# Cyclotron resonance

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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 using this resonance to add kinetic energy to charged particles.

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

$\frac{mv^2}{r} = qBv$

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 $f = \frac{v}{2 \pi r}$ which defines the cyclotron frequency, this leads to

$f = \frac{q B}{2\pi m}$.

## References

1. ^ Physics by M. Alonso & E. Finn, Addison Wesley 1996.