Axial frequency

Ion detection is carried out using image current detection with subsequent Fourier transform of the time-domain signal in the same way as for the Fourier transform ion cyclotron resonance (FTICR) analyzer (see Section 2.2.6). Because frequency can be measured very precisely, high m/z separation can be attained. Here, the axial frequency is measured, since it is independent to the first order on energy and spatial spread of the ions. Since the orbitrap, contrary to the other mass analyzers described, is a recent invention, not many variations of the instrument exist. Apart from Thermo Fischer Scientific s commercial instrument, there is the earlier setup described in References 245 to 247. 

The total potential of a stored ion is the sum of the electric and magnetic potential q< > and /iB, respectively. Both , the quadrupole potential, and the magnetic field B depend on the square of the axial coordinate. Thus the axial oscillation remains harmonic. The frequency, however, depends on the sign of fi, determined by the direction of the spin. We have designed the nickel ring electrode in such a way that the difference in the axial frequency for both spin directions is 0.7 Hz in a total frequency of 364 kHz [9]. Fig. 7 shows an example of the slight difference... 

Fig. 8. Induced quantum jumps between the two spin directions of the electron bound in 12C5+. At each measurement point first the ion is irradiated by microwaves and then the axial frequency of the ion is measured...

For some choices of the parameters, it is possible to obtain very small values for the axial vibrations of the ion along the channel. As we will see, band states for these systems correspond to the nearly free ion limit. On the other hand, it is possible to find other axial frequencies reaching nearly 20 cm 1. In these cases, we have treated (post) the bands in the tight binding limit. With distortions of the channel walls in the vicinity of the ion, a case not specifically illustrated here, it is possible to see the formation of deep traps of several decades in axial frequency. In these cases, the ion transfer along the chain would occur via an activated site-hopping mechanism. The formalism... 

The evaluation of the energy based on these formulae is straightforward. One obtains an estimate of the harmonic frequency via the classical harmonic analysis. The quantity a = wzto/h depends on the effective mass of the ion and the axial frequency. It is possible, of course, to get an immediate estimate of the extent of the band width for... 

Figure 11 shows the dependence of the channel polarized frequency as a function of the number of lattice sites between ions. If the ionic density in the channel is sufficiently great to force ions to occupy adjacent lattice positions, the axial frequency will be observable in the infrared. As the distance between ions increases, however, the... 

In particular, the ion motion in the z (axial) direction may be described as an harmonic oscillation and Eq. 2.18 showed the relationship between the axial frequency and the mJz (m/q) value of the trapped ion. By the same approach used for FT-ICR, in the case of Orbitrap ion detection is obtained by image current detection on the two outside electrodes, and by a FT algorithm the complex signal due to the copresence of ions of different m/z values (and hence exhibiting different coz values) is separated into its single m/z components. The typical mass resolution obtained by this analyzer is up to 105. 

Figure 16.18 shows the spatial-frequency band of a written bit and the transfer-function band of the reading system. " This figure shows a vertical cut of the 3D band of the transfer function (ife-vector) space that includes the axial frequency (1/ ). 1/r is the transaxial spatial frequency of the polar coordinate r - + y where x and y are the two-dimensional coordinates of... 

Figure 18.3 illustrates the loading of HD+ ions into a Be+ ion ensemble prepared beforehand. The shape of such a mixed-species ensemble can be changed in real time by variation of the ratio of radial to axial frequency via variation of the trap parameters, as shown in Figure 18.4. 

The first three natural frequencies and vibration modes were determined using modal analysis. The first natural axial frequency was found to be /, = 3.98 Hz. The seeond natural, and transverse (vertical) frequency (coupled with bending of the pipe) was /2 = 12.35 Hz. The third natural frequency was /j = 30.16 Hz this mode of vibration was the roeking mode of the assembly. The equivalent determinations based on EJMA (1993) are 3.93,15.7, and 27.2 Hz respectively. The axial mode agrees well, but the inclusion of the offset pipe appears to reduce the transverse and increase the rocking modes. 

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