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Fourier Transform Ion Cylotron Resonance, also known as Fourier Transform Mass Spectrometry, is a type of mass analyzer (or mass spectrometer) for determining the mass to charge ratio (m/z) of ions based on the cyclotron frequency of the ions in a magnetic field. The ions are trapped in a Penning trap (a magnetic field with electric trapping plates) where they are excited to a larger cyclotron radius by an oscillating electric field perpendicular to the magnetic field. The excitation also results in the ions moving in phase (in a packet). The signal is detected as an image current on a pair of plates which the packet of ions passes close to as they cyclotron. The resulting signal is called a free induction decay (fid), transient or interferogram that consists of a superposition of sine waves. The useful signal is extracted from this data by performing a Fourier transform to give a mass spectrum. Specifically a fast Fourier transform (FFT) is usually used to transform the discrete fid data.

Fourier Transform ion cylotron resonance (FTICR) mass spectrometry is a very high resolution technique in that masses can be determined with very high accuracy. Many applications of FTICR-MS use this mass accuracy to help determine the composition of molecules based on accurate mass. This is possible due to the mass defect of the elements. Another place that FTICR-MS is useful is in dealing with complex mixtures since the resolution (narrow peak width) allows the signals of two ions of similar mass to charge (m/z) to be detected as distinct ions. This high resolution is also useful in studying large macromolecules such as proteins with multiple charges which can be produced by electrospray ionization. These large molecules contain a distribution of isotopes that produce a series of isotopic peaks. Because the isotopic peaks are close to each other on the m/z axis, due to the multiple charges, the high resolving power of the FTICR is extremely useful.

FTICR-MS differs significantly from other mass spectrometry techniques in that the ions are not detected by hitting a detector such as an electron multiplier but only by passing near detection plates. Additionally the masses are not resolved in space or time as with other techniques but only in frequency. Thus, the different ions are not detected in different places as with sector instruments or at different times as with Time-of-flight instruments but all ions are detected simultaneously over some given period of time.

Theory

The physics of FTICR is similar to that of a cyclotron at least in the first approximation.

In the simplist form (idealized) the relationship between the cyclotron frequency and the mass to charge ratio is given by:

${\displaystyle f={\frac {zeB}{2\pi m}}}$

where ${\displaystyle f}$ =cyclotron frequency, z=number of charges, e=the elementary charge (charge of an electron or proton), B=magnetic field strength & m=mass (all in SI units)

This is more often represented in angular frequency:

${\displaystyle \omega _{c}={\frac {qB}{m}}}$

where ${\displaystyle q=ze}$ or the total charge of the ion and ${\displaystyle \omega _{c}}$ is the angular cyclotron frequency which is related to frequency by the definition ${\displaystyle f={\frac {\omega }{2\pi }}}$.

Because of the quadrupolar electrical field used to trap the ions in the axial direction this relationship is only approximate. The axial electrical trapping results in axial oscillations within the trap with the (angular) frequency:

${\displaystyle \omega _{t}={\sqrt {\frac {q\alpha }{m}}}}$

Where ${\displaystyle \alpha }$ ia a constant similar to the spring constant of a harmonic oscillator and is dependent on voltage and the trap dimensions and geometry.

The electric field and the resulting axial harmonic motion reduces the cyclotron frequency and introduces a second radial motion called magnetron motion that occurs at the magnetron frequency. The cyclotron motion is still the frequency being used but the relationship above is not exact due to this phenomenon. The natural angular frequencies of motion are:

${\displaystyle \omega _{\pm }={\frac {\omega _{c}}{2}}\pm {\sqrt {({\frac {\omega _{c}}{2}})^{2}-({\frac {\omega _{t}}{2}}^{2})}}}$

Where ${\displaystyle \omega _{t}}$ is the axial trapping frequency due the axial electrical trapping and ${\displaystyle \omega _{+}}$ is the reduced cyclotron (angular) frequency and ${\displaystyle \omega _{-}}$ is the magnetron (angular) frequency. Again ${\displaystyle \omega _{+}}$ is what is typically measured in FTICR. The meaning of this equation can be understood qualitatively by considering the case where ${\displaystyle \omega _{t}}$ is small, which is generally true. In that case value of the radical is just slightly less than ${\displaystyle {\frac {\omega _{c}}{2}}}$ and the value of ${\displaystyle \omega _{+}}$ is just slightly less than ${\displaystyle \omega _{c}}$ (the cyclotron frequency has been slightly reduced). For ${\displaystyle \omega _{-}}$ the value of the radical is the same (slightly less than ${\displaystyle {\frac {\omega _{c}}{2}}}$) but it is being subtracted from ${\displaystyle {\frac {\omega _{c}}{2}}}$ resulting in a small numer equal to:

${\displaystyle \omega _{-}=\omega _{c}-\omega _{+}}$

• Mass spectrometry
• Measuring instruments