potential fulfills the Laplace condition ∇2Ψ=0. If the parameter k=½ is selected in this term, then the term simplifies to ΨLapl=−Ψ1r2/2l12. This simplified term is radially symmetric in r, and causes potential distributions to be described which are formed by n inner electrodes of the same cross-section evenly distributed on a circle with corresponding rotation. The resulting ion trap thus has n-fold rotational symmetry; each rotation through the angle 360° ln causes the shape to transform into itself.
Kingdon ion traps are electrostatic ion traps. A constant operating voltage ΔU of several kilovolts is usually applied between the housing electrodes, on the one hand, and the inner electrodes, on the other hand. Ions of specified kinetic energy can then follow quite different types of trajectory in the r-φ-plane of the higher-order Cassini ion traps.
The inner electrodes do not need to have a regular arrangement. The arrangements of the inner electrodes can be distorted within certain limits by a parameter k≠½. In addition, more complex potential distributions can be generated by appropriate superimpositions with further Cassini potentials of the first, second or higher orders.
In the description above, it is always assumed that the n inner electrodes are at the same potential and therefore must have the same cross-section (apart from a rotation through 360° ln). This does not have to be the case in general. It is possible to determine n different forms by means of n different potentials for the inner electrodes; when the different potentials are applied, the forms will then again generate the required overall potential distribution.
The Kingdon ion traps with higher-order Cassini potential distributions according to the invention can be used as ion traps for Fourier transform mass spectrometers, as can the ion traps described in the documents U.S. Pat. No. 5,886,346 (A. A. Makarov) and U.S. Pat. No. 7,994,473 B2 (C. Köster); in this case the image currents induced by the axial oscillations of the ions in the then halved housing electrodes (or halved inner electrodes) are measured and suitably processed to give mass spectra. The electrodes can also be divided into more than two insulated partial segments in order to detect oscillations of a higher order.
The introduction of the ions into the ion trap is difficult because it must coincide with a change of the ratio of the kinetic energy of the ions to the potential difference between inner and housing electrodes in order that the ions in the interior cannot reach the housing electrodes. The ions can, for example, be introduced as described in the document US 2010/0301204 A1 (C. Köster; correspondent to DE 10 2009 020 886 A1 and GB 2470259 A).
While the invention has been shown and described with reference to a number of embodiments thereof, it will be recognized by those skilled in the art that various changes in form and detail may be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
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