Cyclotron motion

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).

The presence of a static magnetic field within a plasma affects microscopic particle motions and microscopic wave motions. The charged particles execute cyclotron motion and their trajectories are altered into heUces along the field lines. The radius of the helix, or the T,arm or radius, is given by the following ... 

Also in 1950 Sakliarov and Tamm proposed an idea for a controlled thermonuclear fusion reactor, the TOKAMAK (acronym for the Russian phrase for toroidal chamber with magnetic coiF ), which achieved the highest ratio of output power to input power of any fusion device of the twentieth centuiy. This reactor grew out of interest in a controlled nuclear fusion reaction, since 1950. Sakharov first considered electrostatic confinement, but soon came to the idea of magnetic confinement. Tamm joined the effort with his work on particle motion in a magnetic field, including cyclotron motion, drifts, and magnetic surfaces. Sakharov and Tamm realized that... 

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.

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... 

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... 

From its very beginnings to the present almost any physical principle ranging from time-of-flight to cyclotron motion has been employed to construct mass-analyzing devices (Fig 4.1). Some of them became extremely successful at the time they were invented, for others it took decades until their potential had fully been recognized. The basic types of mass analyzers employed for analytical mass spectrometry are summarized below (Tab. 4.1). 

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.

Equations (A9) show that the electron exhibits the expected cyclotron motion in the presence of the magnetic field. However, collisions must also be taken into account. Let N(t) be the number of particles that have not experienced a collision for time t (after some arbitrary beginning time, t = 0). Then it is reasonable to assume that the rate of decrease of N(t) will be given by dN oc —Ndt = —Ndt/1. The solution of this equation is N(t) = N0 exp (—t/ ), where N0 is the total number of particles. It can easily be shown that x is simply the mean time between collisions. The probability of having not experienced a collision in time t is, of course, N(t)/N0 = exp(—t/ ). The... 

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... 

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.)...

Cyclotron Motion Orbital motion of an ion or charged particle... 

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

The angular or cyclotron frequency ooc of the ions, which have low, nearly thermal translational energies and random phases in their so-called cyclotron motion, is given to a first approximation by eqn (1), where q is the charge, v the velocity, m the mass of the ion and r the radius of its circular path... 

Fig. 3. Fourier transform of the current induced by the cyclotron motion of 6 ions. The magnetic inhomogeneity causes the frequency to decrease with increasing cyclotron energy...

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