# Cyclotron resonance

**Cyclotron resonance** describes the interaction of external forces with charged particles experiencing a magnetic field, thus already moving on a circular path. It is named after the cyclotron, a cyclic particle accelerator that utilizes an oscillating electric field tuned to this resonance to add kinetic energy to charged particles.

## Cyclotron frequency

The **cyclotron frequency** or **gyrofrequency** is the frequency of a charged particle moving perpendicular to the direction of a uniform magnetic field *B* (constant magnitude and direction). Since that motion is always circular,^{[1]} the cyclotron frequency is given by equality of centripetal force and magnetic Lorentz force

with the particle mass *m*, its charge *q*, velocity *v*, and the circular path radius *r*, also called gyroradius.

By substitution for the circulation frequency which defines the cyclotron frequency, this leads to

- ,

or the angular frequency

- .

It is notable that the cyclotron frequency is independent of the radius and velocity and therefore independent of the particle's kinetic energy.

## See also

## References

- ↑ Physics by M. Alonso & E. Finn, Addison Wesley 1996.