Trapped ions, oscillation frequencies

The heterodyne measurement is performed as follows. The dye laser excites the trapped ion with frequency (Ol while the fluorescence is observed in a direction of about 54 to the exciting laser beam (see Fig. 2). However, both the observation direction and the laser beam are in a plane perpendicular to the symmetry axis of the trap. Before reaching the ion, a fraction of this laser radiation is removed with a beamsplitter and then frequency shifted (by 137 MHz with an acousto-optic modulator (AOM)) to serve as the local oscillator. The local oscillator and fluorescence radiations are then overlapped and simultaneously focused onto the photodiode where the initial frequency mixing occurs. The frequency difference signal is amplified by a narrow band amplifier and then frequency down-converted to 1 kHz so that it could be analyzed by means of a fast Fourier analyzer (FFT). The intermediate frequency for this mixing of the signal was derived from the same frequency-stable synthesizer which was used to drive the accousto-optic modulator producing the sideband of the laser radiation so that any synthesizer fluctuations are canceled out. 

A state-of-the-art example [28] for trapped-ion optical frequency standards is the case of a laser with a line-width of less than 25 Hz locked to a electric quadrupole transition at 282 nm in a single laser-cooled Hg ion. The inherent stability of this trap based on the radiative lifetime of the metastable upper level of this transition is calculated to be about 1,5 x 10" x[29]. This is an exceptional example - in most cases as yet, the lasers used as oscillators for optical frequency standards based on ion traps often do not have a stability which matches the spectral sharpness of the trapped ion reference resonance. 

FIGURE 11.2 Calculated Doppler speetrum of a dipole-forbidden transition of a single trapped ion oscillating at frequencies co/ln = 0.7 MHz and ajlii = 1 MHz and cooled down to the Lamb-Dicke regime sueh that the Lamb-Dieke parameters are 0.1 in both directions (the laser wavevector has the same projeetion along the coordinates axes and O ). (Figure courtesy of Caroline Champenois, PIIM, Marseille.)... 

If we remember that the secular frequency at which an ion oscillates in the 3D trap is given by... 

The trapped ions possess characteristic oscillation frequencies. The stable motion of ions in the trap is assisted by the presence of a helium buffer gas (1 mtorr) to remove kinetic energies from ions by collisions. When a supplementary AC potential, corresponding to the frequency of a certain m/z ion, is applied to the end-cap electrode, ions are resonantly ejected from the trap. This method of resonance ejection is used to effectively extend the mass-to-charge ratio of the ion trap. Some other characteristic features of a 3-D ion trap include high sensitivity, high resolution with slow scan rate, and multiple-stage MS capability (see the section on tandem MS). In addition, it is inexpensive and small in size. As a result, a 3-D ion trap is widely used in LC/MS and LC/MS/MS applications. 

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. 

In order to test the accuracy of the SCSI-MS technique, the masses of the calcium isotopes " a+ and " a+ were measured with reference to the mass of the Ca ion one of the isotopes was trapped together with a Ca ion and the COM resonance frequency was determined by the phase-detection method (see Ref. [3]). As a reference, the COM frequency for two " Ca ions was determined also by the phase-detection method. The experimental oscillation frequencies from a series of measurements... 

Usually, ions of tn/z 69 and 414 from the calibration chemical PFTBA are used to find the values for the two parameters, A and B. The trapping frequency calibration is carried out near = 0.845 at a fixed RF trapping field. A linear relation between q xm and RF c is true only under ideal conditions but, as a first-order approximation, it works well for this two-step isolation method in a non-ideal quadrupole ion trap. Typically, in an ion trap for which the oscillation frequency of the RF potential is 1 MHz, the frequency error of the calibration is less than 1 kHz, which corresponds to an error of < 1 Th in the high-mass isolation step. The amplitude of the broadband waveform is determined empirically by the manufacturer and can be accessed by users. 

FIGURE 15.24 Top, illustration of the modulation of an ion s -value and, thus, its secular frequency, by modulation of the RF trapping field. Bottom, the secular frequency of the ion oscillates about the fixed frequency of the AC field during the CID period. 

In Chapter 1 is presented a review of the instrumental requirements for the study of ion/ion reactions. Particular emphasis is given to the use of an electrodynamic ion trap for the study of multiply-protonated peptide molecules with anions. The trapped ions assume characteristic sets of m/z-dependent frequencies of motion in the oscillating quadrupole field of the ion trap, which allows ready manipulation of ions for ion isolation and activation, both of which are common elements in a tandem mass spectrometric experiment. The tandem-in-time nature of the ion trap MS" experiment provides well-defined conditions for ion/ion reactions and permits determination of ion genealogy. A bath gas, such as helium at ca 1 mTorr, intended originally to cool the ions to the center of the trap so as to enhance both sensitivity and mass resolution upon mass analysis, improves ion/ion reaction efficiencies by maximizing the spatial overlap and minimizing the translational energies of the two ion clouds. 

Assume that an ion in the Paul trap (absorption frequency coq for i = 0) performing a harmonic motion in the x-direction with the velocity Vx = vq cos coyt, is irradiated by a monochromatic wave propagating in the x-direction. In the frame of the oscillating ion, the laser frequency is modulated at the oscillation frequency due to the oscillating Doppler shift. If the linewidth y of the absorbing transition is smaller than cOy, the absorption spectrum of the oscillating ion consists of discrete lines at the frequencies com = coo mcoy. The relative line intensities are given by the mth-order Bessel function [1227, 1228], which depend on the velocity... 

Similar to the situation for a coupled pendulum, normal vibrations can be excited in a Wigner crystal. For example, the two-ion crystal has two normal vibrations where the two ions oscillate in the ion trap potential either in phase or with opposite phases. For the in-phase oscillations, the Coulomb repulsion between the ions does not influence the oscillation frequency because the distance between the... 

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