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# Ion cyclotron resonance

Ion cyclotron resonance is a phenomenon related to the movement of ions in a magnetic field. It is used for accelerating ions in a cyclotron, and for measuring the masses of an ionized analyte in mass spectrometry, particularly with Fourier transform ion cyclotron resonance mass spectrometers.

## Definition of the resonant frequency

An ion in a static and uniform magnetic field will move in a circle due to the Lorentz force. The circular motion may be superimposed with a uniform axial motion, resulting in a helix, or with a uniform motion perpendicular to the field, e.g., in the presence of an electrical or gravitational field, resulting in a cycloid. The angular frequency (ω = 2π f ) of this cyclotron motion for a given magnetic field strength B is given (in SI units[1]) by

$\omega=\frac{zeB}{m}$.

where z is the algebric number of positive or negative charges of the ion, e is the elementary charge and m is the mass of the ion.

The formula above means that an electric excitation signal having a frequency f will resonate with ions having a mass-to-charge ratio m/z given by:

$\frac{m}{z}=\frac{eB}{2\pi f}$.

## References

1. ^ In SI units, the elementary charge e has the value 1.602×10-19 C, the mass of the ion m is often given in atomic mass unit or dalton 1 u = 1 Da ≈ 1.660538782(83) × 10−27 kg, the magnetic field B is measured in tesla, and the angular frequency ω is measured in radians per second.