Ion cyclotron motion

As we know from the discussion of magnetic sectors, an ion of velocity v entering a uniform magnetic field B perpendicular to its direction will, by action of the Lorentz force (Chap. 4.3.2), immediately move on a circular path. Contemplating the path in the direction of the magnetic field reveals that negative ions circulate clockwise while positive ions move counterclockwise (Figs. 4.13, 4.51). 

Upon substitution with v = and rearrangement of the resulting term, the cyclotron angular frequency coc is obtained as  

One realizes that the cyclotron frequency is independent of the ions initial velocity, but proportional to its charge and the magnetic field, and inversely proportional to its mass. Of any physical quantity, frequencies can be measured at the highest accuracy, and thus, cyclotron frequency measurements appear as ideal premises for building powerful m/z analyzers. 

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The basis for FTMS is ion-cyclotron motion. A simple experimental sequence in FTMS is composed of four events quench, ion formation, excitation and ion detection. Ions are created in or injected into a cubic cell where they are held by an electric trapping potential and a constant magnetic field B. Each ion assumes... 

Fourier transform mass spectrometry is made possible by the measurement of an AC current produced from the movement of ions within a magnetic field under ultra-high vacuum, commonly referred to as ion cyclotron motion.21 Ion motion, or the frequency of each ion, is recorded to the precision of one thousandth of a Hertz and may last for several seconds, depending on the vacuum conditions. Waveform motion recorded by the mass analyzer is subjected to a Fourier transform to extract ion frequencies that yield the corresponding mass to charge ratios. To a first approximation, motion of a single ion in a magnetic field can be defined by the equation... 

Figure 7.8 Excitation (a) and detection (b) of the ion cyclotron motion within an FTMS mass analyzer cell. Reprinted from Marshall, A.G. and Flendrickson, C.L., Fourier transform ion cyclotron resonance detection principles and experimental configurations. International Journal of Mass Spectrometry, 215, 59-75. Copyright (2002), with permission from Elsevier.

Figure 2. The synchronization between rf excitation waveform and ion cyclotron motion shown with exaggerated phase 1, e. i + it/2 (Reproduced with permission from Ref. 23 Copyright 1986 Elsevier Science Publishers B.V.)...

Damping Loss of coherent ion cyclotron motion primarily due to... 

Figure 1. The cyclotron resonance principle as applied to mass spectrometers. An alternating electric field whose frequency equals the cyclotron frequency (Equation 1) for a particular ion mass, excites the cyclotron motion of that ion. An oscillator is connected to the plates of a capacitor, whose dimensions define the sample volume, and gives rise to an alternating electric field within the capacitor. If the frequency of the oscillator equals the cyclotron frequency (Equation 1) of an ion located within the capacitor, the radius of the ion s cyclotron orbit will be increased (i.e., the ion cyclotron motion is excited). This phenomenon is called cyclotron resonance. The kinetic energy of the ion increases as the ion follows the spiral path shown, and the presence of cyclotron resonance is detected by measuring the signal that is induced in the plates of the capacitor by the excited ion motion.

FIGURE 5.1 Ion cyclotron motion. The ion describes a circular path perpendicular to the direction of the magnetic field. 

The most widely used type of trap for the study of ion-molecule reactivity is the ion-cyclotron-resonance (ICR) [99] mass spectrometer and its successor, the Fourier-transfomi mass spectrometer (FTMS) [100, 101]. Figure A3.5.8 shows the cubic trapping cell used in many FTMS instmments [101]. Ions are created in or injected into a cubic cell in a vacuum of 10 Pa or lower. A magnetic field, B, confines the motion in the x-y... 

Figure Bl.7.18. (a) Schematic diagram of the trapping cell in an ion cyclotron resonance mass spectrometer excitation plates (E) detector plates (D) trapping plates (T). (b) The magnetron motion due to tire crossing of the magnetic and electric trapping fields is superimposed on the circular cyclotron motion aj taken up by the ions in the magnetic field. Excitation of the cyclotron frequency results in an image current being detected by the detector electrodes which can be Fourier transfonned into a secular frequency related to the m/z ratio of the trapped ion(s).

Figure 4. Ions undergoing coherent cyclotron motion induce image currents in the plates of the FTMS analyzer cell. Reproduced with permission from Ref. 18. Copyright 1985, North-Holland Physics Publishing.

In the ion cyclotron resonance (ICR) analyzer, ions are trapped by a strong magnetic field. The magnetic field will cause the ions to move in a circular motion with a frequency that depends on their m/z.. Ions to be detected are excited to make them move closer to the detection plates. Then a small current will be induced in the plate each time an ion passes by. Since the ions with different m/z have different ICR frequencies, each generated current frequency will correspond to a certain m/z value. 

The ion motion in the cell is complex because of the presence of electrostatic and magnetic trapping fields it consists of three different modes of oscillation. However, the primary mode of interest is the cyclotron motion, whose frequency, v., is directly proportional to the strength of the magnetic field B end inversely proportional to the mass-to-charge ratio m z of the ion v. = kzB/m). 

FT-ICR detection is accomplished by monitoring the image current induced by the orbiting ion packet as it cycles between the two receiver plates of the ceU. After formation by an ionization event, all trapped ions of a given mIz have the same cyclotron frequency but have random positions in the FT-ICR cell. The net motion of the ions under these conditions does not generate a signal on the receiver plates of the FT-ICR cell because of the random locations of ions. To detect cyclotron motion, an excitation pulse must be applied to the FT-ICR cell so that the ions bunch... 

Fig. 1.29 Diagram of an ion cyclotron resonance instrument. The magnetic field is oriented along the z-axis and ions ( ) are trapped according the same axis. Due to the cyclotronic motion the ions rotate around the z-axis in the x-y plane.

The combination of the Lorentz force and the ion s initial velocity upon entering the cell acts upon the ion and creates a circular trajectory—cyclotron motion (Fig. 16). 

The frequency of cyclotron motion, that is, how rapidly an ion precesses about the orbit, is m/z dependent. Applying Newton s Second Law... 

The radius of the cyclotron motion depends on the energy of the ions. Ions are typically injected into the mass analyzer cell with low energies, resulting in small initial cyclotron radii of 0.01-0.1 mm. The frequency/of the cyclotron motion is... 

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