# 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. It can also be used to follow the kinetics of chemical reactions in a dilute gas mixture, provided these involve charged species.

## 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 angular frequency of this cyclotron motion for a given magnetic field strength B is given by

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

where z is the number of positive or negative charges of the ion, e is the elementary charge and m is the mass of the ion.[1] An electric excitation signal having a frequency f will therefore resonate with ions having a mass-to-charge ratio m/z given by

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

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.

## Ion cyclotron resonance heating

Ion cyclotron resonance heating (or ICRH) is a technique in which electromagnetic waves with frequencies corresponding to the ion cyclotron frequency is used to heat up a plasma.[2] The ions in the plasma absorb the electromagnetic radiation and as a result of this, increase in kinetic energy. This technique is commonly used in the heating of tokamak plasmas.[3][4][5][6]

### In the solar wind

On March 8, 2013, NASA released an article according to which ion cyclotron waves were identified by its solar probe spacecraft called WIND as the main cause for the heating of the solar wind as it rises from the sun's surface. Before this discovery, it was unclear why the solar wind particles would heat up instead of cool down, when speeding away from the sun's surface.[7]

## Notes

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 unified atomic mass unit or dalton: 1 u = 1 Da ≈ 1.660539040(20) × 10−27 kg, the magnetic field B is measured in teslas, and the angular frequency ω is measured in radians per second.
2. ^ "ICRH". www.ipp.mpg.de. Retrieved 2020-06-19.
3. ^ Start, D. F. H.; Jacquinot, J.; Bergeaud, V.; Bhatnagar, V. P.; Cottrell, G. A.; Clement, S.; Eriksson, L-G.; Fasoli, A.; Gondhalekar, A.; Gormezano, C.; Grosshoeg, G. (1998). "D-T Fusion with Ion Cyclotron Resonance Heating in the JET Tokamak". Physical Review Letters. 80 (21): 4681–4684. doi:10.1103/PhysRevLett.80.4681.
4. ^ Bécoulet, M.; Colas, L.; Pécoul, S.; Gunn, J.; Ghendrih, Ph.; Bécoulet, A.; Heuraux, S. (2002). "Edge plasma density convection during ion cyclotron resonance heating on Tore Supra". Physics of Plasmas. 9 (6): 2619–2632. doi:10.1063/1.1472501. ISSN 1070-664X.
5. ^ Reinke, M L; Hutchinson, I H; Rice, J E; Howard, N T; Bader, A; Wukitch, S; Lin, Y; Pace, D C; Hubbard, A; Hughes, J W; Podpaly, Y (2012). "Poloidal variation of high- Z impurity density due to hydrogen minority ion cyclotron resonance heating on Alcator C-Mod". Plasma Physics and Controlled Fusion. 54 (4): 045004. doi:10.1088/0741-3335/54/4/045004. ISSN 0741-3335.
6. ^ Van Eester, D.; Lerche, E.; Ragona, R.; Messiaen, A.; Wauters, T. (2019). "Ion cyclotron resonance heating scenarios for DEMO". Nuclear Fusion. 59 (10): 106051. doi:10.1088/1741-4326/ab318b. ISSN 0029-5515.
7. ^ "Solar Wind Energy Source Discovered - NASA Science". science.nasa.gov. Retrieved 2014-01-20.