Theory
The physics of FTICR is similar to that of a cyclotron at least in the first approximation.
In the simplest form (idealized) the relationship between the cyclotron frequency and the mass to charge ratio is given by:
where f = cyclotron frequency, q = ion charge, B = magnetic field strength and m = ion mass.
This is more often represented in angular frequency:
where is the angular cyclotron frequency which is related to frequency by the definition .
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:
Where is a constant similar to the spring constant of a harmonic oscillator and is dependent on applied voltage, trap dimensions and trap 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:
where is the axial trapping frequency due the axial electrical trapping and is the reduced cyclotron (angular) frequency and is the magnetron (angular) frequency. Again is what is typically measured in FTICR. The meaning of this equation can be understood qualitatively by considering the case where is small, which is generally true. In that case the value of the radical is just slightly less than and the value of is just slightly less than (the cyclotron frequency has been slightly reduced). For the value of the radical is the same (slightly less than ) but it is being subtracted from resulting in a small number equal to (i.e. the exact amount that the cyclotron frequency was reduced by).
Read more about this topic: Fourier Transform Ion Cyclotron Resonance
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