Frequency of ion motion

Ion cyclotron resonance (ICR) is the excitation of the cyclotron frequency of ion motion in a magnetic field by an electric rf field at resonance. ICR spectrometry is based on the application of the resonance phenomenon to the detection of ions. 

Ions confined by a pure quadrupolar field and within the bounds 0

fundamental frequencies of oscillation in the r and z directions, co, and co , given by Equations 9.9 and 9.10, where n is an integer. The characteristic fundamental secular frequencies (0, 0 and co o) are unique for a given value of P . Equations 9.9 and 9.10 describe the principal frequencies of ion motion in a quadrupolar field. 

Several methods for constructing a notch waveform have been proposed [34-36]. Marshall developed originally the SWIFT technique [34] for Fourier transform ion cyclotron resonance, FT-ICR, spectrometry. However, because the trajectories of trapped ions in each of an ICR cell and a quadrupole ion trap are characterized by secular frequencies of ion motion, the SWIFT technique can be applied also to the quadrupole ion trap. The SWIFT technique is able to generate a near perfect notch... 

The secular frequency of ion motion in the aiy-plane is given by P r /2, where is a proportionality constant that can be calculated from and q. The term P is equal to for the mass-selective instability mode of operation. 

As the frequency of ion motion can be determined with high precision, the mass determination results with high accuracy below 1 ppm and very high mass resolution above 500000 (Figure 2.190). The mass precision and resolution depends on the measurement time of the trapped ions. Orbitrap MS systems are applied in LC-MS since many years for proteomics and metabolomics especially in life sciences, but also show its high capabilities in the small molecular domain for multi-residue trace analyses of, for example, pesticides or drugs, both in LC-MS (Fiirst and Bernsmann, 2010 Kaklamanos et al., 2013) and GC-MS applications (Peterson et al, 2009, 2010). 

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

Magnetic fields introduce hydromagnetic waves, which are transverse modes of ion motion and wave propagation that do not exist in the absence of an apphed B field. The first of these are Alfven, A, waves and their frequency depends on B and p, the mass density. Such waves move parallel to the apphed field having the following velocity ... 

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

When a gaseous ion drifts into or is formed in a strong magnetic field, its motion becomes circular in a plane perpendicular to the direction of the field. The angular frequency of this motion is called the cyclotron frequency, Equation 20-8 can be rearranged and solved lor v/r. which i.s the cyclotron frequency in radians per second. 

Frequency of rotation depends on the miz of ions and strength of the magnetic field direction of ion motion is such that a positive ion traveling through a magnetic field is set at 90° to the trajectory curves in a clockwise direction radius of the curve is proportional to ionic mass (left-hand rule)... 

The heart of this instrument is a cell (also known as a Penning trap), which is placed in a strong magnetic field. Ions are confined laterally in this trap by a static magnetic field and axially by a static electric field. Ions are excited by a broadband rf pulse to a coherent orbital motion, and from the frequency of this motion, the miq of the trapped ions can be obtained. Over a dozen designs of cell geometry exists [64]. The cubic cell is shown in Figure 3.21. 

FT-MS is the slowest among all MS techniques. The long SAT of FT-MS is due to an extended time for acquiring the transient, which is essential for the accurate determination of frequencies of periodic motions of ions. Moreover, FT mass analyzers need to be installed in ultrahigh vacuum environments, and such environments require long ion transmission paths and several differentially pumped vacuum stages. Because commercial FT mass analyzers are installed downstream of IT mass analyzers, the typical SATs of FT-MS range from hundreds of milliseconds to tens of seconds. 

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